Penrose–Hawking singularity theorems. . . .

The Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.

A singularity in solutions of the Einstein field equations is one of two things:

1. a situation where matter is forced to be compressed to a point (a space-like singularity)
2. a situation where certain light rays come from a region with infinite curvature (a time-like singularity)

Space-like singularities are a feature of non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the property of geodesic incompleteness, in which either some light-path or some particle-path cannot be extended beyond a certain proper-time or affine-parameter (affine-parameter being the null analog of proper-time).

The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside any black hole whenever matter satisfies reasonable energy conditions (It does not hold for matter described by a super-field, i.e., the Dirac field). The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.

Hawking's singularity theorem is for the whole universe, and works backwards in time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in A Brief History of Time (1988) where he stated that "there was in fact no singularity at the beginning of the universe" (p. 50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity.

Penrose's theorem is more restricted and only holds when matter obeys a stronger energy condition, called the dominant energy condition, in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a scalar field, obeys this condition. During inflation, the universe violates the stronger dominant energy condition (but not the weak energy condition), and inflationary cosmologies avoid the initial big-bang singularity. However, inflationary cosmologies are still past-incomplete,and require physics other than inflation to describe the past boundary of the inflating region of spacetime.

It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes, or whether they are artifacts of high symmetry and turn into spacelike singularities when realistic perturbations are added.

Interpretation and significance

In general relativity, a singularity is a place that objects or light rays can reach in a finite time where the curvature becomes infinite, or space-time stops being a manifold. Singularities can be found in all the black-hole spacetimes, the Schwarzschild metric, the Reissner–Nordström metric, the Kerr metric and the Kerr–Newman metric and in all cosmological solutions which don't have a scalar field energy or a cosmological constant.

One cannot predict what might come "out" of a big-bang singularity in our past, or what happens to an observer that falls "in" to a black-hole singularity in the future, so they require a modification of physical law. Before Penrose, it was conceivable that singularities only form in contrived situations. For example, in the collapse of a star to form a black hole, if the star is spinning and thus possesses some angular momentum, maybe the centrifugal force partly counteracts gravity and keeps a singularity from forming. The singularity theorems prove that this cannot happen, and that a singularity will always form once an event horizon forms.

In the collapsing star example, since all matter and energy is a source of gravitational attraction in general relativity, the additional angular momentum only pulls the star together more strongly as it contracts: the part outside the event horizon eventually settles down to a Kerr black hole (see No-hair theorem). The part inside the event horizon necessarily has a singularity somewhere. The proof is somewhat constructive – it shows that the singularity can be found by following light-rays from a surface just inside the horizon. But the proof does not say what type of singularity occurs, spacelike, timelike, orbifold, jump discontinuity in the metric. It only guarantees that if one follows the time-like geodesics into the future, it is impossible for the boundary of the region they form to be generated by the null geodesics from the surface. This means that the boundary must either come from nowhere or the whole future ends at some finite extension.

An interesting "philosophical" feature of general relativity is revealed by the singularity theorems. Because general relativity predicts the inevitable occurrence of singularities, the theory is not complete without a specification for what happens to matter that hits the singularity. One can extend general relativity to a unified field theory, such as the Einstein–Maxwell–Dirac system, where no such singularities occur.

Elements of the theorems

When two nearby parallel geodesics intersect, the extension of either one is no longer the shortest path between the endpoints. The reason is that two parallel geodesic paths necessarily collide after an extension of equal length, and if one path is followed to the intersection then the other, you are connecting the endpoints by a non-geodesic path of equal length. This means that for a geodesic to be a shortest length path, it must never intersect neighboring parallel geodesics.In mathematics, there is a deep connection between the curvature of a manifold and its topology. The Bonnet–Myers theorem states that a complete Riemannian manifold which has Ricci curvature everywhere greater than a certain positive constant must be compact. The condition of positive Ricci curvature is most conveniently stated in the following way: for every geodesic there is a nearby initially parallel geodesic which will bend toward it when extended, and the two will intersect at some finite length.

Starting with a small sphere and sending out parallel geodesics from the boundary, assuming that the manifold has a Ricci curvature bounded below by a positive constant, none of the geodesics are shortest paths after a while, since they all collide with a neighbor. This means that after a certain amount of extension, all potentially new points have been reached. If all points in a connected manifold are at a finite geodesic distance from a small sphere, the manifold must be compact.

Penrose argued analogously in relativity. If null geodesics, the paths of light rays, are followed into the future, points in the future of the region are generated. If a point is on the boundary of the boundaries of the region, it can only be reached by going at the speed of light, no slower, so null geodesics include the entire boundary of Yoda proper future of a region. When the null geodesics intersect, they are no longer on the boundary of the future, they are in the interior of the future. So, if all the null geodesics collide, there is no boundary to the future.

In relativity, the Ricci curvature, which determines the collision properties of geodesics, is determined by the energy tensor, and its projection on light rays is equal to the null-projection of the energy–momentum tensor and is always non-negative. This implies that the volume of a congruence of parallel null geodesics once it starts decreasing, will reach zero in a finite time. Once the volume is zero, there is a collapse in some direction, so every geodesic intersects some neighbor.

Penrose concluded that whenever there is a cube where all the outgoing (and ingoing) light rays are initially converging, the boundary of the future of that region will end after a finite extension, because all the null geodesics will converge. This isn't significant, because the outgoing light rays for any sphere inside the horizon of a black hole solution are all converging, so the boundary of the future of this region is either compact or comes from nowhere. The future of the interior either ends after a finite extension, or has a boundary which is eventually generated by new light rays which cannot be traced back to the original sphere.

Nature of a singularity.

The singularity theorems use the notion of geodesic incompleteness as a stand-in for the presence of infinite curvatures. Geodesic incompleteness is the notion that there aregeodesics, paths of observers through spacetime, that can only be extended for a finite time as measured by an observer traveling along one. Presumably, at the end of the geodesic the observer has fallen into a singularity or encountered some other pathology at which the laws of general relativity break down.

Assumptions of the theorems.

Typically a singularity theorem has three ingredients:

1. An energy condition on the matter,
2. A condition on the global structure of spacetime,
3. Gravity is strong enough (somewhere) to trap a region.

There are various possibilities for each ingredient, and each leads to different singularity theorems.

Tools employed.

A key tool used in the formulation and proof of the singularity theorems is the Raychaudhuri equation, which describes the divergence ${\displaystyle \theta }$ of a congruence (family) of geodesics. The divergence of a congruence is defined as the derivative of the log of the determinant of the congruence volume. The Raychaudhuri equation is

${\displaystyle {\dot {\theta }}=-\sigma _{ab}\sigma ^{ab}-{\frac {1}{3}}\theta ^{2}-{E[{\vec {X}}]^{a}}_{a}}$

where ${\displaystyle \sigma _{ab}}$ is the shear tensor of the congruence (see the congruence page for details). The key point is that ${\displaystyle {E[{\vec {X}}]^{a}}_{a}}$ will be non-negative provided that the Einstein field equations hold and

• the null energy condition holds and the geodesic congruence is null, or
• the strong energy condition holds and the geodesic congruence is timelike.

When these hold, the divergence becomes infinite at some finite value of the affine parameter. Thus all geodesics leaving a point will eventually reconverge after a finite time, provided the appropriate energy condition holds, a result also known as the focusing theorem.

This is relevant for singularities thanks to the following argument:

1. Suppose we have a spacetime that is globally hyperbolic, and two points ${\displaystyle p}$ and ${\displaystyle q}$ that can be connected by a timelike or null curve. Then there exists a geodesic of maximal length connecting ${\displaystyle p}$ and ${\displaystyle q}$. Call this geodesic ${\displaystyle \gamma }$.
2. The geodesic ${\displaystyle \gamma }$ can be varied to a longer curve if another geodesic from ${\displaystyle p}$ intersects ${\displaystyle \gamma }$ at another point, called a conjugate point.
3. From the focusing theorem, we know that all geodesics from ${\displaystyle p}$ have conjugate points at finite values of the affine parameter. In particular, this is true for the geodesic of maximal length. But this is a contradiction – one can therefore conclude that the spacetime is geodesically incomplete.

In general relativity, there are several versions of the Penrose–Hawking singularity theorem. Most versions state, roughly, that if there is a trapped null surface and the energy density is nonnegative, then there exist geodesics of finite length which can't be extended.

These theorems, strictly speaking, prove that there is at least one non-spacelike geodesic that is only finitely extendible into the past but there are cases in which the conditions of these theorems obtain in such a way that all past-directed spacetime paths terminate at a singularity.

Versions.

There are many versions. Here is the null version:

Assume

1. The null energy condition holds.
2. We have a noncompact connected Cauchy surface.
3. We have a closed trapped null surface ${\displaystyle {\mathcal {T}}}$.

Then, we either have null geodesic incompleteness, or closed timelike curves.

Sketch of proof: Proof by contradiction. The boundary of the future of ${\displaystyle {\mathcal {T}}}$, ${\displaystyle {\dot {J}}({\mathcal {T}})}$ is generated by null geodesic segments originating from ${\displaystyle {\mathcal {T}}}$ with tangent vectors orthogonal to it. Being a trapped null surface, by the null Raychaudhuri equation, both families of null rays emanating from ${\displaystyle {\mathcal {T}}}$ will encounter caustics. (A caustic by itself is unproblematic. For instance, the boundary of the future of two spacelike separated points is the union of two future light cones with the interior parts of the intersection removed. Caustics occur where the light cones intersect, but no singularity lies there.) However, the null geodesics generating ${\displaystyle {\dot {J}}({\mathcal {T}})}$ have to terminate, i.e. reach their future endpoints at or before the caustics. Otherwise, we can take two null geodesic segments – changing at the caustic – and then deform them slightly to get a timelike curve connecting a point on the boundary to a point on ${\displaystyle {\mathcal {T}}}$, a contradiction. But as ${\displaystyle {\mathcal {T}}}$ is compact, given a continuous affine parameterization of the geodesic generators, there exists a lower bound to the absolute value of the expansion parameter. So, we know caustics will develop for every generator before a uniform bound in the affine parameter has elapsed. As a result, ${\displaystyle {\dot {J}}({\mathcal {T}})}$ has to be compact. Either we have closed timelike curves, or we can construct a congruence by timelike curves, and every single one of them has to intersect the noncompact Cauchy surface exactly once. Consider all such timelike curves passing through ${\displaystyle {\dot {J}}({\mathcal {T}})}$ and look at their image on the Cauchy surface. Being a continuous map, the image also has to be compact. Being a timelike congruence, the timelike curves can't intersect, and so, the map is injective. If the Cauchy surface were noncompact, then the image has a boundary. We're assuming spacetime comes in one connected piece. But ${\displaystyle {\dot {J}}({\mathcal {T}})}$ is compact and boundariless because the boundary of a boundary is empty. A continuous injective map can't create a boundary, giving us our contradiction.

Loopholes: If closed timelike curves exist, then timelike curves don't have to intersect the partial Cauchy surface. If the Cauchy surface were compact, i.e. space is compact, the null geodesic generators of the boundary can intersect everywhere because they can intersect on the other side of space.

Other versions of the theorem involving the weak or strong energy condition also exist.

Hawking radiation. . .

Hawking radiation also known as Hawking-Zel'dovich radiation is blackbody radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974,when particle and antiparticle collide at event horizon one of them will escape and other fall in black hole and sometimes also after Jacob Bekenstein, who predicted that black holes should have a finiteentropy.

Hawking's work followed his visit to Moscow in 1973 where the Soviet scientists Yakov Zeldovich and Alexei Starobinskyshowed him that, according to the quantum mechanical uncertainty principle, rotating black holes should create and emit particles. Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger emitters of radiation than larger black holes and should shrink and dissipate faster.

In June 2008, NASA launched the Fermi space telescope, which is searching for the terminal gamma-ray flashes expected from evaporating primordial black holes. In the event that speculative large extra dimension theories are correct, CERN'sLarge Hadron Collider may be able to create micro black holes and observe their evaporation.

In September 2010, a signal that is closely related to black hole Hawking radiation (see analog gravity) was claimed to have been observed in a laboratory experiment involving optical light pulses. However, the results remain unverified and debatable. Other projects have been launched to look for this radiation within the framework of analog gravity.

The trans-Planckian problem is the observation that Hawking's original calculation requires talking about quantum particles in which the wavelength becomes shorter than thePlanck length near the black hole's horizon. It is due to the peculiar behavior near a gravitational horizon where time stops as measured from far away. A particle emitted from a black hole with a finite frequency, if traced back to the horizon, must have had an infinite frequency there and a trans-Planckian wavelength.

The Unruh effect and the Hawking effect both talk about field modes in the superficially stationary space-time that change frequency relative to other coordinates which are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration which constantly Doppler shifts the modes.

An outgoing Hawking radiated photon, if the mode is traced back in time, has a frequency which diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external Schwarzschild solution, that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go. That region seems to be unobservable and is physically suspect, so Hawking used a black hole solution without a past region which forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified: a microscopic point right at the moment that the black hole first formed.

The quantum fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon, that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing.

The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a white holesolution. Matter which falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes which end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.

There exist alternative physical pictures which give the Hawking radiation in which the trans-Planckian problem is addressed.^{[citation needed]} The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time. In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial.

The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M. Combining the formulas for the Schwarzschild radius of the black hole, the Stefan–Boltzmann law of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon), several equations can be derived:

Stefan–Boltzmann constant:

${\displaystyle \sigma ={\frac {\pi ^{2}k_{\mathrm {B} }^{4}}{60\hbar ^{3}c^{2}}}}$

Schwarzschild radius:

${\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}}$

Hawking radiation has a blackbody (Planck) spectrum with a temperature T given by:

${\displaystyle E=k_{\mathrm {B} }T={\frac {\hbar g}{2\pi c}}={\frac {\hbar }{2\pi c}}\left({\frac {c^{4}}{4GM}}\right)={\frac {\hbar c^{3}}{8\pi GM}}}$

Hawking radiation temperature:

${\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}}$

The peak wavelength of this radiation is nearly 16 times the Schwarzschild radius of the black hole. Using Wien's displacement constant b = hc/4.9651 k_B = 2.8978×10⁻³ m K:

${\displaystyle \lambda _{\mathrm {max} }={\frac {b}{T_{\mathrm {H} }}}={\frac {8\pi ^{2}}{4.9651}}\,r_{\mathrm {s} }=15.902\,r_{\mathrm {s} }}$

Schwarzschild sphere surface area of Schwarzschild radius r_s:

${\displaystyle A_{\mathrm {s} }=4\pi r_{\mathrm {s} }^{2}=4\pi \left({\frac {2GM}{c^{2}}}\right)^{2}={\frac {16\pi G^{2}M^{2}}{c^{4}}}}$

Stefan–Boltzmann power law:

${\displaystyle P=A_{\mathrm {s} }j^{\star }=A_{s}\varepsilon \sigma T^{4}}$

For simplicity, assume a black hole is a perfect blackbody (ε = 1).

Stefan–Boltzmann–Schwarzschild–Hawking black hole radiation power law derivation:

${\displaystyle P=A_{s}\varepsilon \sigma T_{\mathrm {H} }^{4}=\left({\frac {16\pi G^{2}M^{2}}{c^{4}}}\right)\left({\frac {\pi ^{2}k_{\mathrm {B} }^{4}}{60\hbar ^{3}c^{2}}}\right)\left({\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}\right)^{4}={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}}$

Stefan–Boltzmann–Schwarzschild–Hawking power law:

${\displaystyle P={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}}$

where P is the energy outflow, ħ is the reduced Planck constant, c is the speed of light, and G is the gravitational constant. It is worth mentioning that the above formula has not yet been derived in the framework of semiclassical gravity. Substituting the numerical values of the physical constants in the formula above we obtain P= 3.562×10³² W kg^2/M^2.

The power of the Hawking radiation from a solar mass (M_☉) black hole turns out to be minuscule:

${\displaystyle P={\frac {\hbar c^{6}}{15360\pi G^{2}M_{\odot }^{2}}}=9.007\times 10^{-29}\;{\text{W}}\,.}$

It is indeed an extremely good approximation to call such an object 'black'. Under the assumption of an otherwise empty universe, so that no matter, cosmic microwave background radiation, or other radiation falls into the black hole, it is possible to calculate how long it would take for the black hole to dissipate:

${\displaystyle K_{\mathrm {ev} }={\frac {\hbar c^{6}}{15360\pi G^{2}}}=3.562\times 10^{32}\;{\text{W}}\;{\text{kg}}^{2}\,.}$

Given that the power of the Hawking radiation is the rate of evaporation energy loss of the black hole:

${\displaystyle P=-{\frac {dE}{dt}}={\frac {K_{\mathrm {ev} }}{M^{2}}}\,.}$

Since the total energy E of the black hole is related to its mass M by Einstein's mass–energy formula E = Mc²:

${\displaystyle P=-{\frac {dE}{dt}}=-\left({\frac {d}{dt}}\right)Mc^{2}=-c^{2}{\frac {dM}{dt}}\,.}$

We can then equate this to our above expression for the power:

${\displaystyle -c^{2}{\frac {dM}{dt}}={\frac {K_{\mathrm {ev} }}{M^{2}}}\,.}$

This differential equation is separable, and we can write:

${\displaystyle M^{2}\,dM=-{\frac {K_{\mathrm {ev} }}{c^{2}}}\,dt\,.}$

The black hole's mass is now a function M(t) of time t. Integrating over M from M₀ (the initial mass of the black hole) to zero (complete evaporation), and over t from zero to t_ev:

${\displaystyle \int _{M_{0}}^{0}M^{2}\,dM=-{\frac {K_{\mathrm {ev} }}{c^{2}}}\int _{0}^{t_{\mathrm {ev} }}\,dt\,.}$

The evaporation time of a black hole is proportional to the cube of its mass:

${\displaystyle t_{\mathrm {ev} }={\frac {c^{2}M_{0}^{3}}{3K_{\mathrm {ev} }}}=\left({\frac {c^{2}M_{0}^{3}}{3}}\right)\left({\frac {15360\pi G^{2}}{\hbar c^{6}}}\right)={\frac {5120\pi G^{2}M_{0}^{3}}{\hbar c^{4}}}=8.410\times 10^{-17}\;\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\;\mathrm {s} \,.}$

The time that the black hole takes to dissipate is:

${\displaystyle t_{\mathrm {ev} }={\frac {5120\pi G^{2}M_{0}^{3}}{\hbar c^{4}}}}$

where M₀ is the mass of the black hole.

The lower classical quantum limit for mass for this equation is equivalent to the Planck mass, m_P.

Hawking radiation evaporation time for a Planck mass quantum black hole:

${\displaystyle t_{\mathrm {ev} }={\frac {5120\pi G^{2}m_{\mathrm {P} }^{3}}{\hbar c^{4}}}=5120\pi t_{\mathrm {P} }=5120\pi {\sqrt {\frac {\hbar G}{c^{5}}}}=8.671\times 10^{-40}\;{\text{s}}}$

${\displaystyle t_{\mathrm {ev} }=5120\pi {\sqrt {\frac {\hbar G}{c^{5}}}}}$

where t_P is the Planck time.

For a black hole of one solar mass (M_☉ = 1.98892×10³⁰ kg), we get an evaporation time of 2.098×10⁶⁷ years—much longer than the current age of the universe at(13.799±0.021)×10⁹ years

${\displaystyle t_{\mathrm {ev} }={\frac {5120\pi G^{2}M_{\odot }^{3}}{\hbar c^{4}}}=6.617\times 10^{74}\;{\text{s}}\,.}$

But for a black hole of 10¹¹ kg, the evaporation time is 2.667 billion years. This is why some astronomers are searching for signs of exploding primordial black holes.

However, since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, it must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K = 2.3×10⁻⁴ eV. This implies that M must be less than 0.8% of the mass of the Earth – approximately the mass of theMoon.

Cosmic microwave background radiation universe temperature:

${\displaystyle T_{\mathrm {u} }=2.725\;{\text{K}}}$

Hawking total black hole mass:

${\displaystyle M_{\mathrm {H} }\leq {\frac {\hbar c^{3}}{8\pi Gk_{\mathrm {B} }T_{\mathrm {u} }}}\leq 4.503\times 10^{22}\;{\text{kg}}}$

${\displaystyle M_{\mathrm {H} }\leq {\frac {\hbar c^{3}}{8\pi Gk_{\mathrm {B} }T_{\mathrm {u} }}}}$

${\displaystyle {\frac {M_{\mathrm {H} }}{M_{\oplus }}}=7.539\times 10^{-3}=0.754\;\%}$

where M_⊕ is the total Earth mass.

In common units,

${\displaystyle P=3.563\,45\times 10^{32}\;\left[{\frac {\mathrm {kg} }{M}}\right]^{2}\;\mathrm {W} }$

${\displaystyle t_{\mathrm {ev} }=8.407\,16\times 10^{-17}\;\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\;\mathrm {s} \quad \approx \ 2.66\times 10^{-24}\;\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\;\mathrm {yr} }$

${\displaystyle M_{0}=2.282\,71\times 10^{5}\;\left[{\frac {t_{\mathrm {ev} }}{\mathrm {s} }}\right]^{\frac {1}{3}}\;\mathrm {kg} \quad \approx \ 7.2\times 10^{7}\;\left[{\frac {t_{\mathrm {ev} }}{\mathrm {yr} }}\right]^{\frac {1}{3}}\;\mathrm {kg} }$

So, for instance, a 1-second-life black hole has a mass of 2.28×10⁵ kg, equivalent to an energy of 2.05×10²² J that could be released by 5×10⁶ megatons of TNT. The initial power is 6.84×10²¹ W.

Black hole evaporation has several significant consequences:

• Black hole evaporation produces a more consistent view of black hole thermodynamics by showing how black holes interact thermally with the rest of the universe.
• Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays. A complete description of this dissolution requires a model of quantum gravity, however, as it occurs when the black hole approaches Planck mass and Planck radius.
• The simplest models of black hole evaporation lead to the black hole information paradox. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.

LIGO , laser interferometer gravitational wave observatory

The laser interferometer gravitational-wave observatory is a large-scale Physics experiment and observe the brain to the detect cosmic gravitational waves and to develop gravitational wave observations as an astronomical tool.

Too large of the haters year old in United state with the aims to detecting gravitational wave by laser interferometry.

The initial ligo observatory is well founded by National Science foundation and concept dual and operated by caltech and MIT.

The advantage ligo project to enhance the original ligo detectors begin in 2008 and continue to be supported by NH app with important contribution from the UK Science and Technology facilities Council the max planck Society of German and the Australian research Council and improve detective big and operation in 2015.

The detection of gravitational wave was reported in 2016 by riko scientific collaboration and bhaiya ko collaboration with international participation of scientist from several Universities and Research institutions.

Scientific involved in the project in the analysis of the data for the gravitational wave observatory or organised by this and SC which include more than 1000 scientist worldwide as well as about 440000 active.

Near total shut down in the hill for the fifth day

The Darjeeling hill on Monday observed a near total shut down for the fifth consecutive day since Gorkha janmukti Morcha gjm called for an indefinite strike in support of the demand for a separate state of Gorkhaland.

Edinburgh Billo continuous political parties and the people of the hills have find their hopes on all party meeting scheduled in Darjeeling on June 20.

Representatives of Gorkha janmukti Morcha and Gorkha National Liberation front Communist Party of Revolutionary Marxist, Bhartiya Gorkha Pari song and Gorkha Rashtriya Nirmal Manchu will hold a meeting at Darjeeling gym khana club on Tuesday.

The meeting is expected to be crucial as it may decide the course of the ongoing agitation.

Set back to the economy

Formal gjm MLA and President of Jan Andolan party harka Bahadur chettri the demand for Oakland is demand static demand and the movement for it has a democratic goal and mission.

Chief Minister Mamata Banerjee who left for the Netherlands during the day called for peace in the hills.

Instead of playing with the fire trying to safeguard peace solution through meeting and dialogues can happen only if the peace is maintained.

He confirmed that his party would attend the all party meeting and blamed the chief minister for the violence.

The DJ MN other political parties in the hills have described the absence of Darjeeling BJP and m p s s Abdullah at the time of ongoing crisis as unfortunate.

On both location the BJP has give its Assurance that party will sympathetically examined and approximately considered the long standing demand of the people of Darjeeling tarai and dooars..

So peoples of Darjeeling must be understand the matter and after that decide to do some violence.

The Ross sea.

The ross sea preservation Refugee for marine life and for science

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The ross sea has incredible biological diversity and a long history of human exploitation and scientific research.
Marine life is an abundant now as it was 1000 rupee hour ago and recent scientific study determined that regions has the lowest level of disturbance from the human activity among the world ocean.

It is important that it to be protected from the activities that would distract this fact Refugee for the open Ocean marine life scientific research to better understand how the maritime systems well before human exploitation.

View a report on the scientific basic for the uniqueness of Rose sea.

The rows she has longest history of scientific research in the southern Ocean this mean the scientist have data beginning 170 years ago and the continuously record going back over the 50 years.

Having a reliable data for long periods of times help scientist to grow more accurate conclusions and better understanding environment ecological changes particularly in the field of climate research.

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TTP tareek e taleban Pakistan let's discuss about it

The government and security establishment came under fire in a Senate Body Meeting when a lawmaker said that some splinter group of Band Tariq e taleban Pakistan have been allowed to open offices in some parts of Khyber Pakhtunkhwa.

At a hotel of Senate standing committee on interior lawmakers also come down hard on the security establishment for what they called glorified surrendered ttp spoke person ahsanullah Ahsan on TV channel.

The critically Marg, Vile additional Secretary of the Minister Defence rear Admiral facilities briefly committee on the revolution made by SR and after his son and dad and the government policy to treat such terrorist.

Avatar senators Shailesh out all the committee the government was fascinating some of the ttp groups and they had opened their offices in Tank there are Islamim Khan and Banno.

He mentioned that group of DTP and lead by Hakimullah has not and Mulla Mulla had been using cards of foreign countries while Sajna group using local cards of resources.

Some of these silent hearts group with the Desolation of Government have established their offices and they are providing justice to the local through their own judicial system.

The government had given incentive to those group who while using foreign cards he said he'll criticisms the government unannounced policy of integration of military

The additional secretary told the committee that a sandwich Elisa 3 form in the number of the onslaught including Badshah Khan airport attack terror heat on tourist in the gilgit Balochistan Wagah border pumping Mohammad agency attack and the Killing of formal Punjab home minister Shuja khanzada.

Describing the reason for S Ansar and dad he said this was because a large number of yours of his age group who are involved in such activities oil doubtful about their future because of ripped within taliban.

The rule of the law and the divorce process of the lord be followed in the cases and this case I should not be dropped this post in instantly he said adding that there was no good all bad taleban and this was the stated policy of the government wine mqm Senator Barista Muhammad Ali safe said there was useful and non useful taliban.

Apec Asia Pacific economic cooperation expert consultations on food losses

We must discuss about the APEC Asia Pacific economic cooperation it is a organisation which is build to improve the business facilities manufacturing unit and import and export facilities to add the specific ocean and their neighbourhood countries.

There is a specific economic cooperation on export consulta songs on food losses and wealth tax and meeting rape sup June 3rd incapacity with around 60 representative from 70 members economic discussion best practices and Odissi making for car telling Food West and strengthening food security throughout the region.

Optimised by the cabinet level Council of Agricultural the today meeting get artificial stockholders and exports from the public and private sector to examine the measures of receiving a 10% reduction in food losses and busters in the effect member economic by 2020 compared with 2011 and 12 levels.

Attendees also reached a consensus on following the Epic food losses watched according to reporting partnership.

C o a Deputy Minister chain cheating in an address on opening day of the event highlight it the Vital role that were listed food loss assessment and control the method can play a strengthening productivity noting that a 10% reduction in food losses and busters across the effect members economic could save the estimated 14.3 billion dollar in a year.

Epic has identified carbon food wastage as a top priority in promoting balanced inclusive and sustainable growth in a CI specific according to the CA losses and watched account for 26.7% of animal food production in apec members economic this is equivalent to around 671 emery an amount capable of sustaining 800 million peoples.