Research paper guide on black holes
Black holes and thermodynamics
A black hole of given mass, angular momentum, and charge can have a large number of different
unobservable internal configurations which reflect the possible different initial configurations of the matter
which collapsed to produce the hole. The logarithm of this number can be regarded as the entropy of the
black hole and is a measure of the amount of information about the initial state which was lost in the
formation of the black hole. If one makes the hypothesis that the entropy is finite, one can deduce that the
black holes must emit thermal radiation at some nonzero temperature.
Conversely, the recently derived quantum-mechanical result that black holes do emit thermal radiation at temperature κℏ2πkc, where κ is thesurface gravity, enables one to prove that the entropy is finite and is equal to c3A4Gℏ, where A is the surface areaof the event horizon or boundary of the black hole. Because black holes have negative specific heat, they
cannot be in stable thermal equilibrium except when the additional energy available is less than 1/4 the mass
of the black hole. This means that the standard statistical-mechanical canonical ensemble cannot be applied
when gravitational interactions are important. Black holes behave in a completely random and time-
symmetric way and are indistinguishable, for an external observer, from white holes. The irreversibility that
appears in the classical limit is merely a statistical effect.
Particle Creation by Black Holes
In the classical theory black holes can only absorb and not emit particles. However it
is shown that quantum mechanical effects cause black holes to create and emit
particles as if they were hot bodies with temperature
hk2πk ≈ 10−6 (M⊙M) ∘Khk2πk ≈ 10−6 (M⊙M) ∘K where k is the surface gravity of the
black hole. This thermal emission leads to a slow decrease in the mass of the black
hole and to its eventual disappearance: any primordial black hole of mass less than
about 1015 g would have evaporated by now. Although these quantum effects violate
the classical law that the area of the event horizon of a black hole cannot decrease,
there remains a Generalized Second Law: S+14AS+14A never decreases never
decreases where S is the entropy of matter outside black holes and A is the sum ofthe surface areas of the event horizons.
This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon https://www.worldscientific.com/doi/abs/10.1142/9789814539395_0011 Evanescent black holes A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two spacetime dimensions is analyzed. The theory is shown to be exactly solvable classically. Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter.
The problem of Hawking radiation and back reaction of the metric is analyzed to leading order in a 1N expansion, where N is the number of matter fields. The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum- mechanical spectrum. It is argued that the matter asymptotically approaches a zero-energy “bound state” which can carry global quantum numbers and that a unitary S matrix including such states should exist. Black holes in higher dimensional space-times Black hole solutions to Einstein’s equations are examined in asymptotically flat N + 1 dimensional space-times.
First generalizations of Schwarzschild and Reissner- Nordstrøm solutions are examined in a discussion of static black holes in N + 1 dimensions. Then a new family of solutions is found which describe spinning black holes in higher dimensional space-times. In many respects these new solutions are similar to the familiar Kerr and Schwarzschild metrics which are recovered for N = 3. One exceptional case though is that for N ≥ 5, black holes with a fixed mass may have arbitrarily large angular momentum.
PHYSICS OF BLACK HOLES
Black Holes and the Second Law
Black-hole physics seems to provide at least two ways in which the second law of thermodynamics may be transcended or violated:
a) Let an observer drop or lower a package of entropy into a black hole; the entropy of the exterior world decreases. Furthermore, from an exterior observer’s point of view a black hole in equilibrium has only three degrees of freedom: mass, charge and angular momentum. Thus, once the black hole has settled down to equilibrium, there is no way for the observer to determine its interior entropy. Therefore, he cannot exclude the possibility that the total entropy of the universe may have decreased in the process.
It is in this sense that the second law appears to be transcended. b) A method for violating the second law has been proposed by GEROCH: By means of a string one slowly lowers a body of rest mass m and nonzero temperature toward a Sehwarzschild black hole of mass M. By the time the body nears the horizon, its energy as measured from infinity, E=m(1−2M/r)12E=m(1−2M/r)12, is nearly zero; the body has already done work m on the agent which lowers the string. At this point the body is allowed to radiate into the black hole until its rest mass is m − Δm. Finally, by expending work m − Δm, one hauls the body back up