Hawking Evaporation Of Black Hole In Massive Gravity

Einstein's general relativity is the most successful theory of gravity.It is able to successfully describe physics within the scale of the solar system,but when applied to the larger scale of spacetime,there are still some unsolve mysteries,such as the accelerating expansion of the universe.These problems have motivated the search for a theory that can replace general relativity,or modify general relativity to get an extended theory.From the point of view of particle physics,general relativity is a field theory whose the dynamics are governed by particles with a zero mass and a spin of 2 called graviton,Quite naturally,one can contemplate the possibility of endowing these gravitons a nonzero mass.Fierz and Pauli first tried to come up with such a theory,but their theory had problems with discontinuity;Vainshtein extended the theory to a non-linear case and solved the discontinuity problem,but at the same time,the Boulware-Deser(BD)ghost problem appeared.In the end,de Rham,Gabadadze and Tolley put forward a more mature dRGT massive gravity theory without the BD ghost problem.We know that black holes behave like thermodynamic systems,and indeed there are laws of thermodynamics for black holes.The third law of thermodynamics for black hole states that a black hole cannot reach zero temperature in a finite time.In studying the remnants of black holes,we have put forward a complementary conclusion to the thermodynamics law of black hole:black holes cannot reach a state of non-zero temperature but zero mass.We call it the complementary theorem of the third law of thermodynamics.And we found that the Hawking evaporation of black holes in massive gravity can satisfied this complementary theorem.In addition,we also prove the theorem in the general case.Applying geometrical optics approximation and using Stephen-Boltzmann's law to study the evaporative evolution of black holes in massive gravity,we have found that black holes will have remnants in some cases.These remnants only exist in anti-de Sitter spacetime,not in de Sitter spacetime.We further studied the evaporative evolution of a class of(3+1)-dimensional spherically symmetric black holes of dRGT massive gravity in anti-de Sitter spacetime.The graviton mass term generates three terms in the black hole metric.These terms make the thermodynamics of black holes in dRGT massive gravity far richer than black holes in general relativity.Depending in the values of the black hole parameters,there may be more than one horizon;the effective emission surface may be proportional to the square of the effective AdS length,or to the square of the impact parameter that corresponds to the photon orbit.In some cases,when the black hole loses its mass,the emitting surface type may also change.