Research On Gravity And Quantum Effect

General relativity is a classical theory,which is very effective in describing the evolution of celestial bodies and even the entire universe.Among them,black holes are also one of the subjects of general relativity research.The classical black hole satisfies a property akin to the second law of thermodynamics:its area,like entropy,can only increase.But after considering quantum effects,the black hole will evaporate due to the process of Hawking radiation.This is completely different from the classical theory.Therefore,it is necessary to further explore whether quantum corrections give rise to new phenomena in the physics of black holes and compact stars.In general relativity,it is generally believed thatthere is a "cosmic censorship conjecture"that prevents the appearance of naked singularities.The spherically symmetric Reissner-Nordstrom(RN)black holes are the simplest example to discuss cosmic censor conjecture:once Q/M>1,naked singularities appear.An interesting question is whether a RN black hole can reach Q/M>1 via Hawking radiation.In the previous work,Hiscock and Weems proved that an isolated asymptotically flat Reissner-Nordstrom(RN)black hole evolves in a surprising manner under Hawking radiation:if it starts with a relatively small value of charge-to-mass ratio Q/M,then Q/M will temporarily increases,then turns over and finally decreases towards zero.However,the one with sufficiently large charge simply radiates away its charge steadily.The combination of these two effects uphold cosmic censorship:there exists "an attractor" that flows towards the Schwarzschild limit,which ensures that extremality can never be reached.Therefore,there will be no naked singularity under Hawking radiation.We apply the method of Hiscock and Weems to the evaporation of an asymptotically flat dilaton charge black hole known as the Garfinkle-Horowitz-Strominger(GHS)black hole.We found that upholding the cosmic censorship requires us to modify the charged particle production rate.This is consistent with the expression obtained by directly calculating the rate of charged particle production rate in the background of curved spacetime.This not only further supports the cosmic censorship,but also provides an example where the cosmic censorship can be a useful principle for inferring other physics.We also found that the behavior of "attractor" is not necessarily related to specific heat,which is different from the properties of RN black holes studied by Hiscock and Weems.The effect of quantum gravity must be considered because of the large quantum effect of black holes during the late stage of evaporation.One of the effects is that gravity modifies and generalizes the uncertainty principle of quantum mechanics.We consider the simplest model of generalized uncertainty principle(GUP)and find that it seems to permit the existence of arbitrarily large white dwarfs,which is not consistent with observation.We then need to study how to restore the Chandrasekhar limit of the white dwarf in this framework.It has been previously discussed that the generalized uncertainty principle with positive parameters eliminates the Chandrasekhar limit.One way to restore the limit is to set the GUP parameter to be negative.In this work,we discussed an alternative approach that achieves the same effect by including a cosmological constant term in GUP(known in the literature as the "extended uncertainty principle",EUP).We have shown that an arbitrarily small but non-zero cosmological constant can restore the Chandrasekhar limit.We also note that if the so-called EGUP(Extended Generalized Uncertainty Principle),which includes both GUP and EUP,is correct,then the existence of a white dwarf gives an upper bound on the cosmological constant.While the upper bound is still larger than the observed value,it is about 86 orders of magnitude smaller than the natural order of magnitude inferred from the quantum field theory.