AdS Black Holes And Boundary Condition

Einstein's general relativity is one of the mainstream theories of gravity,and black holes are mysterious celestial bodies predicted in general relativity.At the same time,as the solution of Einstein's field equation,the physical problems related to black hole physics are also one of the frontier hotspots in the field of physics,astronomy and cosmology.Since the discovery of black hole thermodynamics,which include Stephen Hawking's derivation of black hole evaporation in the 1970s,physicists have since brought in various quantum perspectives into the study of black hole physics.Hawking radiation is one of the crucial aspects of the thermal effect of black holes.The evolution of black holes under Hawking radiation is one of the important aspects to be studied.Therefore,the purpose of this paper is to investigate the dynamic evolution process of black hole evaporation by setting different boundary conditions under the background of Anti-de Sitter(AdS)spacetime,and in turn examine its physical properties.In short,because of the special spacetime causal structures of AdS spacetime,particles radiated from black holes are not simply "radiated" like other spacetimes.Instead,they have different,"effects" on the black hole,depending on the boundary conditions set at the infinity boundary of AdS spacetime.By choosing different topological conditions of AdS spacetime,we can see that the evaporation of AdS black hole under a completely absorptive boundary condition and a completely reflective boundary condition have completely different evolutions.Moreover,the physical model of an evaporating black hole with a complete reflective boundary condition is far more complex than that of a completely absorptive boundary condition.Firstly,we need to construct the evolution equation of black hole from the perspective of thermodynamics through Stefan-Boltzmann equation,and model the round-trip situation of particles radiated from the black hole back to the black hole by using a delay differential equation,which leads to a dynamical cyclic process.In view of the difficulties involved,we construct a simplified model first by considering a fixed particle round-trip duration t*,then we follow up with a model with round-trip duration t*that is not fixed.These models reveal the physical characteristics of Hawking evaporation under the two different models,and clarify how the black hole can reach thermal equilibrium with its own reflected Hawking radiation.We also analyze the results obtained to determine whether it meets our initial physical expectations and the feasibility of the model.Through the comparison between the two models,we find that the black hole in the background of AdS spacetime with flat spatial section will eventually reach a thermal equilibrium state when a completely reflective boundary condition is imposed.Before reaching thermal equilibrium,we observe that the mass of the black hole undergoes oscillatory behavior.Under this oscillation,the black hole eventually tends to a stable state(with the oscillation becomes progressively smaller in time).In addition,we also find the special case of the evolution of a large black hole into a small black hole,summarize the characteristics and properties of the black hole in the evolution process under different parameters,and define the stable conditions for the black hole to reach thermal equilibrium.This provides a good foundation for future study of the Hawking evolution of AdS black hole and the related thermodynamic problems.