Pravin Kumar Dahal: The Hawking temperature via conformal transformations - RQI Circuit Sydney 2023

Title: The Hawking temperature of dynamical black holes via Conformal transformations
Abstract: Assumptions of finite-time formation of a trapped region and finiteness of curvature scalars on its boundary are sufficient to constrain a general spherically symmetric metric to correspond to two classes of solutions of the Einstein equations. Depending on the dynamic behavior of the horizon, each solution can describe an expanding white hole or an evaporating black hole. In the leading order approximation, evaporating black hole (or accreting white hole) solution takes the form of the ingoing (or outgoing) Vaidya metric. This suggests a universal description of the near-horizon geometry of evaporating black (or accreting white) holes in terms of the Vaidya metric. As the Vaidya metric captures many essential features of evaporating black hole spacetimes, we demonstrate that the linear Vaidya metric can be brought into manifestly conformally static form, allowing us to determine its Hawking temperature with respect to the conformal vacuum. Since back-reaction is implicitly accounted for, we conclude that slowly evaporating black holes are indeed accurately described by quasistatic sequences of Schwarzschild metrics even when dynamical effects are present.