Backreacted black holes

Abstract

This report delves into the Arnowitt-Deser-Misner (ADM) formalism, focusing on its application in deriving the time evolution equation. By exploring the dynamics of gravitational fields within the framework of general relativity, particular attention is given to calculating the expectation value for the stress-energy tensor. Notably, this tensor encapsulates the Riemannian curvature tensor, necessitating the determination of Christoffel symbols for the Schwarzschild metric. Additionally, the report delves into the computation of the scalar curvature and extrinsic curvature tensor, energy density, and momentum density for the Schwarzschild metric. Our primary objective lies in determining the change in the metric tensor using the time evolution equation, shedding light on the dynamical evaluation of spacetime curvature. Through these analyses, a comprehensive understanding of the gravitational field dynamics is synthesized, offering valuable insights into Hawking radiation.