Black Hole Entropy Calculated via Wavefunction Approximations on a Schwarzschild Spacetime.

摘要

The study of thermodynamics of a black hole is at the interface of general relativity (GR) and quantum mechanics (QM). We will calculate the thermodynamic quantities using a first quantized theory which allows for only forward evolution in time but causes formal complications. The first approximation method used is a semiclassical approximation. To gain further understanding, we use perturbation theory in order to incorporate angular degrees of freedom. The calculations will give us insight on the relationship between GR and QM. We will begin by calculating the dynamics of a free particle in Minkowski (flat) spacetime where there is no gravity. We will then calculate the dynamics of a point particle on a Schwarzschild or black hole space-time. Our use of quantum mechanics as opposed to quantum field theory, as has been done in the past, is a unique approach to this problem. This approach can reproduce the Hawking temperature and Hawking-Bekenstein law at the semiclassical level and quantum gravitational corrections are observed using perturbation theory.