The Conical Singularity And Quantum Corrections To Entropy Of Black Hole

TL;DR

This paper investigates quantum corrections to black hole entropy caused by conical singularities at finite temperatures, calculating divergences and finite effects in 2D and 4D black hole models using path integral methods.

Contribution

It provides a detailed analysis of quantum entropy corrections due to conical singularities, including divergences and finite terms, in both two and four-dimensional black hole spacetimes.

Findings

Logarithmic divergence of entropy in 2D Rindler space

Quadratic divergence of entropy in 4D Rindler space

Finite, mass-dependent correction to 2D black hole entropy

Abstract

For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.