Black Holes with a Generalized Gravitational Action

TL;DR

This paper investigates how higher dimension operators in the gravitational action affect microscopic black holes, revealing corrections to their thermodynamic properties and entropy calculations.

Contribution

It provides a perturbative analysis of the impact of all dimension six, time reversal invariant operators on Schwarzschild black holes, extending previous work limited to lower dimensions.

Findings

Corrections to Hawking temperature-mass relation identified.

Entropy deviates from the standard 1/4 area formula.

Both Euclidean path integral and thermodynamic methods agree on entropy.

Abstract

Microscopic black holes are sensitive to higher dimension operators in the gravitational action. We compute the influence of these operators on the Schwarzschild solution using perturbation theory. All (time reversal invariant) operators of dimension six are included (dimension four operators don't alter the Schwarzschild solution). Corrections to the relation between the Hawking temperature and the black hole mass are found. The entropy is calculated using the Gibbons-Hawking prescription for the Euclidean path integral and using naive thermodynamic reasoning. These two methods agree, however, the entropy is not equal to 1/4 the area of the horizon.