Quantum-Corrected Entropy for 1+1-Dimensional Gravity Revisited

TL;DR

This paper revisits quantum corrections to black hole entropy in 1+1-dimensional gravity, deriving a well-defined partition function and highlighting discrepancies with previous results on quantum entropy corrections.

Contribution

It provides a new formulation of the Lorentzian partition function and analyzes quantum entropy corrections, revealing differences from earlier studies.

Findings

Quantum correction to entropy is logarithmic in classical entropy.

Discrepancy in the magnitude and sign of the correction compared to prior work.

Partition function is expressed in a calculable, well-defined form.

Abstract

In this paper, we examine a generic theory of 1+1-dimensional gravity with coupling to a scalar field. Special attention is paid to a class of models that have a power-law form of dilaton potential and can capably admit black hole solutions. The study focuses on the formulation of a Lorentzian partition function. We incorporate the principles of Hamiltonian thermodynamics, as well as black hole spectroscopy, and find that the partition function can be expressed in a well-defined, calculable form. We then go on to extract the black hole entropy, including the leading-order quantum correction. As anticipated, this correction can be expressed as the logarithm of the classical entropy. Interestingly, the prefactor for this logarithmic correction disagrees, in both magnitude and sign, with the findings from a prior study (on the very same model). We comment on this discrepancy and provide a possible rationalization.