Noncommutativity and logarithmic correction to the black hole entropy

TL;DR

This paper investigates how noncommutative geometry introduces a natural logarithmic correction to black hole entropy, suggesting noncommutativity can encode quantum effects in curved spacetime.

Contribution

It demonstrates that noncommutative corrections lead to logarithmic entropy corrections at lowest order, unlike the commutative case where such corrections appear only with quantum effects.

Findings

Noncommutative effects produce logarithmic entropy corrections at lowest order.

Logarithmic corrections in the commutative case require higher quantum effects.

Noncommutativity may encode quantum effects in curved spacetime.

Abstract

We study the noncommutative corrections to the entropy of the Reissner-Nordstr\"{o}m black hole using a $\kappa$-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordstr\"{o}m black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding quantum effects in curved spacetime.