The Cardy-Verlinde Formula and Asymptotically Flat Charged Black Holes

TL;DR

This paper demonstrates that the modified Cardy-Verlinde formula applies to asymptotically flat charged black holes across dimensions, linking their thermodynamics to two-dimensional conformal field theories and supporting a dimensional reduction perspective.

Contribution

It shows the validity of the modified Cardy-Verlinde formula for higher-dimensional charged black holes without the Casimir term, and connects black hole thermodynamics to 2D CFT descriptions.

Findings

The modified Cardy-Verlinde formula holds for asymptotically flat charged black holes.

Black hole thermodynamics obeys the energy-temperature relation of 2D CFTs.

The Cardy formula is verified for black holes derived from higher-dimensional dilatonic solutions.

Abstract

We show that the modified Cardy-Verlinde formula without the Casimir effect term is satisfied by asymptotically flat charged black holes in arbitrary dimensions. Thermodynamic quantities of the charged black holes are shown to satisfy the energy-temperature relation of a two-dimensional CFT, which supports the claim in our previous work (Phys. Rev. D61, 044013, hep-th/9910244) that thermodynamics of charged black holes in higher dimensions can be effectively described by two-dimensional theories. We also check the Cardy formula for the two-dimensional black hole compactified from a dilatonic charged black hole in higher dimensions.