A Cardy-like expression for charged rotating solitons and black holes

TL;DR

This paper introduces a generalized Cardy-like formula for charged rotating black holes and solitons, incorporating mass, charge, angular momentum, and other parameters, validated through multiple examples including static and rotating solutions.

Contribution

It proposes a new Cardy-like expression that accounts for charge, rotation, and dynamical exponents, extending previous formulas to more complex black hole and soliton configurations.

Findings

Derived a formula matching semiclassical entropy for solitons with additional thermodynamic quantities

Applied Lorentz boosts to static black hole solutions to compute thermodynamic parameters

Validated the formula with a rotating configuration without Lorentz boost

Abstract

This paper aims to propose a Cardy-like formula characterized by the mass, charge, and angular components of the black hole, along with their corresponding solitonic configuration, obtained through a double Wick rotation. The expression also incorporates the dynamical exponent and effective spatial dimensionality as key elements. To validate the proposal, we first present a new concrete example in which recovering the semiclassical entropy requires the soliton to possess thermodynamic quantities beyond its mass. Additionally, we show more examples derived from static black hole solutions, employing a Lorentz boost to calculate their thermodynamic parameters. Finally, we include a case of a rotating configuration where the Lorentz boost is not required.