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

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.