Cardy formula for charged black holes with anisotropic scaling

Understand

We first observe that for Lifshitz black holes whose only charge is the mass, the resulting Smarr relation is a direct consequence of the Lifshitz Cardy formula.

• From this observation, we propose to extend the Cardy formula to the case of electrically charged Lifshitz black holes satisfying as well a Smarr relation.
• The expression of our formula depends on the dynamical exponent, the energy and the charge of the ground state which is played by a magnetically charged soliton obtained through a double Wick rotation.
• The expression also involves a factor multiplying the chemical potentials which varies in function of the electromagnetic theory considered.