Dirac-Born-Infeld Counter-Term and Black Hole Thermodynamics

We revisit the Dirac-Born-Infeld–like boundary counter-term for four dimensional theory of gravity. We show that it correctly executes complete background subtraction for both asymptotically AdS and asymptotically flat geometries. With an appropriate choice of ensemble, we reproduce dyonic black hole thermodynamics with both types of asymptotics by studying local thermodynamics on the cut-off surface.