Background subtraction method is not only much simpler, but also as applicable as covariant counterterm method

TL;DR

This paper demonstrates that the background subtraction method is as broadly applicable and simpler than the covariant counterterm method for black hole thermodynamics, extending to higher derivative gravity and providing a universal Gibbs free energy expression.

Contribution

It establishes the applicability of the background subtraction method to higher derivative gravity and derives a universal Gibbs free energy expression beyond Einstein's gravity.

Findings

Background subtraction method is as applicable as covariant counterterm method.

Framework applies to Einstein's gravity and higher derivative corrections.

Provides a universal expression for Gibbs free energy in black hole thermodynamics.

Abstract

As the criterion for the applicability of the background subtraction method, not only the finiteness condition of the resulting Hamiltonian but also the condition for the validity of the first law of black hole thermodynamics can be reduced to the form amenable to much simpler analysis at infinity by using the covariant phase space formalism. With this, we further establish that the background subtraction method is as applicable as the covariant counterterm method not only to Einstein's gravity, but also to its higher derivative corrections for black hole thermodynamics in both asymptotically flat and AdS spacetimes. In addition, our framework also provides us with the first derivation of the universal expression of the Gibbs free energy in terms of the Euclidean on-shell action beyond Einstein's gravity. Among others, our findings have a far reaching impact on the shift in methodology for the Euclidean approach to black hole thermodynamics, where the well justified background subtraction method by our wieldy criterion is supposed to be the favored choice compared to the covariant counterterm method.