A Note on Smarr Relation and Coupling Constants

TL;DR

This paper examines the limitations of deriving the Smarr relation in black hole thermodynamics when dimensionful coupling constants are involved, highlighting issues in identifying thermodynamical variables.

Contribution

It clarifies the conditions under which the Smarr relation can be correctly formulated in the presence of dimensionful couplings.

Findings

The standard scaling argument for the Smarr relation may fail with dimensionful couplings.

Proper identification of thermodynamical variables is crucial in such cases.

The paper discusses the implications for black hole thermodynamics theory.

Abstract

The Smarr relation plays an important role in black hole thermodynamics. It is often claimed that the Smarr relation can be written down simply by observing the scaling behavior of the various thermodynamical quantities. We point out that this is not necessarily so in the presence of dimensionful coupling constants, and discuss the issues involving the identification of thermodynamical variables.