Black Hole Enthalpy and Scalar Fields

TL;DR

This paper explores how scalar fields with exponential potentials affect the thermodynamics and mass-energy relations of AdS black holes, revealing new contributions to their enthalpy and extending thermodynamic laws.

Contribution

It introduces a novel analysis of dilaton-AdS black holes, showing scalar fields alter asymptotic spacetime and modify the first law and Smarr formula for these systems.

Findings

Scalar fields contribute to ADM mass and tensions.

Mass of black holes still represents enthalpy.

Derived first law and Smarr formula for dilaton-AdS black holes.

Abstract

The mass of an AdS black hole represents its enthalpy, which in addition to internal energy, generally includes the energy required to assemble the system in its environment. In this paper, we consider black holes immersed in a more complex environment, generated by a scalar field with an exponential potential. In the analogue of the AdS vacuum, which we call dilaton-AdS, the scalar field has non-trivial behavior, breaking the hyperscaling symmetry of AdS and modifying the asymptotic form of the spacetime. We find that the scalar field falloff at infinity makes novel contributions to the ADM mass and spatial tensions of dilaton-AdS black holes. We derive a first law and Smarr formula for planar dilaton-AdS black holes. We study the analogue of thermodynamic volume in this system and show that the mass of a black hole again represents its enthalpy.