# Geometrothermodynamics of black hole binary systems

## TL;DR

This paper applies geometrothermodynamics to a binary Kerr black hole system, revealing that the spatial distance acts as a thermodynamic variable influencing the system's thermodynamic behavior and phase transitions.

## Contribution

It introduces the spatial distance as a thermodynamic variable in black hole binaries using geometrothermodynamics, linking geometry to thermodynamic stability and phase transitions.

## Key findings

- Thermodynamic properties depend on black hole separation.
- Phase transition structure is linked to curvature singularities.
- System stability varies with inter-black hole distance.

## Abstract

We study a stationary and axisymmetric binary system composed of two identical Kerr black holes, whose physical parameters satisfy the Smarr thermodynamic formula. Then, we use the formalism of geometrothermodynamics to show that the spatial distance between the black holes must be considered as a thermodynamic variable. We investigate the main thermodynamic properties of the system by using the contact structure of the phase space, which generates the first law of thermodynamics and the equilibrium conditions. The phase transition structure of the system is investigated through the curvature singularities of the equilibrium space. It is shown that the thermodynamic and stability properties and the phase transition structure of the binary system strongly depend on the distance between the black holes.