# Black Hole Thermodynamics with Conical Defects

## TL;DR

This paper extends black hole thermodynamics to include varying conical deficits, introducing a new thermodynamic potential and analyzing phase transitions and critical phenomena of accelerating black holes.

## Contribution

It generalizes previous formulations by allowing conical deficits to vary, defining a new thermodynamic length, and exploring phase space and critical behavior.

## Key findings

- Derived a new thermodynamic potential called 'thermodynamic length' for varying conical deficits.
- Mapped the phase space of accelerating black holes and identified critical phenomena.
- Discussed physical processes involving tension variation in black hole-string systems.

## Abstract

Recently we have shown [1604.08812] how to formulate a thermodynamic first law for a single (charged) accelerated black hole in AdS space by fixing the conical deficit angles present in the spacetime. Here we show how to generalise this result, formulating thermodynamics for black holes with varying conical deficits. We derive a new potential for the varying tension defects: the "thermodynamic length", both for accelerating and static black holes. We discuss possible physical processes in which the tension of a string ending on a black hole might vary, and also map out the thermodynamic phase space of accelerating black holes and explore their critical phenomena.