# Interior Volume of Banados-Teitelboim-Zanelli Black Hole

## TL;DR

This paper computes the interior volume of the BTZ black hole by deriving a volume functional, numerically extremizing it, and obtaining an analytical expression for the interior volume based on the extremal path.

## Contribution

The paper introduces a method to calculate the interior volume of the BTZ black hole using a combination of numerical and analytical techniques.

## Key findings

- Derived a volume functional for the BTZ black hole
- Numerically found extremal paths for the volume functional
- Obtained an analytical expression for the interior volume

## Abstract

We calculate the interior volume for the three-dimensional Banados-Teitelboim-Zanelli black hole in this paper. To that end, we obtain the volume functional and numerically find a path to extremize it, before choosing a spacelike hypersurface to get an asymptotic analytical expression for the interior volume based on the characteristics of the path.