# Maximal volume behind horizons without curvature singularity

## TL;DR

This paper calculates the maximal interior volume of regular black holes without singularities in various spacetimes and explores implications for the complexity/volume duality, providing new analytical insights.

## Contribution

It introduces a method to compute the maximal volume inside regular black holes and applies the complexity/volume duality to these non-singular solutions.

## Key findings

- Maximal volume inside regular black holes is computed analytically.
- The complexity/volume duality is extended to regular black holes in AdS.
- An analytical expression for maximal volume outside de Sitter horizon is derived.

## Abstract

The black hole information paradox is related to the area of event horizon, and potentially to the volume and singularity behind it. One example is the complexity/volume duality conjectured by Stanford and Susskind. Accepting the proposal of Christodoulou and Rovelli, we calculate the maximal volume inside regular black holes, which are free of curvature singularity, in asymptotically flat and anti-de Sitter spacetimes respectively. The complexity/volume duality is then applied to anti-de Sitter regular black holes. We also present an analytical expression for the maximal volume outside the de Sitter horizon.