# Condensates beyond the horizons

## TL;DR

This paper investigates the theoretical possibility of Bose-Einstein condensates existing inside black holes and cosmological horizons, using quasilocal energy to analyze their energetic favorability and potential formation mechanisms.

## Contribution

It extends previous studies to Reissner-Nordstr"om and de Sitter horizons, introducing a quasilocal potential approach to explore condensate formation in these contexts.

## Key findings

- Condensates are energetically favorable inside horizons.
- The quasilocal potential suggests a possible graviton condensate mechanism.
- Condensate formation is unlikely behind the de Sitter horizon.

## Abstract

In this work we continue our previous studies concerning the possibility of the existence of a Bose-Einstein condensate in the interior of a static black hole, a possibility first advocated by Dvali and G\'omez. We find that the phenomenon seems to be rather generic and it is associated to the presence of an horizon, acting as a confining potential. We extend the previous considerations to a Reissner-Nordstr\"om black hole and to the de Sitter cosmological horizon. In the latter case the use of static coordinates is essential to understand the physical picture. In order to see whether a BEC is preferred, we use the Brown-York quasilocal energy, finding that a condensate is energetically favourable in all cases in the classically forbidden region. The Brown-York quasilocal energy also allows us to derive a quasilocal potential, whose consequences we explore. Assuming the validity of this quasilocal potential allows us to suggest a possible mechanism to generate a graviton condensate in black holes. However, this mechanism appears not to be feasible in order to generate a quantum condensate behind the cosmological de Sitter horizon.