# Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space

## TL;DR

This paper investigates the possibility of globally embedding certain black hole spacetimes into flat spaces, providing explicit constructions for some cases and proving non-existence for others, advancing the geometric understanding of black holes.

## Contribution

It offers the first explicit embedding of the BTZ black hole in 6D flat space and extends this to embed higher-dimensional Schwarzschild-AdS black holes, while also classifying cases with no such embedding.

## Key findings

- No global embedding for 4D RN-AdS black hole in 6D flat space.
- Explicit embedding of non-spinning BTZ black hole in 6D flat space.
- Constructed a global embedding of d-dimensional Schwarzschild-AdS black hole in (d+3)-dimensional flat space.

## Abstract

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of (d)-dimensional Schwarzschild-AdS black hole in a flat (d+3)-dimensional ambient space.