Higher dimensional flat embedding of Taub-NUT-AdS spacetime

TL;DR

This paper constructs a high-dimensional flat embedding of Taub-NUT-AdS spacetime, explores its limits, and analyzes the embedding structure inside event horizons, providing new insights into spacetime embeddings.

Contribution

It introduces a novel (6+5)-dimensional global embedding of Taub-NUT-AdS spacetime and examines parameter reductions to related spacetimes, including inside event horizons.

Findings

Successful embedding of Taub-NUT-AdS in (6+5) dimensions

Parameter reduction schemes connect Taub-NUT-AdS to Schwarzschild-AdS and other spacetimes

Embedding inside event horizons constructed for extended manifolds

Abstract

We construct a global flat embedding structure of a Taub-NUT-AdS spacetime to yield a (6+5)-dimensional novel global embedding Minkowski spacetime. We also investigate Taub-NUT, Schwarzschild-AdS and Schwarzschild limits of the global embedding by exploiting parameter reduction scheme. In particular, we observe in the vanishing monopole strength limit of the Taub-NUT-AdS that the parameter reduction is not smoothly applicable to the Schwarzschild-AdS, due to the presence of imaginary roots of its lapse function associated with event horizon. Moreover, reductions from the Taub-NUT-AdS and Schwarzschild-AdS to Taub-NUT and Schwarzschild, respectively, are successfully performed. Finally, we construct the global embedding Minkowski spacetimes for the patches inside the event horizons of the Taub-NUT-AdS and its extended manifolds.