Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 003, 10 pages      arXiv:1304.6550      https://doi.org/10.3842/SIGMA.2014.003

Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space

Sergey A. Paston and Anton A. Sheykin
Saint Petersburg State University, St. Petersburg, Russia

Received November 22, 2013, in final form January 03, 2014; Published online January 07, 2014

Abstract
We study isometric embeddings of non-extremal Reissner-Nordström metric describing a charged black hole. We obtain three new embeddings in the flat ambient space with minimal possible dimension. These embeddings are global, i.e. corresponding surfaces are smooth at all values of radius, including horizons. Each of the given embeddings covers one instance of the regions outside the horizon, one instance between the horizons and one instance inside the internal horizon. The lines of time for these embeddings turn out to be more complicated than circles or hyperbolas.

Key words: isometric embedding; global embedding Minkowski space; GEMS; Reissner-Nordström metric; charged black hole.

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