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

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. The obtained embeddings are also smooth at all values of radius for extremal and hyperextremal black holes.

LaTeX, 12 pages, in this version we stressed that obtained new embeddings are also global and smooth for extremal and hyperextremal black holes

References in corpus (4)

• A New Global Embedding Approach to Study Hawking and Unruh Effects
• Gravity as a field theory in flat space-time
• From the Embedding Theory to General Relativity in a result of inflation
• Embedding the Reissner-Nordstrom spacetime in Euclidean and Minkowski spaces

Cited by in corpus (9)

• Hawking into Unruh mapping for embeddings of hyperbolic type
• Classics Illustrated: Limits of Spacetimes
• When does the Hawking into Unruh mapping for global embeddings work?
• Classification of global minimal embeddings for nonrotating black holes
• Embeddings of the black holes in a flat space
• Explicit isometric embeddings of collapsing dust ball
• Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction
• Mapping Hawking into Unruh for global embeddings
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)