$α-$surfaces and global coordinates in black hole spacetimes

Fuente: arXiv
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Autores principales: Araneda, Bernardo, Whiting, Bernard F.
Formato: Preprint
Publicado: 2024
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author Araneda, Bernardo
Whiting, Bernard F.
author_facet Araneda, Bernardo
Whiting, Bernard F.
contents We present a discussion of the periodicity in imaginary time of maximally extended black hole spacetimes without reference to Euclidean manifolds. As motivation, we first demonstrate our approach for the Rindler geometry in flat space before then applying it for the case of Schwarzschild time in the maximally extended Kruskal geometry. One notable advantage of our approach is that it can be utilized in the Kerr case, again without reference to a Euclidean manifold, and without complexifying the angular momentum parameter, $a$. One unusual feature of our application in the Kerr case is that, even for the purely Lorentzian geometry, it is developed in terms of explicitly complex coordinates which are associated with distinct families of $α-$surfaces. Moreover, coordinatization of these gives a single set of coordinates which cover the entire geometry outside the inner horizon.
format Preprint
id arxiv_https___arxiv_org_abs_2408_15189
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle $α-$surfaces and global coordinates in black hole spacetimes
Araneda, Bernardo
Whiting, Bernard F.
General Relativity and Quantum Cosmology
High Energy Physics - Theory
We present a discussion of the periodicity in imaginary time of maximally extended black hole spacetimes without reference to Euclidean manifolds. As motivation, we first demonstrate our approach for the Rindler geometry in flat space before then applying it for the case of Schwarzschild time in the maximally extended Kruskal geometry. One notable advantage of our approach is that it can be utilized in the Kerr case, again without reference to a Euclidean manifold, and without complexifying the angular momentum parameter, $a$. One unusual feature of our application in the Kerr case is that, even for the purely Lorentzian geometry, it is developed in terms of explicitly complex coordinates which are associated with distinct families of $α-$surfaces. Moreover, coordinatization of these gives a single set of coordinates which cover the entire geometry outside the inner horizon.
title $α-$surfaces and global coordinates in black hole spacetimes
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2408.15189