Yet another family of diagonal metrics for de Sitter and anti–de Sitter spacetimes

Yet another family of diagonal metrics for de Sitter and anti–de Sitter spacetimes In this work we present and analyze a new class of coordinate representations of de Sitter and anti–de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1+3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2+2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti–)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1,0,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ>0 and 8 subcases for Λ<0. We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti–)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti–de Sitter metrics. Using these results, we also provide a physical interpretation of B-metrics as exact gravitational fields of a tachyon. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Yet another family of diagonal metrics for de Sitter and anti–de Sitter spacetimes

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Yet another family of diagonal metrics for de Sitter and anti–de Sitter spacetimes

Abstract

In this work we present and analyze a new class of coordinate representations of de Sitter and anti–de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1+3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2+2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti–)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1,0,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ>0 and 8 subcases for Λ<0. We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti–)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti–de Sitter metrics. Using these results, we also provide a physical interpretation of B-metrics as exact gravitational fields of a tachyon.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.95.124052
Publisher site
See Article on Publisher Site

Abstract

In this work we present and analyze a new class of coordinate representations of de Sitter and anti–de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1+3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2+2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti–)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1,0,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ>0 and 8 subcases for Λ<0. We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti–)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti–de Sitter metrics. Using these results, we also provide a physical interpretation of B-metrics as exact gravitational fields of a tachyon.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jun 15, 2017

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