On higher dimensional Einstein spacetimes with a warped extra dimension

Details On higher dimensional Einstein spacetimes with a warped extra dimension On higher dimensional Einstein spacetimes with a warped extra dimension

2010-11-13

arxiv.org/abs/1011.3153v2

Class. Quant. Grav. 28:105006, 2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, minor changes in the text, mainly in Section 2.1

Scientific paper

10.1088/0264-9381/28/10/105006

We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have subsequently appeared in various contexts to describe, e.g., different braneworld models or warped black strings. After clarifying the relation between the general Brinkmann metric and other more specific coordinate systems, we analyze the algebraic type of the Weyl tensor of the solutions. In particular, we describe the relation between Weyl aligned null directions (WANDs) of the lower dimensional Einstein slices and of the full spacetime, which in some cases can be algebraically more special. Possible spacetime singularities introduced by the warp factor are determined via a study of scalar curvature invariants and of Weyl components measured by geodetic observers. Finally, we illustrate how Brinkmann's metric can be employed to generate new solutions by presenting the metric of spinning and accelerating black strings in five dimensional anti-de Sitter space.

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