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Title: Type III and N Einstein spacetimes in higher dimensions: General properties

Abstract

The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding (possibly twisting) solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behavior of the Weyl 'physical' components for large values of r, and thus to discuss, e.g., how the presence of twist affects polarization modes, and qualitative differences between four and higher dimensions. Further, the r dependence of certain nonzero scalar curvature invariants of expanding spacetimes is used to demonstrate that curvature singularities may generically be present. As an illustration, several explicit type N/III spacetimes that solve Einstein's vacuum equations (with a possible cosmological constant) in higher dimensions are finally presented.

Authors:
; ;  [1]
  1. Institute of Mathematics, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1 (Czech Republic)
Publication Date:
OSTI Identifier:
21421183
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.82.064043; (c) 2010 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGICAL CONSTANT; EINSTEIN FIELD EQUATIONS; EQUATIONS; EVOLUTION; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; METRICS; POLARIZATION; SINGULARITY; SPACE-TIME; FIELD EQUATIONS

Citation Formats

Ortaggio, Marcello, Pravda, Vojtech, and Pravdova, Alena. Type III and N Einstein spacetimes in higher dimensions: General properties. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.064043.
Ortaggio, Marcello, Pravda, Vojtech, & Pravdova, Alena. Type III and N Einstein spacetimes in higher dimensions: General properties. United States. https://doi.org/10.1103/PHYSREVD.82.064043
Ortaggio, Marcello, Pravda, Vojtech, and Pravdova, Alena. 2010. "Type III and N Einstein spacetimes in higher dimensions: General properties". United States. https://doi.org/10.1103/PHYSREVD.82.064043.
@article{osti_21421183,
title = {Type III and N Einstein spacetimes in higher dimensions: General properties},
author = {Ortaggio, Marcello and Pravda, Vojtech and Pravdova, Alena},
abstractNote = {The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding (possibly twisting) solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behavior of the Weyl 'physical' components for large values of r, and thus to discuss, e.g., how the presence of twist affects polarization modes, and qualitative differences between four and higher dimensions. Further, the r dependence of certain nonzero scalar curvature invariants of expanding spacetimes is used to demonstrate that curvature singularities may generically be present. As an illustration, several explicit type N/III spacetimes that solve Einstein's vacuum equations (with a possible cosmological constant) in higher dimensions are finally presented.},
doi = {10.1103/PHYSREVD.82.064043},
url = {https://www.osti.gov/biblio/21421183}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 82,
place = {United States},
year = {Wed Sep 15 00:00:00 EDT 2010},
month = {Wed Sep 15 00:00:00 EDT 2010}
}