Type III and N Einstein spacetimes in higher dimensions: General properties
- Institute of Mathematics, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1 (Czech Republic)
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.
- OSTI ID:
- 21421183
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.064043; (c) 2010 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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