Article

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

(Impact Factor: 4.86). 05/2010; 82:064043. DOI: 10.1103/PhysRevD.82.064043
Source: arXiv

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 behaviour 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 non-zero 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. Comment: 19 pages

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Available from: Vojtech Pravda
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• "Scalar curvature invariants of vacuum Einstein equations were also studied [10]. There are also attempts to generalise vacuum Einstein solutions of type N space-times to higher dimensions [11]. "
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Preview · Article · Jan 2012 · Physical review D: Particles and fields
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• "that U ⊂ KCSI. ppIII RF are examples of spacetimes which are KCSI (and VSI) but not U. Notice however that QG E ⊂ CSI since examples of QG E metrics with non-vanishing expansion mentioned in this section have in general non-trivial curvature invariants [21] "
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