Type III and N Einstein spacetimes in higher dimensions: general properties - General Relativity and Quantum CosmologyReportar como inadecuado




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Abstract: The Sachs equations governing the evolution of the optical matrix of geodeticWANDs Weyl aligned null directions are explicitly solved in n-dimensions inseveral cases which are of interest in potential applications. This is thenused to study Einstein spacetimes of type III and N in the higher dimensionalNewman-Penrose formalism, considering both Kundt and expanding possiblytwisting solutions. In particular, the general dependence of the metric and ofthe Weyl tensor on an affine parameter r is obtained in a closed form. Thisallows us to characterize the peeling behaviour of the Weyl -physical-components for large values of r, and thus to discuss, e.g., how the presenceof twist affects polarization modes, and qualitative differences between fourand higher dimensions. Further, the r-dependence of certain non-zero scalarcurvature invariants of expanding spacetimes is used to demonstrate thatcurvature singularities may generically be present. As an illustration, severalexplicit type N-III spacetimes that solve Einstein-s vacuum equations with apossible cosmological constant in higher dimensions are finally presented.



Autor: Marcello Ortaggio, Vojtech Pravda, Alena Pravdova

Fuente: https://arxiv.org/



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