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Lorentzian Manifolds: A characterization with semiconformal curvature tensor

Uday Chand De|Chiranjib Dey
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 911-920|DOI 10.4134/CKMS.c180248

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참고문헌

키워드

Lorentzian manifoldsconformal curvature tensorsemiconformal curvature tensor
주제분류수학

초록

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension $n=4$, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type $I$, $D$ or $O$ and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

Abstract

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension $n=4$, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type $I$, $D$ or $O$ and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

참고문헌 (37)

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