Topic
Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
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TL;DR: In this article, a method for calculating the curvature tensor was developed and applied to the Scharzschild case, which employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
Abstract: A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
30 citations
30 citations
TL;DR: The regularized stress energy tensor of the quantized massive scalar, spinor, and vector fields inside the degenerate horizon of the regular charged black hole in the (anti-de Sitter) universe is constructed and examined in this article.
Abstract: The regularized stress-energy tensor of the quantized massive scalar, spinor, and vector fields inside the degenerate horizon of the regular charged black hole in the (anti)-de Sitter universe is constructed and examined. It is shown that, although the components of the stress-energy tensor are small in the vicinity of the black hole degenerate horizon and near the regular center, they are quite big in the intermediate region. The oscillatory character of the stress-energy tensor can be ascribed to various responses of the higher curvature terms to the changes of the metric inside the (degenerate) event horizon, especially in the region adjacent to the region described by the nearly flat metric potentials. Special emphasis is put on the stress-energy tensor in the geometries being the product of the constant curvature two-dimensional subspaces.
30 citations
TL;DR: In this paper, the authors derived a gradient estimate for the logarithm of the heat kernel on a Riemannian manifold with Ricci curvature bounded from below.
30 citations
TL;DR: In this article, a classification of generalized m-quasi-Einstein manifolds with parallel Ricci tensor was established and the scalar curvature was determined in explicit form.
30 citations