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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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33 citations
TL;DR: It is shown that the Pontrjagin forms of a Riemannian manifold can be expressed uniquely in terms of the conformal curvature tensor: this provides a new proof of Chern and Simons' result.
Abstract: In a recent paper, Chern and Simons proved that the Pontrjagin forms of a Riemannian manifold remain invariant under a conformal deformation. We show that these forms can be expressed uniquely in terms of the conformal curvature tensor: this provides a new proof of their result. Similar techniques can be applied to Euler-Poincare characteristic class, as suggested to me by A. Taub. We obtain the following: If the Weyl tensor of a compact space time is of type III of Bel-Petrov, then it cannot carry a perfect fluid + electromagnetic field.
33 citations
TL;DR: A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors.
Abstract: This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.
33 citations
TL;DR: In this article, the Ricci scalar, Ricci tensor and Riemann tensor were investigated for the top-Higgs sector with an additional scalar field and the effect of these terms on the stability of the scalar effective potential was investigated.
Abstract: We investigate stability of the Higgs effective potential in curved spacetime. To this end, we consider the gauge-less top-Higgs sector with an additional scalar field. Explicit form of the terms proportional to the squares of the Ricci scalar, the Ricci tensor and the Riemann tensor that arise at the one-loop level in the effective action has been determined. We have investigated the influence of these terms on the stability of the scalar effective potential. The result depends on background geometry. In general, the potential becomes modified both in the region of the electroweak minimum and in the region of large field strength.
33 citations
TL;DR: In this article, the authors derived a general formalism by taking two arbitrary spherically symmetric spacetimes with g00 = 1 and derived the surface energy density and the tangential pressure.
Abstract: In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with g00 = 1. Israel's junction conditions are used to develop this formalism. The formulas for extrinsic curvature tensor are obtained. The general form of the surface energy–momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.
32 citations