Topic
Riemann curvature tensor
About: Riemann curvature tensor is a research topic. Over the lifetime, 6248 publications have been published within this topic receiving 138871 citations. The topic is also known as: Riemann–Christoffel tensor.
Papers published on a yearly basis
Papers
More filters
29 Apr 2016
TL;DR: In this paper, a torsion-free parity-invariant covariant theory of gravity was constructed, which is free from ghost-like and tachyonic instabilities around constant curvature space-times in four dimensions.
Abstract: In this article we will construct the most general torsion-free parity-invariant covariant theory of gravity that is free from ghost-like and tachyonic instabilities around constant curvature space-times in four dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de Sitter backgrounds. We will first argue in details how starting from a general covariant action for the metric one arrives at an “equivalent” action that at most contains terms that are quadratic in curvatures but nevertheless is sufficient for the purpose of studying stability of the original action. We will then briefly discuss how such a “quadratic curvature action” can be decomposed in a covariant formalism into separate sectors involving the tensor, vector and scalar modes of the metric tensor; most of the details of the analysis however, will be presented in an accompanying paper. We will find that only the transverse and trace-less spin-2 graviton with its two helicity states and possibly a spin-0 Brans-Dicke type scalar degree of freedom are left to propagate in 4 dimensions. This will also enable us to arrive at the consistency conditions required to make the theory perturbatively stable around constant curvature backgrounds.
75 citations
75 citations
TL;DR: In this article, it was shown that some hypersurfaces do not contract during this flow, but straighten out and become totally geodesic, i.e. they converge to a big S.
Abstract: is satisfied. In [6] we studied hypersurfaces moving along their mean curvature vector in a general Riemannian manifold N" + 1. It was shown that all hypersurfaces Mo satisfying a suitable convexity condition will contract to a single point in finite time during this evolution. Here we want to show that in a spherical spaceform some convergence results can be obtained without assuming convexity for the initial hypersurface Mo. In particular, we will see that some hypersurfaces do not contract during this flow, but straighten out and become totally geodesic, i.e. in case N" + 1 = S" + 1 they converge to a "big S" ". To be precise, let g = {gij} and A = {hi j} be the induced metric and the second fundamental form on M and denote by H = giih~j, [A 12= h~Jh~j the mean curvature and the squared norm of the second fundamental form respectively.
75 citations
TL;DR: In this article, the most general N = 2 supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y7 were analyzed.
Abstract: We analyse the most general N = 2 supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y7. We show that the necessary and sufficient conditions for supersymmetry can be phrased interms of a local SU(2)-structure on Y7. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS4 × S 7 solution with non-trivial four-form flux.
75 citations
TL;DR: In this article, a non-minimal non-linear extension of the standard Einstein-Hilbert-Maxwell action is proposed to describe a spherically symmetric charged object.
Abstract: We establish a new self-consistent system of equations for the gravitational and electromagnetic fields. The procedure is based on a non-minimal non-linear extension of the standard Einstein-Hilbert-Maxwell action. General properties of a three-parameter family of non-minimal linear models are discussed. In addition, we show explicitly, that a static spherically symmetric charged object can be described by a non-minimal model, second order in the derivatives of the metric, when the susceptibility tensor is proportional to the double-dual Riemann tensor
74 citations