Topic

# Einstein tensor

About: Einstein tensor is a research topic. Over the lifetime, 2191 publications have been published within this topic receiving 53792 citations. The topic is also known as: Einstein curvature & Einstein curvature tensor.

##### Papers published on a yearly basis

##### Papers

More filters

•

[...]

TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.

Abstract: A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

3,502 citations

••

[...]

TL;DR: In this paper, the number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.

Abstract: The Einstein tensorGij is symmetric, divergence free, and a concomitant of the metric tensorgab together with its first two derivatives. In this paper all tensors of valency two with these properties are displayed explicitly. The number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.

2,450 citations

••

[...]

TL;DR: In this paper, the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space is computed, and the conformal anomalies in two and four dimensions are recovered.

Abstract: We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS5, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S
3×R.

2,220 citations

••

[...]

TL;DR: In this article, it was shown that a static, spherically symmetric gravitational field is given by the Schwarzschild metric, and that in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons.

Abstract: A gravitational theory is formulated on the Weitzenb\"ock space-time, characterized by the vanishing curvature tensor (absolute parallelism) and by the torsion tensor formed of four parallel vector fields. This theory is called new general relativity, since Einstein in 1928 first gave its original form. New general relativity has three parameters ${c}_{1}$, ${c}_{2}$, and $\ensuremath{\lambda}$, besides the Einstein constant $\ensuremath{\kappa}$. In this paper we choose ${c}_{1}=0={c}_{2}$, leaving open $\ensuremath{\lambda}$. We prove, among other things, that (i) a static, spherically symmetric gravitational field is given by the Schwarzschild metric, that (ii) in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons, and that (iii) new general relativity agrees with all the experiments so far carried out.

948 citations