Quartic equations and algorithms for riemann tensor classification

2005 ◽  
pp. 47-58 ◽  
Author(s):  
J. E. Åman ◽  
R. A. d'Inverno ◽  
G. C. Joly ◽  
M. A. H. MacCallum
Keyword(s):  
Riemann Tensor

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

Spacetimes in which the Ricci equations characterize the Riemann tensor

1993 ◽  
Vol 32 (1) ◽  
pp. 121-135 ◽  
Author(s):  
S. Brian Edgar
Keyword(s):  
Riemann Tensor

Sets of Vectors in a V 4 Defined by the Riemann Tensor

1944 ◽  
Vol 19 (75_Part_3) ◽  
pp. 168-178 ◽  
Author(s):  
H. S. Ruse
Keyword(s):  
Riemann Tensor

scholarly journals Riemann tensor of the ambient universe, the dilaton, and Newton’s constant

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
Rossen I. Ivanov ◽  
Emil M. Prodanov
Keyword(s):  
Riemann Tensor

On the problem of algebraic completeness for the invariants of the Riemann tensor. II

2002 ◽  
Vol 43 (1) ◽  
pp. 492-507 ◽  
Author(s):  
J. Carminati ◽  
E. Zakhary ◽  
R. G. McLenaghan
Keyword(s):  
Riemann Tensor

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

A spatially homogeneous gravitational field

1966 ◽  
Vol 62 (1) ◽  
pp. 87-89 ◽  
Author(s):  
V. Joseph
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Riemann Tensor ◽  
Vacuum Field ◽  
Type I ◽  
Field Equations ◽  
Parameter Group ◽  
Spatially Homogeneous ◽  
Homogeneous Gravitational Field ◽  
Type V

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

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