scholarly journals Kerr–Schild–Kundt metrics in generic gravity theories with modified Horndeski couplings

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade ◽  
Çetin Şentürk
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Scalar Fields ◽  
Vacuum Field ◽  
Field Equations ◽  
Complete Proof ◽  
Universality Theorem ◽  
Covariant Derivatives ◽  
Matter Fields ◽  
Insight Into

AbstractThe Kerr–Schild–Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the “universality theorem” to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of modified Horndeski theories with Maxwell’s field. We obtain exact solutions of these theories representing the pp-waves and AdS-plane waves in arbitrary D dimensions.

scholarly journals THE CAUCHY PROBLEM FOR f(R)-GRAVITY: AN OVERVIEW

2012 ◽  
Vol 09 (01) ◽  
pp. 1250006 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
S. VIGNOLO
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Field Equations ◽  
The Cauchy Problem ◽  
Theories Of Gravity ◽  
Matter Fields

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine formulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-formulation and the well-position of the problem. Finally, criteria of viability of the f(R)-models are considered according to the various matter fields acting as sources.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

Exact solutions of the field equations: twist-free pure radiation fields

1962 ◽  
Vol 270 (1342) ◽  
pp. 328-334 ◽  
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Radiation Field ◽  
Relativity Theory ◽  
Vacuum Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Null Congruence

This note is intended to give a rough survey of the results obtained in the study of twist-free pure radiation fields in general relativity theory. Here we are using the following Definition. A space-time ( V 4 of signature +2) is called a pure radiation field if it contains a distortion-free geodetic null congruence (a so-called ray congruence ), and if it satisfies certain field equations which we will specify below (e.g. Einstein’s vacuum-field equations). A (null) congruence is called twist-free if it is hypersurface-orthogonal (or ‘normal’). The results listed below were obtained by introducing special (‘canonical’) co-ordinates adapted to the ray congruence. Detailed proofs were given by Robinson & Trautman (1962) and by Jordan, Kundt & Ehlers (1961) (see also Kundt 1961). For the sake of completeness we include in our survey the subclass of expanding fields, and make use of some formulae first obtained by Robinson & Trautman.

scholarly journals Minimal coupling in presence of non-metricity and torsion

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Adrià Delhom
Keyword(s):  
Riemannian Space ◽  
Field Equations ◽  
Lagrange Equations ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Matter Fields

Abstract We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

Numerical relativity. II. Numerical methods for the characteristic initial value problem and the evolution of the vacuum field equations for space‒times with two Killing vectors

1983 ◽  
Vol 386 (1791) ◽  
pp. 373-391 ◽  
Keyword(s):  
General Relativity ◽  
Numerical Methods ◽  
Plane Wave ◽  
Numerical Solution ◽  
Initial Value Problem ◽  
Vacuum Field ◽  
Field Equations ◽  
Initial Value ◽  
Wave Space ◽  
Characteristic Initial Value Problem

This is the second of a sequence of papers on the numerical solution of the characteristic initial value problem in general relativity. Although the equations to be integrated have regular coefficients, the nonlinearity leads to the occurrence of singularities after a finite evolution time. In this paper we first discuss some novel techniques for integrating the equations right up to the singularities. The second half of the paper presents as examples the numerical evolution of the Schwarzschild and certain colliding plane wave space‒times.

scholarly journals Nonlocal gravity: Conformally flat spacetimes

2016 ◽  
Vol 13 (06) ◽  
pp. 1650081 ◽  
Author(s):  
Donato Bini ◽  
Bahram Mashhoon
Keyword(s):  
General Relativity ◽  
Killing Vector ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Nonlocal Field ◽  
Theory Of Gravitation ◽  
Flat Spacetimes ◽  
Conformally Flat Spacetimes ◽  
Insight Into

The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.

scholarly journals Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 142 ◽  
Author(s):  
Laur Järv ◽  
Manuel Hohmann ◽  
Martin Krššák ◽  
Christian Pfeifer
Keyword(s):  
General Relativity ◽  
Coordinate Transformation ◽  
Teleparallel Gravity ◽  
Analytic Solutions ◽  
Vacuum Field ◽  
Spin Connection ◽  
Flat Connection ◽  
Canonical Coordinates ◽  
Field Equations ◽  
Levi Civita Connection

Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.

The use of algebraic structures in physics

1961 ◽  
Vol 57 (4) ◽  
pp. 851-864 ◽  
Author(s):  
C. W. Kilmister ◽  
D. J. Newman
Keyword(s):  
General Relativity ◽  
Field Theories ◽  
Algebraic Structures ◽  
Field Equations ◽  
Maxwell Electrodynamics ◽  
Insight Into ◽  
Made In

ABSTRACTThe hypothesis of the existence of abstract structures in physics, which has been made in recent papers, is made precise. Difficulties in previous formulations are removed and insight into Maxwell electrodynamics is obtained. General relativity is related to other field theories which deal with flux from sources, and new field equations for general relativity are proposed.

scholarly journals An Approach to Colliding Plane Waves in General Relativity

2021 ◽  
Vol 9 (12) ◽  
pp. 981-988
Author(s):  
Dr. Shailendra Kumar Srivastava
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Vast Number ◽  
Gravitational Fields ◽  
Time Singularities ◽  
Linearized Theory ◽  
High Degree

Abstract: For many years after Einstein proposed his general theory of relativity, only a few exact solutions were known. Today the situation is completely different, and we now have a vast number of such solutions. However, very few are well understood in the sense that they can be clearly interpreted as the fields of real physical sources. The obvious exceptions are the Schwarzschild and Kerr solutions. These have been very thoroughly analysed, and clearly describe the gravitational fields surrounding static and rotating black holes respectively. In practice, one of the great difficulties of relating the particular features of general relativity to real physical problems, arises from the high degree of non-linearity of the field equations. Although the linearized theory has been used in some applications, its use is severely limited. Many of the most interesting properties of space-time, such as the occurrence of singularities, are consequences of the non-linearity of the equations. Keywords: General Relativity , Space-Time, Singularities, Non-linearity of the Equations.

Sign in / Sign up

Export Citation Format

Share Document