scholarly journals A complementary covariant approach to gravito-electromagnetism

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Sergio Giardino
Keyword(s):  
General Relativity ◽  
Continuity Equation ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Lagrangian Formulation ◽  
Field Tensor ◽  
Simple Formulation ◽  
Covariant Approach

From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor equations of motion, the gravitational continuity equation, the conservation of the energy, the energy-momentum tensor, the field tensor, and the constraints concerning these fields. The Lagrangian formulation is also exhibited as an unified and simple formulation that will be useful for future investigation.

scholarly journals The Motion of Spinless Particles in General Relativity

1978 ◽  
Vol 31 (1) ◽  
pp. 105
Author(s):  
LJ Gregory ◽  
AH Klotz
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Geodesic Equations ◽  
General Energy

A technique is developed, which uses a general energy-momentum tensor, to derive the equations of motion in general relativity. This enables the geodesic equations for spinless particles to be deduced.

Primordial quantum perturbations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Slow Roll ◽  
Inflationary Models

This chapter shows that fluctuations of quantum origin are generated during inflation and that this process supplies initial conditions compatible with the observations. These fluctuations are therefore an important prediction of inflationary models. The chapter thus begins with a study of perturbations during inflation, proceeding in a similar manner to the previous chapter by finding the perturbation of the energy–momentum tensor of the scalar field. Another method of deriving the equations of motion of the perturbations is to start from the action of general relativity coupled to a scalar field, and expand to second order in the metric and scalar field perturbations. The chapter then proceeds with the determination of the initial conditions and the slow-roll inflation.

scholarly journals Spinning bodies in general relativity

2016 ◽  
Vol 13 (08) ◽  
pp. 1640002 ◽  
Author(s):  
J. W. van Holten
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Curved Space ◽  
Constants Of Motion ◽  
Spinning Bodies ◽  
Compact Spinning ◽  
Independent Derivation

A covariant Hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of Hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal Hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy–momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.

The foundations of a generalization of gravitation theory

1957 ◽  
Vol 53 (2) ◽  
pp. 473-488 ◽  
Author(s):  
John Moffat
Keyword(s):  
Electromagnetic Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Original Form ◽  
Geometric Description ◽  
Field Equations ◽  
Electrically Charged

1. Introduction. Among the more notable attempts to derive a generalization of Einstein's gravitational theory is the recent one of Einstein and Schrodinger ((1)–(8)). This was formulated by dropping the symmetry of the fundamental tensor gμν and the components of the affine connexion. The most serious defect of these non-symmetric theories is that the field equations, in their original form, do not determine the motion of electrically charged particles in an electromagnetic field, as has been proved by Infeld(9), Callaway (10) and Bonnor (n). Together with the lack of an energy-momentum tensor and a geometric description of the paths of charged particles, this seems to indicate that the concept of motion is missing in this type of theory. It is clear that one of the most important results which should follow from a generalization of Einstein's gravitational theory is the correct equations of motion of charged particles in an electromagnetic field.

scholarly journals Particle paths of general relativity as geodesics of an affine connection

1970 ◽  
Vol 3 (3) ◽  
pp. 325-335 ◽  
Author(s):  
R. Burman
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Affine Connection ◽  
Momentum Tensor ◽  
Field Equations ◽  
Test Particles ◽  
Special Cases ◽  
Particle Paths ◽  
Arbitrary Energy

This paper deals with the motion of incoherent matter, and hence of test particles, in the presence of fields with an arbitrary energy-momentum tensor. The equations of motion are obtained from Einstein's field equations and are written in the form of geodesic equations of an affine connection. The special cases of the electromagnetic field, the Proca field and a scalar field are discussed.

The Coordinate Conditions and the Equations of Motion

1953 ◽  
Vol 5 ◽  
pp. 17-25 ◽  
Author(s):  
L. Infeld
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Coordinate Conditions

The problem of the field equations and the equations of motion in general relativity theory is now sufficiently clarified. The equations of motion can be deduced from pure field equations by treating matter as singularities, [2; 3], or from field equations with the energy momentum tensor [4]. Recently two papers appeared in which the problem of the coordinate system was considered [5; 8]. The two papers are in general agreement as far as the role of the coordinate system is concerned. Yet there are some differences which require clarification.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

scholarly journals Gödel and Gödel-type solutions in the Palatini f(R,T) gravity theory

2020 ◽  
pp. 2150014
Author(s):  
J. S. Gonçalves ◽  
A. F. Santos
Keyword(s):  
Trace Formula ◽  
Arbitrary Function ◽  
Critical Radius ◽  
Energy Momentum Tensor ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Gravity Theory ◽  
Ricci Scalar ◽  
Independent Variables ◽  
Hilbert Action

The Palatini [Formula: see text] gravity theory is considered. The standard Einstein–Hilbert action is replaced by an arbitrary function of the Ricci scalar [Formula: see text] and of the trace [Formula: see text] of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independent variables. Then, it is examined whether Palatini [Formula: see text] gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type spacetimes are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, noncausal solutions can be avoided in this Palatini gravitational theory.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

UNUSUAL HYDRODYNAMICS

1987 ◽  
Vol 02 (05) ◽  
pp. 1591-1615 ◽  
Author(s):  
V.A. BEREZIN
Keyword(s):  
Black Hole ◽  
Cosmological Model ◽  
Production Process ◽  
Particle Production ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Point Of View ◽  
Modified Equations ◽  
Nonsingular Cosmological Model

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

Sign in / Sign up

Export Citation Format

Share Document