Scale invariance and the energy–momentum tensor

1970 ◽  
Vol 48 (20) ◽  
pp. 2371-2375
Author(s):  
Peter Bendix
Keyword(s):  
Gravitational Field ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Scale Invariant ◽  
New Energy ◽  
Klein Gordon

A method is described by which an energy–momentum tensor can be constructed such that in addition to the usual properties of this tensor it acquires the property of scale invariance in the absence of masses and charges. (The new energy–momentum tensor constructed here is not the source of the gravitational field, however.) It is shown that the usual construction for the massless Klein–Gordon field yields an energy–momentum tensor which is not scale invariant, whereas using the construction described here, one finds a scale invariant energy–momentum tensor for this case.

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 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.

scholarly journals Klein Gordon Field in FLRW Space-Time

2020 ◽  
Vol 13 (13) ◽  
pp. 1-4
Author(s):  
S.K. Sharma ◽  
P.R. Dhungel ◽  
U. Khanal
Keyword(s):  
Spherical Harmonics ◽  
Energy Momentum Tensor ◽  
Equation Of Motion ◽  
Momentum Tensor ◽  
Space Time ◽  
Wkb Approximation ◽  
Temporal Parts ◽  
Klein Gordon ◽  
Current Energy ◽  
Particle Current

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

scholarly journals INTRINSIC AMBIGUITY IN SECOND-ORDER VISCOSITY PARAMETERS IN RELATIVISTIC HYDRODYNAMICS

2012 ◽  
Vol 27 (22) ◽  
pp. 1250125 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Minkowski Space ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Second Order ◽  
Relativistic Hydrodynamics ◽  
Conformal Invariant ◽  
Scale Invariant ◽  
Minkowski Space Time

We show that relativistic hydrodynamics in Minkowski space–time has intrinsic ambiguity in second-order viscosity parameters in the Landau–Lifshitz frame. This stems from the possibility of improvements of energy–momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly nonconformal hydrodynamic theories can be hiddenly conformal invariant.

SCALE AND CONFORMAL INVARIANCE AND VARIATION OF THE METRIC

2006 ◽  
Vol 21 (17) ◽  
pp. 3641-3647 ◽  
Author(s):  
J. SADEGHI ◽  
A. TOFIGHI ◽  
A. BANIJAMALI
Keyword(s):  
Conformal Invariance ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conserved Currents

We consider the relation between scale invariance and conformal invariance. In our analysis the variation of the metric is taken into account. By imposing some conditions on the trace of the energy–momentum tensor and on the variation of the action, we find that the scale dimensions of the fields are not affected. We also obtain the conserved currents. We find that the conditions for conformal invariance are stronger than for scale invariance.

scholarly journals Unification of Gravity and Electromagnetism

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Mathematical Structure ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Field Equations ◽  
Mathematical Structures ◽  
Gravitational Field Equations ◽  
Definition Of ◽  
Two Sides

Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are representing by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure. Symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian

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