scholarly journals Nonconservative Unimodular Gravity: Gravitational Waves

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 87
Author(s):  
Júlio C. Fabris ◽  
Marcelo H. Alvarenga ◽  
Mahamadou Hamani Daouda ◽  
Hermano Velten
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Extra Condition ◽  
Symmetry Properties ◽  
The Standard Model ◽  
The Universe

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.

scholarly journals RECONSTRUCTING f(R, T) GRAVITY FROM HOLOGRAPHIC DARK ENERGY

2012 ◽  
Vol 21 (03) ◽  
pp. 1250024 ◽  
Author(s):  
M. J. S. HOUNDJO ◽  
OLIVER F. PIATTELLA
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Holographic Dark Energy ◽  
Momentum Tensor ◽  
Ricci Scalar ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Theories Of Gravity

We consider cosmological scenarios based on f(R, T) theories of gravity (R is the Ricci scalar and T is the trace of the energy–momentum tensor) and numerically reconstruct the function f(R, T) which is able to reproduce the same expansion history generated, in the standard General Relativity theory, by dark matter and holographic dark energy. We consider two special f(R, T) models: in the first instance, we investigate the modification R + 2f(T), i.e. the usual Einstein–Hilbert term plus a f(T) correction. In the second instance, we consider a f(R) + λT theory, i.e. a T correction to the renown f(R) theory of gravity.

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.

Evolution of the Universe with two rotating fluids

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040042
Author(s):  
V. F. Panov ◽  
O. V. Sandakova ◽  
E. V. Kuvshinova ◽  
D. M. Yanishevsky
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Scalar Field ◽  
Bianchi Type ◽  
Relativity Theory ◽  
Anisotropic Fluid ◽  
Rotating Fluids ◽  
General Relativity Theory ◽  
Exponential Expansion ◽  
The Universe

An anisotropic cosmological model with expansion and rotation and the Bianchi type IX metric has been constructed within the framework of general relativity theory. The first inflation stage of the Universe filled with a scalar field and an anisotropic fluid is considered. The model describes the Friedman stage of cosmological evolution with subsequent transition to accelerated exponential expansion observed in the present epoch. The model has two rotating fluids: the anisotropic fluid and dust-like fluid. In the approach realized in the model, the anisotropic fluid describes the rotating dark energy.

scholarly journals On Hilbert's world-function

1927 ◽  
Vol 113 (765) ◽  
pp. 496-511 ◽  
Keyword(s):  
Dynamical System ◽  
General Relativity ◽  
Minimum Principle ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Least Action ◽  
Principle Of Least Action ◽  
The Universe ◽  
World Function

The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx 0 dx 1 dx 2 dx 3 where ( x 0 , x 1 , x 2 , x 3 ) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials g v q , which specify the metric by means of the equation dx 2 = ∑ p, q g vq dx v dx q . In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the g vq 's and in the electromagnetic potentials, regarded as functions of x 0 , x 1 , x 2 , x 3 .

scholarly journals Gravitational Waves from Compact Bodies

1996 ◽  
Vol 165 ◽  
pp. 153-183
Author(s):  
Kip S. Thorne
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Neutron Stars ◽  
Gravitational Radiation ◽  
Relativity Theory ◽  
Energy Concentration ◽  
Speed Of Light ◽  
General Relativity Theory ◽  
Concentration Changes ◽  
The Universe

According to general relativity theory, compact concentrations of energy (e.g., neutron stars and black holes) should warp spacetime strongly, and whenever such an energy concentration changes shape, it should create a dynamically changing spacetime warpage that propagates out through the Universe at the speed of light. This propagating warpage is called gravitational radiation — a name that arises from general relativity's description of gravity as a consequence of spacetime warpage.

Gravitational waves and the radiative field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Gravitational Waves ◽  
Radiation Field ◽  
Gravitational Radiation ◽  
Gravitational Force ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Maxwell Theory

This chapter turns to the gravitational radiation produced by a system of massive objects. The discussion is confined to the linear approximation of general relativity, which is compared with the Maxwell theory of electromagnetism. In the first part of the chapter, the properties of gravitational waves, which are the general solution of the linearized vacuum Einstein equations, are studied. Next, it relates these waves to the energy–momentum tensor of the sources creating them. The chapter then turns to the ‘first quadrupole formula’, giving the gravitational radiation field of these sources when their motion is due to forces other than the gravitational force.

scholarly journals THE ROBERTSON–WALKER METRIC IN A PSEUDO-COMPLEX GENERAL RELATIVITY

2010 ◽  
Vol 19 (07) ◽  
pp. 1315-1339 ◽  
Author(s):  
PETER O. HESS ◽  
LEILA MAGHLAOUI ◽  
WALTER GREINER
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Walker Metric ◽  
The Universe ◽  
Complex General Relativity

We investigate the consequences of the pseudo-complex General Relativity within a pseudo-complexified Robertson–Walker metric. A contribution to the energy–momentum tensor arises, which corresponds to a dark energy and may change with the radius of the universe, i.e., time. Only when the Hubble function H does not change in time, the solution is consistent with a constant Λ.

scholarly journals Incompleteness of General Relativity Regarding Einstein's Program

2018 ◽  
Vol 10 (5) ◽  
pp. 47
Author(s):  
Claude Elbaz
Keyword(s):  
General Relativity ◽  
Momentum Conservation ◽  
Matter Field ◽  
Relativity Theory ◽  
Speed Of Light ◽  
General Relativity Theory ◽  
Least Action ◽  
Electromagnetic Interactions ◽  
The Standard Model ◽  
Classical And Quantum Mechanics

The detection of gravitational waves substantiates the undeniable achievement of general relativity theory by increasing its theoretical and experimental accuracy. One century after predicting it has set again Einstein's works at the front of research. Absence of quantum particle associated to gravitation emphasizes that general relativity theory remains not included in the standard model of physics. Then Einstein’s disagreement about it incompleteness regarding wave-particle and matter-field becomes actualized. In order to circumvent these difficulties he privileged field, rather than matter for universe description in his program. In consequence a scalar field e(r0,t0) propagating at speed of light c yields matter from standing waves moving at speed strictly inferior to c, and interactions from progressive waves. Electromagnetic interactions derive from local variations of frequencies, and gravitation from local variations of speed of light. A space-like amplitude functions u0(k0r0) supplements fundamental time-like functions of classical and quantum mechanics. It tends toward Dirac’s distribution Delta (r0) in geometrical optics approximation conditions, when frequencies are infinitely high, and then hidden. More generally, it allows theoretical economies by deriving energy-momentum conservation laws, and least action law. Quantum domain corresponds to wave optics approximation conditions. Variations of frequencies give rise to an adiabatic constant, formally identical with Planck's constant, leading to first quantification for electromagnetic interactions and to second quantification for matter.

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