scholarly journals The Wave-Front Equation of Gravitational Signals in Classical General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 216
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Wave Front ◽  
Value Theory ◽  
Space Time ◽  
Classical General Relativity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Wave Fronts ◽  
Curved Space

In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015–2019). The Hamilton–Jacobi equation obtained in this way yields a wave-front description of gravitational field dynamics. It is shown that on a suitable subset of configuration space the latter equation reduces to a Klein–Gordon type equation associated with a 4-scalar field which identifies the wave-front surface of a gravitational signal. Its physical role and mathematical interpretation are discussed. Radiation-field wave-front solutions are pointed out, proving that according to this description, gravitational wave-fronts propagate in a given background space-time as waves characterized by the invariant speed-of-light c. The outcome is independent of the actual shape of the same wave-fronts and includes the case of gravitational waves which are characterized by an eikonal representation and propagate in a generic curved space-time along a null geodetics. The same waves are shown: (a) to correspond to the geometric-optics limit of the same curved space-time solutions; (b) to propagate in a flat space-time as plane waves with constant amplitude; (c) to display also the corresponding form of the wave-front in curved space-time. The result is consistent with the theory of the linearized Einstein field equations and the existence of gravitational waves achieved in such an asymptotic regime. Consistency with the non-linear Trautman boundary-value theory is also displayed.

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

scholarly journals Gravitational waves — A review on the theoretical foundations of gravitational radiation

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1830013 ◽  
Author(s):  
Alain Dirkes
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Wave Zone ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiative Losses ◽  
Zone Field ◽  
Theoretical Foundations

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

scholarly journals ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

2007 ◽  
Vol 22 (10) ◽  
pp. 1935-1951 ◽  
Author(s):  
M. SHARIF ◽  
M. AZAM
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Momentum Distribution ◽  
Special Class ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Degenerate Solution ◽  
Dust Solution

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

Weyl static axially symmetric field equations in modified f(T) gravity

2017 ◽  
Vol 14 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Saeed Nayeh ◽  
Mehrdad Ghominejad
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Radial Component ◽  
Momentum Tensor ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Torsion Scalar

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

scholarly journals Proposal for a New Quantum Theory of Gravity

2019 ◽  
Vol 74 (7) ◽  
pp. 617-633 ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Noncommutative Geometry ◽  
Measurement Problem ◽  
Black Hole Entropy ◽  
Space Time ◽  
Classical General Relativity ◽  
Field Equations ◽  
Symmetry Principle ◽  
Theory Of Gravity

AbstractWe recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

scholarly journals From Micro Gravitational Waves to the Quantum Indeterminism

2015 ◽  
Vol 25 (3) ◽  
pp. 247
Author(s):  
Vo Van Thuan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Waves ◽  
Space Time ◽  
Quantum Mechanical ◽  
Curved Space ◽  
Time Symmetry ◽  
Extended Space

An attempt to search for the links b etween general relativity and quantum mechanics is prop osed which bases on an extended space-time symmetry. A simplified cylindrical mo del of gravitational geometrical dynamics leads to a micro geo desic description of strongly curved space-time which implies a duality b etween quantum mechanical equations and the emission law of a sp ecific mo de of micro gravitational waves.

scholarly journals Massive Gravitons in General Relativity

1997 ◽  
Vol 50 (5) ◽  
pp. 879 ◽  
Author(s):  
John Argyris ◽  
Corneliu Ciubotariu
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Lagrangian Density ◽  
Rest Mass ◽  
Mass Term ◽  
Space Time ◽  
Fundamental Constants ◽  
Conformally Flat ◽  
Light Velocity ◽  
Curved Space

In the framework of a generalisation of linear gravitation to the case when the gravitons have nonzero rest mass, we obtain a result analogous to that obtained by Regge and Wheeler, that is, the energy of the gravitational waves is trapped in the ‘material’ (interior) metric of the curved space–time. We show that the concept of a nonzero rest mass graviton may be defined in two ways: (i) phenomenologically, by introducing of a mass term in the linear Lagrangian density, as in Proca electrodynamics, and (ii) self-consistently, by solving Einstein’s equations in the conformally flat case. We find that the rest mass of the graviton may be given in terms of the three fundamental constants (gravitational, Planck, and light velocity constants) and it is a function of the density of cosmic matter.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Wave Fronts in a Causality-Violating Gödel-Type Metric

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Thomas P. Kling ◽  
Faizuddin Ahmed ◽  
Megan Lalumiere
Keyword(s):  
Wave Front ◽  
Space Time ◽  
Wave Fronts ◽  
Light Rays ◽  
Synchronized Clocks

The light rays and wave fronts in a linear class of the Gödel-type metric are examined to reveal the causality-violating features of the space-time. Noncausal features demonstrated by the development of unusual wave front singularities are shown to be related to the nonmonotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

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