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 Pseudo-Complex General Relativity

2017 ◽  
Vol 45 ◽  
pp. 1760002 ◽  
Author(s):  
Peter O. Hess
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Accretion Disks ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Minimal Length ◽  
Einstein Equations ◽  
Vacuum Fluctuations ◽  
The Right ◽  
Complex General Relativity

The present status of the pseudo-complex General Relativity is presented. The pcGR includes many known theories with a minimal length. Restricting to its simplest form, an energy-momentum tensor is added at the right hand side of the Einstein equations, representing a dark energy, related to vacuum fluctuations. We use a phenomenological ansatz for the density and discuss observable consequences: Quaisperiodic Oscillations (QPO), effects on accretion disks and gravitational waves.

scholarly journals Tractor Beams, Pressor Beams and Stressor Beams in General Relativity

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 271
Author(s):  
Jessica Santiago ◽  
Sebastian Schuster ◽  
Matt Visser
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Frequent Use ◽  
Advanced Civilization

The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these into the Einstein equations. This latter approach has found frequent use when confronted with creative input from fiction, wormholes and warp drives being the most famous examples. In this paper, we again take inspiration from fiction and see what general relativity can tell us about the possibility of a gravitationally induced tractor beam. We base our construction on warp drives and show how versatile this ansatz alone proves to be. Not only can we easily find tractor beams (attracting objects), but repulsor/pressor beams are just as attainable, and a generalization to “stressor” beams is seen to present itself quite naturally. We show that all of these metrics would violate various energy conditions. This provides an opportunity to ruminate on the meaning of energy conditions as such and what we can learn about whether an arbitrarily advanced civilization might have access to such beams.

Gravitational radiation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Linear Approximation ◽  
Gravitational Radiation ◽  
A Priori ◽  
Einstein Equations ◽  
Maxwell Theory ◽  
Radiated Energy ◽  
Gravitational Analog ◽  
Gravitating Systems ◽  
Quadratic Order

This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitating systems, the Einstein equations to quadratic order must be solved, and the radiative field in the post-linear approximation of general relativity obtained.

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.

The Einstein pseudo-tensor and the flux integral for perturbed static space-times

1991 ◽  
Vol 435 (1895) ◽  
pp. 645-657 ◽  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Second Variation ◽  
Common Procedure ◽  
Static Vacuum ◽  
Linear Perturbations ◽  
Maxwell Space ◽  
The Common ◽  
Static Space

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

Do electromagnetic waves harbour gravitational waves?

2006 ◽  
Vol 462 (2071) ◽  
pp. 1987-2000 ◽  
Author(s):  
Brian Bramson
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electric Dipole ◽  
Electromagnetic Waves ◽  
Maxwell Theory ◽  
Flat Spacetime

In linearized, Einstein–Maxwell theory on flat spacetime, an oscillating electric dipole is the source of a spin-2 field. Within this approximation to general relativity, it is shown that electromagnetic waves harbour gravitational waves.

scholarly journals Semi-Classical Einstein Equations: Descend to the Ground State

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 74
Author(s):  
Zbigniew Haba
Keyword(s):  
Ground State ◽  
Energy Momentum Tensor ◽  
Local Maximum ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Thermal Dissipation ◽  
Stationary Probability Distribution ◽  
Expectation Value ◽  
Warm Inflation ◽  
The Right

The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the right hand side of Einstein equations in various (approximate) quantum pure as well as mixed states. We apply the classical slow-roll field evolution as well as the Starobinsky and warm inflation stochastic equations in order to calculate the expectation value. We show that, in the state concentrated at the local maximum of the double-well potential, the expectation value is decreasing exponentially. We confirm the descent of the expectation value in the stochastic inflation model. We calculate the cosmological constant Λ at large time as the expectation value of the energy density with respect to the stationary probability distribution. We show that Λ ≃ γ 4 3 where γ is the thermal dissipation rate.

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