scholarly journals Stochastic gravity and turbulence

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sebastian Waeber ◽  
Amos Yarom
Keyword(s):  
Power Spectrum ◽  
Energy Momentum Tensor ◽  
Boundary Behavior ◽  
Stochastic Theory ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Boundary Theory ◽  
Relativistic Energy ◽  
Expectation Value ◽  
Stochastic Gravity

Abstract We study the ensemble average of the thermal expectation value of an energy momentum tensor in the presence of a random external metric. In a holographic setup this quantity can be read off of the near boundary behavior of the metric in a stochastic theory of gravity. By numerically solving the associated Einstein equations and mapping the result to the dual boundary theory, we find that the non relativistic energy power spectrum exhibits a power law behavior as expected by the theory of Kolmogorov and Kraichnan.

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.

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.

scholarly journals Gravitational energy in the framework of embedding and splitting theories

2018 ◽  
Vol 27 (02) ◽  
pp. 1750188 ◽  
Author(s):  
D. A. Grad ◽  
R. V. Ilin ◽  
S. A. Paston ◽  
A. A. Sheykin
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gravitational Energy ◽  
Einstein Equations ◽  
Field Energy ◽  
Energy Localization ◽  
Embedding Theory ◽  
Isometric Embeddings ◽  
Definition Of ◽  
Noether Current

We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge–Teitelboim approach. For the embedding theory, we consider the coordinate translations on the surface as well as the coordinate translations in the flat bulk. In the latter case, the independent definition of gravitational energy–momentum tensor appears as a Noether current corresponding to global inner symmetry. In the field-theoretic form of this approach (splitting theory), we consider Noether procedure and the alternative method of energy–momentum tensor defining by varying the action of the theory with respect to flat bulk metric. As a result, we obtain energy definition in field-theoretic form of embedding theory which, among the other features, gives a nontrivial result for the solutions of embedding theory which are also solutions of Einstein equations. The question of energy localization is also discussed.

scholarly journals Inverse problem: What can we tell about the matter and energy in our Universe from its dimensionality and evolution

2018 ◽  
Vol 27 (07) ◽  
pp. 1841005
Author(s):  
Hanna Makaruk ◽  
James Langenbrunner
Keyword(s):  
Energy Momentum Tensor ◽  
Physical Space ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Time Dimension ◽  
Superstring Theory ◽  
Anisotropic Energy ◽  
The One ◽  
Multidimensional Models ◽  
Additional Space

The most popular theories of everything are various versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in [Formula: see text] space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and [Formula: see text]-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of [Formula: see text]-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.

The relativistic energy-momentum tensor in polarized media

Physica ◽  
1967 ◽  
Vol 37 (2) ◽  
pp. 297-308 ◽  
Author(s):  
S.R. De Groot ◽  
L.G. Suttorp
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Relativistic Energy

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.

BRS ANALYSIS OF THE ENERGY MOMENTUM TENSOR IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (18) ◽  
pp. 1679-1684
Author(s):  
W. S. L'YI ◽  
YOUNG-JAI PARK ◽  
KEE YONG KIM ◽  
YONGDUK KIM
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Majorana Fermion ◽  
Two Dimensional ◽  
Expectation Value ◽  
Dimensional Gravity

Majorana fermion coupled to a 2-dimensional background gravitational field is investigated by employing the BRS quantization technique. Upon introduction of a quasicon-formal map ζ determined by the Beltrami differential h, the background gravitational field amazingly disappeared leaving just the free Majorana field ψ and ghosts b, c. In this way the vacuum expectation value of the energy-momentum tensor under the background gravitational field is explicitly computed.

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.

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