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 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 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.

scholarly journals Revised theory of tachyons in general relativity

2017 ◽  
Vol 32 (24) ◽  
pp. 1750126 ◽  
Author(s):  
Charles Schwartz
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Good Reason ◽  
Momentum Tensor ◽  
Minus Sign

A minus sign is inserted, for good reason, into the formula for the energy–momentum tensor for tachyons. This leads to remarkable theoretical consequences and a plausible explanation for the phenomenon called dark energy in the cosmos.

scholarly journals Field Equations in C4 Space-Time

2018 ◽  
Author(s):  
Dimitris Mastoridis ◽  
K. Kalogirou
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Complex Space ◽  
Energy Momentum Tensor ◽  
Real Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Field Equations ◽  
Geometric Information

We explore the field equations in a 4-d complex space-time, in the same way, that general relativity does for our usual 4-d real space-time, forming this way, a new "general  relativity" in C4 space-time, free of sources. Afterwards, by embedding our usual 4-d real space-time in C4 space-time, we describe  geometrically the energy-momentum tensor Tμν as the lost geometric information of this embedding. We further give possible explanation of dark eld and dark energy.

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 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 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 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.

Gravitational collapse of interacting combination of dark matter and dark energy in the context of brane world regime

2018 ◽  
Vol 33 (23) ◽  
pp. 1850132 ◽  
Author(s):  
Hasrat Hussain Shah ◽  
Farook Rahaman
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Gravitational Collapse ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Brane World ◽  
Anisotropic Pressure ◽  
Isotropic Pressure ◽  
Polytropic Equation ◽  
De Formula

In the scenario of an optimal consideration that is, homogeneous and flat spacetime, we study the Black Hole (BH) formation from the gravitational collapse of a spherical symmetric clump of matter in the case of the specific Dark Matter (DM) model interacting with Dark Energy (DE) in the context of the brane world regime. This clump of matter constituted of DM, [Formula: see text] and DE, [Formula: see text]. In the present model, we consider anisotropic pressure in the energy–momentum tensor with a polytropic equation of state (EoS), [Formula: see text] and [Formula: see text], [Formula: see text]. Our results show that the gravitational collapse of an interacting combination of DM and DE leads to the formation of BH in the presence of brane tension. Recent work provides the generalization of isotropic pressure to an-isotropic pressure in the energy–momentum tensor for the specific interacting combination model of DM and DE in a brane world regime.

Various dark energy models for variables G and Λ in f(R, T) modified theory

2019 ◽  
Vol 34 (13) ◽  
pp. 1950098 ◽  
Author(s):  
Can Aktaş
Keyword(s):  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Tachyon Field ◽  
Field Equations ◽  
Frw Universe ◽  
Linearly Varying Deceleration Parameter ◽  
Energy Models ◽  
Modified Theory ◽  
Friedmann Robertson Walker

In this paper, we have researched tachyon field, k-essence and quintessence dark energy (DE) models for Friedmann–Robertson–Walker (FRW) universe with varying G and [Formula: see text] in f(R, T) gravitation theory. The theory of f(R, T) is proposed by Harko et al. [Phys. Rev. D 84, 024020, 2011]. In this theory, R is the Ricci scalar and T is the trace of energy–momentum tensor. For the solutions of field equations, we have used linearly varying deceleration parameter (LVDP), the equation of state (EoS) and the ratio between [Formula: see text] and Hubble parameter. Also, we have discussed some physical behavior of the models with various graphics.

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