scholarly journals CAUSAL ANOMALIES IN KALUZA–KLEIN GRAVITY THEORIES

1998 ◽  
Vol 13 (18) ◽  
pp. 3181-3191 ◽  
Author(s):  
M. J. REBOUÇAS ◽  
A. F. F. TEIXEIRA
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Momentum Tensor ◽  
Causality Principle ◽  
Field Equations ◽  
Perfect Fluid Solution ◽  
Dust Solution ◽  
Gravity Theories ◽  
Induced Matter ◽  
Kaluza Klein

Causal anomalies in two Kaluza–Klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. It is found that similarly to general relativity the field equations of the space–time–mass Kaluza–Klein (STM-KK) gravity theory do not exclude violation of causality of Gödel type, whereas the induced matter Kaluza–Klein (IM-KK) gravity rules out noncausal Gödel-type models. The induced matter version of general relativity is shown to be an efficient therapy for causal anomalies that occurs in a wide class of noncausal geometries. Perfect fluid and dust Gödel-type solutions of the STM-KK field equations are studied. It is shown that every Gödel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5D Gödel-type noncausal geometries induce any physically acceptable 4D energy–momentum tensor is also addressed.

scholarly journals FLRW-cosmology in generic gravity theories

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade
Keyword(s):  
Perfect Fluid ◽  
Gravity Theory ◽  
Fluid Type ◽  
Field Equations ◽  
Walker Metric ◽  
Flrw Cosmology ◽  
Arbitrary Dimensions ◽  
Gravity Theories

AbstractWe prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$ F ( R , G ) theories are given as examples.

scholarly journals Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Sanjay Oli
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Space Time ◽  
Time Dependent ◽  
Field Equations ◽  
Current Observation ◽  
Kinematical Parameters ◽  
Kaluza Klein

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

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 Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

Least Action and Classical Fields

2021 ◽  
pp. 286-325
Author(s):  
Moataz H. Emam
Keyword(s):  
General Relativity ◽  
Momentum Tensor ◽  
Point Particle ◽  
Kerr Metric ◽  
Field Equations ◽  
Tensor Fields ◽  
Particle Mechanics ◽  
Least Action ◽  
Principle Of Least Action ◽  
Maxwell Fields

We present the principle of least action and see how it is used in non-relativistic point particle mechanics, relativistic point particle mechanics, general relativity, derivation of field equations for scalar, vector and tensor fields as well as the energy momentum tensor. Towards the end we present examples of solutions of Einstein-Maxwell fields: The Reissner-Nordstrom metric, Kerr metric, and Kerr- Newman metric.

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.

FIELD EQUATIONS FOR SPACE–TIME–MATTER THEORY

2013 ◽  
Vol 10 (09) ◽  
pp. 1350038
Author(s):  
AUREL BEJANCU
Keyword(s):  
Tensor Field ◽  
Momentum Tensor ◽  
Brane World ◽  
Field Equations ◽  
Tensor Fields ◽  
Full Generality ◽  
Matter Theory ◽  
Warp Function ◽  
Brane Theory ◽  
Kaluza Klein

In the present paper we obtain, in a covariant form, and in their full generality, the field equations in a relativistic general Kaluza–Klein space. This is done by using the Riemannian horizontal connection defined in [3], and some 4D horizontal tensor fields, as for instance: horizontal Ricci tensor, horizontal Einstein gravitational tensor field, horizontal electromagnetic energy–momentum tensor field, etc. Also, we present some inter-relations between STM theory and brane-world theory. This enables us to introduce in brane theory some electromagnetic potentials constructed by means of the warp function.

scholarly journals Blackhole in nonlocal gravity: comparing metric from Newmann–Janis algorithm with slowly rotating solution

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Utkarsh Kumar ◽  
Sukanta Panda ◽  
Avani Patel
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Modified Gravity ◽  
Kerr Metric ◽  
Slow Rotation ◽  
Field Equations ◽  
External Region ◽  
Modified Gravity Theories ◽  
Spacetime Metric ◽  
Gravity Theories

Abstract The strong gravitational field near massive blackhole is an interesting regime to test General Relativity (GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving field equations for rotating blackhole is extremely challenging task for the most modified gravity theories. Though the derivation of Kerr metric of GR is also demanding job, the magical Newmann–Janis algorithm does it without actually solving Einstein equation for rotating blackhole. Due to this notable success of Newmann–Janis algorithm in the case of Kerr metric, it has been being used to obtain rotating blackhole solution in modified gravity theories. In this work, we derive the spacetime metric for the external region of a rotating blackhole in a nonlocal gravity theory using Newmann–Janis algorithm. We also derive metric for a slowly rotating blackhole by perturbatively solving field equations of the theory. We discuss the applicability of Newmann–Janis algorithm to nonlocal gravity by comparing slow rotation limit of the metric obtained through Newmann–Janis algorithm with slowly rotating solution of the field equation.

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