scholarly journals Analysis of Einstein Field Equations of Static Plane Symmetric Space-Time in General Relativity via Lie Approach

2019 ◽  
pp. 14-17
Author(s):  
Adil Jhangeer
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Space Time ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Static Plane

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.

A study of energy conditions in static plane symmetric space–times via homothetic symmetries

2019 ◽  
Vol 34 (35) ◽  
pp. 1950238
Author(s):  
Tahir Hussain ◽  
Uzma Nasib ◽  
Muhammad Farhan ◽  
Ashfaque H. Bokhari
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Field Equations ◽  
New Approach ◽  
Plane Symmetric ◽  
Homothetic Vector ◽  
Integration Techniques ◽  
Static Plane

The aim of this study is twofold. First, we use a new approach to study the homothetic vector fields (HVFs) of static plane symmetric space–times by an algorithm which we have developed using the Maple platform. The interesting feature of this algorithm is that it provides the most general form of metrics admitting HVFs as compared to those obtained in an earlier study where direct integration techniques were used. Second, the obtained metrics are used in Einstein’s field equations to compute the energy–momentum tensor and it is shown how the parameters involved in the obtained space–time metrics are associated with certain important energy conditions.

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.

Conformal vector fields in proper non-static plane symmetric spacetimes in f(R) gravity

2020 ◽  
Vol 17 (05) ◽  
pp. 2050077 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
F. M. Mahomed ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Integration Approach ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

Nonstatic plane symmetric spacetimes are considered to study conformal vector fields (VFs) in the [Formula: see text] theory of gravity. Firstly, we investigate some proper nonstatic plane symmetric spacetimes by solving the Einstein field equations (EFEs) in the [Formula: see text] theory of gravity using algebraic techniques. Secondly, we find CVFs of the obtained spacetimes by means of the direct integration approach. There exist seven cases. Studying each case in detail, we find that the CVFs are of dimension three, five, six and fifteen.

scholarly journals PLANE SYMMETRIC SOLUTIONS IN f(R) GRAVITY

2010 ◽  
Vol 25 (15) ◽  
pp. 1281-1288 ◽  
Author(s):  
M. SHARIF ◽  
M. FARASAT SHAMIR
Keyword(s):  
General Relativity ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Modified Theories Of Gravity ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Vacuum ◽  
Theories Of Gravity ◽  
Static Plane ◽  
Vacuum Solutions

The modified theories of gravity, especially the f(R) theory, have attracted much attention in recent years. In this context, we explore static plane symmetric vacuum solutions using the metric approach of this theory. The field equations are solved using the assumption of constant scalar curvature which may be zero or nonzero. We have found a total of three plane symmetric solutions. The correspondence of these solutions with the well-known solutions in General Relativity is given.

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.

Sign in / Sign up

Export Citation Format

Share Document