scholarly journals Varieties of Parametric Classes of Exact Solutions in General Relativity Representing Static Fluid Balls

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Neeraj Pant
Keyword(s):  
Causal Model ◽  
Density Ratio ◽  
Analytic Solutions ◽  
Canonical Coordinates ◽  
Field Equations ◽  
Relativistic Field ◽  
Linear Dimensions ◽  
Neutron Star Mass ◽  
Static Fluid ◽  
General Relativistic

We have presented a method of obtaining parametric classes of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions have been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less than one. From the solution of one of the newly discovered classes, we have constructed a causal model in which outmarch of pressure and density is positive and monotonically decreasing, and pressure-density ratio is positive and less than one throughout within the balls. Corresponding to this model, we have maximized the Neutron star mass 2.40MΘ with the linear dimensions of 28.43 kms and surface red shift of 0.4142.

scholarly journals To Conserve, or Not to Conserve: A Review of Nonconservative Theories of Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 38
Author(s):  
Hermano Velten ◽  
Thiago R. P. Caramês
Keyword(s):  
Conservation Law ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Additional Constraint ◽  
Field Equations ◽  
Relativistic Field ◽  
Extended Theories Of Gravity ◽  
General Relativistic ◽  
Theories Of Gravity ◽  
Extended Theories

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

scholarly journals Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 142 ◽  
Author(s):  
Laur Järv ◽  
Manuel Hohmann ◽  
Martin Krššák ◽  
Christian Pfeifer
Keyword(s):  
General Relativity ◽  
Coordinate Transformation ◽  
Teleparallel Gravity ◽  
Analytic Solutions ◽  
Vacuum Field ◽  
Spin Connection ◽  
Flat Connection ◽  
Canonical Coordinates ◽  
Field Equations ◽  
Levi Civita Connection

Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.

scholarly journals Accretion onto a quintessence contaminated rotating black hole: violating the lower limit for eta over s

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Ritabrata Biswas ◽  
Promila Biswas ◽  
Parthajit Roy
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Lower Limit ◽  
Density Ratio ◽  
Density Variation ◽  
Entropy Density ◽  
Newtonian Potential ◽  
Field Equations ◽  
Spin Parameter ◽  
General Relativistic

AbstractViscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole’s gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole’s center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian flow is assumed to take place. Fluid speed, sonic speed profile and specific angular momentum to Keplerian angular momentum ratio are found out for different values of spin parameter and quintessence parameter. Density variation is built and tallied with observations. Shear viscosity to entropy density ratio is constructed for our model and a comparison with theoretical lower limit is done.

A static spherically symmetric solution of the Einstein—Maxwell—Yukawa field equations

1962 ◽  
Vol 58 (3) ◽  
pp. 521-526 ◽  
Author(s):  
G. Stephenson
Keyword(s):  
Gravitational Constant ◽  
Spherically Symmetric ◽  
Field Tensor ◽  
Field Equations ◽  
Relativistic Field ◽  
Metric Tensor ◽  
Spherically Symmetric Solution ◽  
Electromagnetic Field Tensor ◽  
General Relativistic ◽  
Image Position

The general relativistic field equations for regions of space containing electromagnetic fields but no matter are,where,and κ = 8ΠG/c4 is the gravitational constant. Here giκ is the metric tensor and Fiκ is the electromagnetic field tensor which satisfies Maxwell's equations ifand,where Ai is the electromagnetic four-potential.

Relativistic Theory of the Non-symmetric Field

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Field Theory ◽  
Displacement Field ◽  
Relativistic Theory ◽  
Inertial System ◽  
Field Equations ◽  
Relativistic Field ◽  
Relativistic Field Theory ◽  
Symmetric Field ◽  
Free Data ◽  
General Relativistic

This chapter attempts to find a measure for the “strength” of a system of field equations, which is determined by the amount of free data consistent with the system. It introduces the infinitesimal displacement field as a necessary remedy in general relativistic theory, as one can no longer form new tensors from a given tensor by simple differentiation and that in such a theory there are much fewer invariant formations. The infinitesimal displacement field replaces the inertial system inasmuch as it makes it possible to compare vectors at infinitesimally close points. After introducing these concepts, the chapter presents a discussion on relativistic field theory.

A New Form of the General Relativistic Field Equations

1955 ◽  
Vol 62 (1) ◽  
pp. 128 ◽  
Author(s):  
A. Einstein ◽  
B. Kaufman
Keyword(s):  
Field Equations ◽  
Relativistic Field ◽  
General Relativistic ◽  
New Form

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.

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