Massless field equations in comoving spherically symmetric metric and solution in LTB cosmology

2021 ◽  
Vol 15 (2) ◽  
pp. 53-60
Author(s):  
Antonio Zecca
Keyword(s):  
Spherically Symmetric ◽  
Field Equations ◽  
Massless Field ◽  
Spherically Symmetric Metric

scholarly journals Metric-Affine Geometries with Spherical Symmetry

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 453 ◽  
Author(s):  
Manuel Hohmann
Keyword(s):  
Spherical Symmetry ◽  
Rotation Group ◽  
Spin Connection ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Comprehensive Overview ◽  
Pure Rotation ◽  
Affine Geometries ◽  
Spherically Symmetric Metric

We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the tetrad/spin connection formulation, and show its characteristic properties: torsion, curvature and nonmetricity. We then use these properties to derive a classification of all possible subclasses of spherically symmetric metric-affine geometries, depending on which of the aforementioned quantities are vanishing or non-vanishing. We discuss both the cases of the pure rotation group SO ( 3 ) , which has been previously studied in the literature, and extend these previous results to the full orthogonal group O ( 3 ) , which also includes reflections. As an example for a potential physical application of the results we present here, we study circular orbits arising from autoparallel motion. Finally, we mention how these results can be extended to cosmological symmetry.

Static spherically symmetric solutions in f(G) gravity

2016 ◽  
Vol 25 (07) ◽  
pp. 1650083 ◽  
Author(s):  
M. Sharif ◽  
H. Ismat Fatima
Keyword(s):  
Equation Of State ◽  
State Parameter ◽  
Energy Conditions ◽  
Conformal Killing ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Anisotropic Matter ◽  
Physical Validity ◽  
Spherically Symmetric Metric ◽  
Anisotropic Case

We investigate interior solutions for static spherically symmetric metric in the background of [Formula: see text] gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law [Formula: see text] model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter [Formula: see text]. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman–Oppenheimer–Volkoff equation.

Charged perfect fluid gravitational collapse in f(R, T) gravity

2019 ◽  
Vol 34 (20) ◽  
pp. 1950153 ◽  
Author(s):  
G. Abbas ◽  
Riaz Ahmed
Keyword(s):  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Coupling Parameter ◽  
Apparent Horizon ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Apparent Horizons ◽  
Spherically Symmetric Metric

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

scholarly journals ON THE MOTION OF A TEST PARTICLE AROUND A GLOBAL MONOPOLE IN A MODIFIED GRAVITY

2012 ◽  
Vol 27 (30) ◽  
pp. 1250177 ◽  
Author(s):  
T. R. P. CARAMÊS ◽  
E. R. BEZERRA DE MELLO ◽  
M. E. X. GUIMARÃES
Keyword(s):  
Test Particle ◽  
Modified Gravity ◽  
Functional Form ◽  
Weak Field ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Field Equations ◽  
Metric Tensor ◽  
Spherically Symmetric Metric

In this paper we suggest an approach to analyze the motion of a test particle in the spacetime of a global monopole within a f(R)-like modified gravity. The field equations are written in a simplified form in terms of [Formula: see text]. Since we are dealing with a spherically symmetric metric, we express F(R) as a function of the radial coordinate only, e.g., [Formula: see text]. So, the choice of a specific form for f(R) will be equivalent to adopt an Ansatz for [Formula: see text] . By choosing an explicit functional form for [Formula: see text], we obtain the weak field solutions for the metric tensor also compute the time-like geodesics and analyze the motion of a massive test particle. An interesting feature is an emerging attractive force exerted by the monopole on the particle.

On exact-shearing perfect-fluid solutions of the nonstatic spherically symmetric Einstein field equations

1990 ◽  
Vol 68 (12) ◽  
pp. 1403-1409 ◽  
Author(s):  
T. Biech ◽  
A Das
Keyword(s):  
Perfect Fluid ◽  
Functional Relationship ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Stress Energy ◽  
Spherically Symmetric Metric ◽  
Lorentzian Warped Product

In this paper we have sought solutions of the nonstatic spherically symmetric field equations that exhibit nonzero shear. The Lorentzian-warped product construction is used to present the spherically symmetric metric tensor in double-null coordinates. The field equations, kinematical quantities, and Riemann invariants are computed for a perfect-fluid stress-energy tensor. For a special observer, one of the field equations reduces to a form that admits wavelike solutions. Assuming a functional relationship between the metric coefficients, the remaining field equation becomes a second-order nonlinear differential equation that may be reduced as well.

scholarly journals String Theory Explanation of Galactic Rotation Found Using the Geodesic Constraint

2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
Mark D. Roberts
Keyword(s):  
String Theory ◽  
Low Energy ◽  
Galactic Rotation ◽  
Spherically Symmetric ◽  
Scalar Tensor Theory ◽  
De Sitter ◽  
Energy Limit ◽  
Field Equations ◽  
Tensor Theory ◽  
Spherically Symmetric Metric

The unique spherically symmetric metric which has vanishing Weyl tensor, is asymptotically de-Sitter, and can model constant galactic rotation curves is presented. Two types of field equations are shown to have this metric as an exact solution. The first is Palatini varied scalar-tensor theory. The second is the low energy limit of string theory modified by inclusion of a contrived potential.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation

1968 ◽  
Vol 306 (1487) ◽  
pp. 487-501 ◽  
Keyword(s):  
Boundary Conditions ◽  
Special Solution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Conformal Theory ◽  
Usual Form ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined in detail. This metric is assumed to be of the usual form d s 2 = e v d t 2 —e λ d r 2 — r 2 (d θ 2 + sin 2 θ d ψ 2 ) where λ and v are functions of r only. Hoyle & Narlikar obtained a solution of the field equations under the assumption λ + v = 0. In this paper the case λ + v ǂ 0 is investigated, and it is shown that the only solution that satisfies all the boundary conditions is the special solution obtained by setting λ + v = 0. The significance of this result is discussed.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

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