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.

Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

2018 ◽  
Vol 33 (12) ◽  
pp. 1850065 ◽  
Author(s):  
Suhail Khan ◽  
Muhammad Shoaib Khan ◽  
Amjad Ali
Keyword(s):  
Perfect Fluid ◽  
Outer Region ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Higher Dimensional ◽  
Stress Energy ◽  
Inner Region ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress–energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

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 GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

WEAK GRAVITATIONAL FIELD AROUND A GLOBAL TEXTURE

1994 ◽  
Vol 09 (21) ◽  
pp. 1905-1910
Author(s):  
CHUL H. LEE
Keyword(s):  
Gravitational Field ◽  
Flat Space ◽  
Asymptotic Region ◽  
Energy Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Model Approximation ◽  
Weak Gravitational Field ◽  
Stress Energy ◽  
Self Similar Solution

Weak gravitational field in the asymptotic region far outside the core of a global texture is investigated without the nonlinear σ-model approximation. We solve the linearized Einstein field equations with the stress-energy tensor contributed by a spherically symmetric global texture to obtain the asymptotic form of the metric. It is shown that, even in this more general case than that of the self-similar solution in the nonlinear σ-model approximation, the metric of the spatial hyperspace in the asymptotic region is that of a flat space with a deficit solid angle whose magnitude is independent of time.

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.

scholarly journals Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 531 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Space Time ◽  
Energy Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Screening Effect ◽  
Periodic Perturbations ◽  
Desitter Space

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

2020 ◽  
Vol 17 (13) ◽  
pp. 2050202 ◽  
Author(s):  
Shabeela Malik ◽  
Fiaz Hussain ◽  
Ghulam Shabbir
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Gravity Models ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

scholarly journals Radially symmetric distribution of matter

1966 ◽  
Vol 6 (2) ◽  
pp. 153-156 ◽  
Author(s):  
A. L. Mehra
Keyword(s):  
Perfect Fluid ◽  
Variable Density ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spherically Symmetric Distribution

SummaryIn this paper a solution of the Einstein field equations for a spherically symmetric distribution of a perfect fluid of variable density has been obtained.

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