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

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.

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TYPE II FLUID SOLUTIONS TO EINSTEIN'S FIELD EQUATIONS IN N-DIMENSIONAL SPHERICAL SPACETIMES

International Journal of Modern Physics D ◽

10.1142/s0218271802001421 ◽

2002 ◽

Vol 11 (01) ◽

pp. 113-124 ◽

Cited By ~ 11

Author(s):

JAIME F. VILLAS Da ROCHA

Keyword(s):

Black Holes ◽

Large Class ◽

Type Ii ◽

Einstein Field Equations ◽

Spacetime Dimension ◽

Einstein’S Field Equations ◽

Field Equations ◽

Self Similarity ◽

Naked Singularities ◽

Type Ii Fluid

A large class of Type II fluid solutions to Einstein field equations in N-dimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant λ, is studied, and found that when λ>λ c (N), the collapse always forms black holes, and when λ<λ c (N), it always forms naked singularities, where λ c (N) is function of the spacetime dimension N only.

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GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

International Journal of Modern Physics D ◽

10.1142/s0218271803003657 ◽

2003 ◽

Vol 12 (07) ◽

pp. 1315-1332 ◽

Cited By ~ 7

Author(s):

C. F. C. BRANDT ◽

M. F. A. DA SILVA ◽

JAIME F. VILLAS DA ROCHA ◽

R. CHAN

Keyword(s):

Physical Properties ◽

Gravitational Collapse ◽

Energy Conditions ◽

Anisotropic Fluid ◽

Spherically Symmetric ◽

Einstein Field Equations ◽

Field Equations ◽

Self Similarity ◽

Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

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Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions

Advances in Mathematical Physics ◽

10.1155/2012/638726 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14

Author(s):

Filipe C. Mena

Keyword(s):

Black Holes ◽

Exact Solutions ◽

Gravitational Waves ◽

Gravitational Collapse ◽

Higher Dimensions ◽

Fluid Solution ◽

Einstein Field Equations ◽

Field Equations ◽

Naked Singularities ◽

Geometrical Properties

We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.

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

Modern Physics Letters A ◽

10.1142/s0217732319501530 ◽

2019 ◽

Vol 34 (20) ◽

pp. 1950153 ◽

Cited By ~ 4

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.

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COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271805006882 ◽

2005 ◽

Vol 14 (06) ◽

pp. 1049-1061 ◽

Cited By ~ 9

Author(s):

R. CHAN ◽

M. F. A. DA SILVA ◽

J. F. VILLAS DA ROCHA ◽

ANZHONG WANG

Keyword(s):

Black Holes ◽

Scalar Field ◽

Gravitational Collapse ◽

Massless Scalar ◽

Massless Scalar Field ◽

Field Equations ◽

Self Similarity ◽

Global Properties ◽

Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

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Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08572-w ◽

2020 ◽

Vol 80 (11) ◽

Author(s):

Haroldo C. D. Lima Junior ◽

Luís C. B. Crispino ◽

Pedro V. P. Cunha ◽

Carlos A. R. Herdeiro

Keyword(s):

Black Holes ◽

Jacobi Equation ◽

Plasma Frequency ◽

Conformal Factor ◽

Matter Content ◽

Spherically Symmetric ◽

Einstein Field Equations ◽

Field Equations ◽

Original Procedure ◽

Hamilton Jacobi Equation

AbstractObtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

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Thermodynamic structure of field equations near apparent horizon for radiating black holes

Modern Physics Letters A ◽

10.1142/s0217732314501880 ◽

2014 ◽

Vol 29 (34) ◽

pp. 1450188 ◽

Cited By ~ 1

Author(s):

Uma Papnoi ◽

Megan Govender ◽

Sushant G. Ghosh

Keyword(s):

Black Holes ◽

Apparent Horizon ◽

Higher Dimensions ◽

Spherically Symmetric ◽

Einstein Field Equations ◽

Field Equations ◽

Four Dimensions ◽

Thermodynamic Structure ◽

Kinematical Parameters

We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity T dS = dE+P dV.

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ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

International Journal of Modern Physics D ◽

10.1142/s0218271806008838 ◽

2006 ◽

Vol 15 (07) ◽

pp. 991-999 ◽

Cited By ~ 12

Author(s):

P. R. PEREIRA ◽

M. F. A. DA SILVA ◽

R. CHAN

Keyword(s):

Dark Energy ◽

Energy Conditions ◽

Anisotropic Fluid ◽

Accelerating Universe ◽

Spherically Symmetric ◽

Einstein Field Equations ◽

Field Equations ◽

Self Similarity ◽

Normal Matter ◽

Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

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A new type of nonsingular black-hole solution in general relativity

Modern Physics Letters A ◽

10.1142/s0217732314300183 ◽

2014 ◽

Vol 29 (19) ◽

pp. 1430018 ◽

Cited By ~ 12

Author(s):

F. R. Klinkhamer

Keyword(s):

Black Hole ◽

Spherically Symmetric ◽

Curvature Singularity ◽

Einstein Field Equations ◽

Field Equations ◽

Schwarzschild Solution ◽

Gravity Effects ◽

New Type ◽

Nontrivial Topology ◽

Spacetime Foam

Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard Schwarzschild solution with a curvature singularity at the center. Spherically symmetric collapse of matter in ℝ4 may result in these nonsingular black-hole solutions, if quantum-gravity effects allow for topology change near the center or if nontrivial topology is already present as a remnant from a quantum spacetime foam.

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