scholarly journals Velocity and velocity bounds in static spherically symmetric metrics

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ivan Arraut ◽  
Davide Batic ◽  
Marek Nowakowski
Keyword(s):  
Radial Velocity ◽  
Density Profile ◽  
Local Minimum ◽  
Naked Singularity ◽  
Massless Particle ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Naked Singularities ◽  
Symmetric Metrics

AbstractWe find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.

scholarly journals GENERICITY ASPECTS IN GRAVITATIONAL COLLAPSE TO BLACK HOLES AND NAKED SINGULARITIES

2012 ◽  
Vol 21 (08) ◽  
pp. 1250066 ◽  
Author(s):  
PANKAJ S. JOSHI ◽  
DANIELE MALAFARINA ◽  
RAVINDRA V. SARAYKAR
Keyword(s):  
Black Holes ◽  
Initial Data ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Matter Field ◽  
Einstein Equations ◽  
Type I ◽  
Naked Singularities ◽  
Physical Conditions ◽  
Perfect Fluids

Here we investigate the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. Here, we first study in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.

IS THE NAKED SINGULARITY INCOMPATIBLE TO QUANTUM GRAVITY?

2005 ◽  
Vol 20 (24) ◽  
pp. 1823-1829 ◽  
Author(s):  
LI XIANG ◽  
YOU-GEN SHEN
Keyword(s):  
Generalized Uncertainty Principle ◽  
Charged Particles ◽  
Naked Singularity ◽  
Cosmic Censorship ◽  
Second Law ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Naked Singularities ◽  
Sitter Spacetime ◽  
Cosmic Censorship Hypothesis

In this paper two consequences of the generalized uncertainty principle (GUP) are discussed in a heuristic manner. Both could be regarded as the evidences that prefer the cosmic censorship hypothesis (CCH). The first one is that the second law tends to decline the massless charged particles if the effects of the GUP on the thermodynamics of a de Sitter spacetime are considered. This weakens the threat to the horizon of an extreme charged black hole. The second one is that the uv/ir correspondence provides a constraint on the relation between the energy and the size of a system, which is incompatible to the naked singularities.

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.

scholarly journals COSMOLOGICAL CONSTANT IN LOW ENERGY d = 4 STRING LEADS TO (STATIC SPHERICALLY SYMMETRIC) NAKED SINGULARITY

1995 ◽  
Vol 10 (10) ◽  
pp. 789-797 ◽  
Author(s):  
S. KALYANA RAMA
Keyword(s):  
Cosmological Constant ◽  
Sigma Model ◽  
Naked Singularity ◽  
Point Of View ◽  
Low Energy ◽  
Tree Level ◽  
Spherically Symmetric ◽  
Naked Singularities ◽  
Noncritical Strings ◽  
Β Function

In the sigma model approach, the β-function equations for noncritical strings contain a term which acts like a tree level cosmological constant, Λ. We analyze the static, spherically symmetric solutions to these equations in d = 4 space-time, which will describe the gravitational field of a point star up to a distance r*, of the order of parsecs. We show that the curvature scalar seen by the strings is singular in these solutions if Λ ≠ 0. This singularity is naked. Requiring its absence up to a distance r* imposes the constraint [Formula: see text] in natural units. Thus if r* ≃ 1 Mpc then |Λ| < 10−114, and if r* extends all the way up to the edge of the universe (1028 cm) then |Λ| < 10−122 in natural units. From another point of view, our analysis implies that low energy d = 4 noncritical strings in the sigma model formulation lead to naked singularities.

scholarly journals ON NEGATIVE MASS

2013 ◽  
Vol 22 (12) ◽  
pp. 1341017 ◽  
Author(s):  
JONATHAN BELLETÊTE ◽  
M. B. PARANJAPE
Keyword(s):  
Free Parameter ◽  
Energy Condition ◽  
Einstein Equations ◽  
Dominant Energy Condition ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Matter Distribution ◽  
Negative Mass ◽  
Schwarzschild Solution ◽  
Tunneling Transition

The Schwarzschild solution to the matter free, spherically symmetric Einstein equations has one free parameter, the mass. But the mass can be of any sign. What is the meaning of the negative mass solutions? The answer to this question for the case of a pure Schwarzschild negative mass black solution is still elusive, however, in this essay, we will consider negative mass solutions within a Schwarzschild–de Sitter geometry. We show that there exist reasonable configurations of matter, bubbles of distributions of matter, that satisfy the dominant energy condition everywhere, that are nonsingular and well behaved everywhere, but correspond to the negative mass Schwarzschild–de Sitter geometry outside the matter distribution. These negative mass bubbles could occur as the end state of a quantum tunneling transition.

scholarly journals Genericity aspects of black hole formation in the collapse of spherically symmetric slightly inhomogeneous perfect fluids

2016 ◽  
Vol 25 (02) ◽  
pp. 1650023 ◽  
Author(s):  
Seema Satin ◽  
Daniele Malafarina ◽  
Pankaj S. Joshi
Keyword(s):  
Black Hole ◽  
Perfect Fluid ◽  
Naked Singularity ◽  
Spherically Symmetric ◽  
Final State ◽  
Naked Singularities ◽  
Perfect Fluids ◽  
Special Cases ◽  
Collapse Models ◽  
Mass Profile

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.

scholarly journals NAKED SINGULARITIES AS CANDIDATES FOR GAMMA-RAY BURSTERS

1994 ◽  
Vol 03 (03) ◽  
pp. 647-651 ◽  
Author(s):  
SANDIP K. CHAKRABARTI ◽  
PANKAJ S. JOSHI
Keyword(s):  
Gravitational Waves ◽  
Gamma Rays ◽  
Gamma Ray ◽  
Naked Singularity ◽  
Shift Factor ◽  
Red Shift ◽  
Einstein Equations ◽  
Pure Radiation ◽  
Naked Singularities ◽  
Perfect Fluids

Naked singularities appear naturally in dynamically evolving solutions of Einstein equations involving gravitational collapse of radiation, dust, and perfect fluids provided the rate of accretion is less than a critical value. We propose that the gamma-ray bursters (GRBs) are examples of these naked singularity solutions. For illustration, we show that according to solutions involving spherically symmetric collapse of pure radiation field, the energy Eγ and the observed duration Δt0 of a GRB should satisfy, [Formula: see text] being the fraction (10−2 to 10−3) of energy released as gamma rays and the rest possibly as gravitational waves. All the presently observed GRBs satisfy this condition; those satisfying the condition close to equality must necessarily be of cosmological origin with the red-shift factor z not exceeding ~1−10 depending on exact observed flux, red-shift and conversion efficiency of gamma rays. If GRBs are indeed from naked singular regions, they should also be accompanied by a strong burst of gravitational waves which, if detectible, will constitute a basic test for our model.

scholarly journals Singularities in Static Spherically Symmetric Configurations of General Relativity with Strongly Nonlinear Scalar Fields

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleksandr Stashko ◽  
Valery I. Zhdanov
Keyword(s):  
Scalar Field ◽  
Asymptotic Properties ◽  
Field Potential ◽  
Scalar Fields ◽  
Einstein Equations ◽  
Large Field ◽  
Spherically Symmetric ◽  
Schwarzschild Solution ◽  
Naked Singularities ◽  
Strongly Nonlinear

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly nonlinear scalar field, which allow the appearance of singularities of a new type (“spherical singularities”) outside the center of curvature coordinates. As the example, we consider a scalar field potential ∼sinh(ϕ2n),n>2, which grows rapidly for large field values. The space-time is assumed to be asymptotically flat. We fulfill a numerical investigation of solutions with different n for different parameters, which define asymptotic properties at spatial infinity. Depending on the configuration parameters, we show that the distribution of the stable circular orbits of test bodies around the configuration is either similar to that in the case of the Schwarzschild solution (thus mimicking an ordinary black hole), or it contains additional rings of unstable orbits.

scholarly journals NAKED SINGULARITIES IN THE CHARGED VAIDYA–De SITTER SPACETIME

2003 ◽  
Vol 12 (05) ◽  
pp. 801-809 ◽  
Author(s):  
A. BEESHAM ◽  
S. G. GHOSH
Keyword(s):  
Cosmic Censorship ◽  
Spherically Symmetric ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Naked Singularities ◽  
Sitter Spacetime ◽  
Sitter Background ◽  
Cosmic Censorship Hypothesis

We study the occurrence of naked singularities in the spherically symmetric collapse of a charged null fluid in an expanding de Sitter background — a piece of charged Vaidya–de Sitter spacetime. The naked singularities are found to be gravitationally strong in Tipler's sense and thus violate the cosmic censorship hypothesis.

scholarly journals NAKED SINGULARITIES, TOPOLOGICAL DEFECTS AND BRANE COUPLINGS

2011 ◽  
Vol 20 (05) ◽  
pp. 839-849 ◽  
Author(s):  
JOSÉ D. EDELSTEIN ◽  
ALAN GARBARZ ◽  
OLIVERA MIŠKOVIĆ ◽  
JORGE ZANELLI
Keyword(s):  
Mass Parameter ◽  
Natural Extension ◽  
Topological Defects ◽  
Naked Singularity ◽  
Point Particle ◽  
De Sitter ◽  
Naked Singularities ◽  
Spacetime Curvature ◽  
Conical Defect ◽  
Chern Simons

A conical defect in 2 + 1 anti-de Sitter space is a BTZ solution with a negative mass parameter. This is a naked singularity, but a rather harmless one: it is a point particle. Naturally, the energy density and the spacetime curvature have a δ-like singularity at the conical defect, but that does not give rise to any unphysical situations. Since the conical solution implies the presence of a source, applying reverse enginnering, one can identify the coupling term that is required in the action to account for that source. In that way, a relation is established between the identification operation that gives rise to the topological defect and the interaction term in the action that produces it. This idea has a natural extension to higher dimensions, where instead of a point particle (zero-brane) one finds membranes of even spatial dimensions (p-branes, with p = 2n). The generalization to other abelian and nonabelian gauge theories — including (super-) gravities — is fairly straightforward: the 2n-brane couples to a (2n + 1) Chern–Simons form. The construction suggests a generic role for Chern–Simons forms as the natural way to couple a gauge connection to a brane and avoids the inconsistency that results from the minimal coupling between a brane and a fundamental p-form field.

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