scholarly journals Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions

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.

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 SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

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

2002 ◽  
Vol 11 (01) ◽  
pp. 113-124 ◽  
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.

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

2014 ◽  
Vol 29 (34) ◽  
pp. 1450188 ◽  
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.

scholarly journals ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

2007 ◽  
Vol 22 (10) ◽  
pp. 1935-1951 ◽  
Author(s):  
M. SHARIF ◽  
M. AZAM
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Momentum Distribution ◽  
Special Class ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Degenerate Solution ◽  
Dust Solution

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

scholarly journals GRAVITATIONAL COLLAPSE OF SELF-SIMILAR AND SHEAR-FREE FLUID WITH HEAT FLOW

2003 ◽  
Vol 12 (03) ◽  
pp. 347-368 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Heat Flow ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Free Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spherical Shells ◽  
Naked Singularities ◽  
Self Similar

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

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

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
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.

scholarly journals An Analysis of Gravitational waves

2021 ◽  
Author(s):  
Vaibhav Kalvakota
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Mathematical Structure ◽  
Gauge Condition ◽  
Field Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Wave Detector ◽  
The Masses

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

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