GRAVITATIONAL COLLAPSE OF THICK DOMAIN WALLS: AN ANALYTIC MODEL

An exact solution to the Einstein field equations is found, which represents the gravitational collapse of a thick domain wall. During the collapse, the wall emits gravitational radiation, which can be measured as a gravitational pp wave at the spacelike infinity. The time-reversed solution represents an expanding universe, in which a domain wall resides. It is shown explicitly that such a wall can be inflated away.

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Evolution of a domain wall in expanding universe: inflation and after it

EPJ Web of Conferences ◽

10.1051/epjconf/201819108004 ◽

2018 ◽

Vol 191 ◽

pp. 08004

Author(s):

A.D. Dolgov ◽

S.I. Godunov ◽

A.S. Rudenko

Keyword(s):

Domain Wall ◽

Hubble Parameter ◽

Domain Walls ◽

Flat Space ◽

Space Time ◽

Time Dependent ◽

Expanding Universe ◽

Large Size ◽

Dependent Parameter ◽

Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

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Gravitational waves — A review on the theoretical foundations of gravitational radiation

International Journal of Modern Physics A ◽

10.1142/s0217751x18300132 ◽

2018 ◽

Vol 33 (14n15) ◽

pp. 1830013 ◽

Cited By ~ 2

Author(s):

Alain Dirkes

Keyword(s):

General Relativity ◽

Gravitational Wave ◽

Gravitational Waves ◽

Gravitational Radiation ◽

Wave Zone ◽

Einstein Field Equations ◽

Field Equations ◽

Radiative Losses ◽

Zone Field ◽

Theoretical Foundations

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

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

International Journal of Modern Physics D ◽

10.1142/s0218271802001500 ◽

2002 ◽

Vol 11 (02) ◽

pp. 155-186 ◽

Cited By ~ 13

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.

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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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Comparative study of transit FLRW and axially symmetric cosmological structures with domain walls in f(R, T)-gravity

Canadian Journal of Physics ◽

10.1139/cjp-2020-0343 ◽

2020 ◽

Author(s):

Umesh Kumar Sharma ◽

Ambuj Kumar Mishra ◽

Anirudh Pradhan

Keyword(s):

Domain Walls ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Axially Symmetric ◽

Field Equations ◽

Stress Energy ◽

Thick Domain Walls ◽

Theory Of Gravitation ◽

The Universe ◽

Stress Energy Momentum Tensor

In the present article, we study the physical and geometric scene of the inflection of the Friedmann- Lemaitre-Robertson-Walker (FLRW) and an axially symmetric (AS) perfect fluid Universe with thick domain walls in f(R, T) theory of gravitation [Harko et al., Phys. Rev. D {84} (2011) 024020], where R and T represent Ricci scalar and trace of the stress energy-momentum tensor respectively in the scenario of decelerating-accelerating transition phases. To ascertain the exact solution of the corresponding field equations, we use the concept of a time-subordinate deceleration parameter (DP) which brings forth the scale factor a(t) = sinh^{\frac{1}{n}}(\alpha t), where n and \alpha are positive parameters. For n\in (0.27, 1], a class of accelerating phase is ensured while for n > 1, the Universe attains a phase transition from positive (decelerating) to negative (accelerating) which is uniform with recent observations. The models have been tested for physically acceptable by using stability. More or less physical and geometric behavior of the models are also devoted.

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

International Journal of Modern Physics D ◽

10.1142/s021827180300327x ◽

2003 ◽

Vol 12 (03) ◽

pp. 347-368 ◽

Cited By ~ 29

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.

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Charged anisotropic spherical collapse with heat flow

The European Physical Journal C ◽

10.1140/epjc/s10052-021-08865-8 ◽

2021 ◽

Vol 81 (1) ◽

Author(s):

Kali Charan ◽

Om Prakash Yadav ◽

B. C. Tewari

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Gravitational Collapse ◽

Energy Conditions ◽

Junction Conditions ◽

Einstein Field Equations ◽

Field Equations ◽

Radiating Star ◽

Large Round ◽

High Degree

AbstractIn this article, we study the shear-free gravitational collapse of a charged radiating star. The Einstein field equations of gravitational collapse for the charged stars are known to give rise to a high degree of non-linearity in the ordinary differential equation coming from junction conditions. The attempts to solve it analytically proved to be unfortunate. Numerical methods have been suggested in the past. However, the high degree of non-linearity tends to introduce fluctuations and large round off errors in the numerical calculation. A new ansatz is proposed in the present work to reduce the degree of non-linearity. An ordinary differential equation is derived by satisfying junction conditions, and its numerical solution is demonstrated. Physical quantities associated with the collapse process are plotted to observe the effect of charge on these quantities. It is concluded that the charge can delay the collapse of a star and can even prevent it depending upon the amount of charge. It is also verified that the solution satisfies all the energy conditions.

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