A general class of Euclidean stars

Govinder, K. S.; Govender, M.

doi:10.1007/s10714-011-1268-5

Cited by 32 publications

(45 citation statements)

References 20 publications

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“…Finally, putting in order the four-dimensional case will help to lessen the efforts in investigating shear-free radiating collapse in higher dimensions [11,36].…”

Section: Discussionmentioning

confidence: 99%

Collapsing shear-free perfect fluid spheres with heat flow

Иванов¹

2012

Gen Relativ Gravit

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A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time- dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.Comment: 26 page

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“…Finally, putting in order the four-dimensional case will help to lessen the efforts in investigating shear-free radiating collapse in higher dimensions [11,36].…”

Section: Discussionmentioning

confidence: 99%

Collapsing shear-free perfect fluid spheres with heat flow

Иванов¹

2012

Gen Relativ Gravit

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“…Herrera and Santos introduced the concept of euclidean stars [15], simplifying the metric in order to introduce non null shear in an exact solution. This kind of source has been explored in G. Govender et al [16], Govinder and M. Govender [17], and Abede et al [18].…”

Section: Introductionmentioning

confidence: 99%

Gravitational collapse for a radiating anisotropic fluid

Veneroni

Silva

2019

Int. J. Mod. Phys. D

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Interested in the collapse of a radiating star, we study the temporal evolution of a fluid with heat flux and bulk viscosity, including anisotropic pressure. As a starting point, we adopt an initial configuration that satisfies the regularities conditions as well as the energy conditions to a certain range of the mass-radius ratio for the star, defining acceptable models. For this set of models, we verify that the energy conditions remain satisfied until the black hole formation. Astrophysical relevant quantities, such as the luminosity perceived by an observer at infinity, the time of event horizon formation and the loss of mass during the collapse are presented.

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“…Their thermal behaviour was studied [30]. A class of Euclidean stars with no horizon was found [31]. Finally, the Lie symmetry approach has been applied to the general case with shear and classes of new solutions were produced.…”

Section: Introductionmentioning

confidence: 99%

A different approach to anisotropic spherical collapse with shear and heat radiation

Иванов

2016

Int. J. Mod. Phys. D

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In order to study the type of collapse, mentioned in the title, we introduce a physically meaningful object, called the horizon function. It directly enters the expressions for many of the stellar characteristics. The main junction equation, which governs the collapse, transforms into a Riccati equation with simple coefficients for the horizon function. We integrate this equation in the geodesic case. The same is done in the general case when one or another of the coefficients vanish. It is shown how to build classes of star models in this formulation of the problem and simple solutions are given.

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A general class of Euclidean stars

Cited by 32 publications

References 20 publications

Collapsing shear-free perfect fluid spheres with heat flow

Collapsing shear-free perfect fluid spheres with heat flow

Gravitational collapse for a radiating anisotropic fluid

A different approach to anisotropic spherical collapse with shear and heat radiation

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