Lie Symmetries for a Conformally Flat Radiating Star

Abebe, G. Z.; Govinder, K. S.; Maharaj, S. D.

doi:10.1007/s10773-013-1620-5

Cited by 17 publications

(19 citation statements)

References 34 publications

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“…which is a self-similar solution for the master equation. It has been obtained previously by Abebe et al [23] when analyzing a conformally flat radiating star.…”

Section: Hence We Have the Potentialsmentioning

confidence: 60%

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A group theoretic approach to shear-free radiating stars

2015

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A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shearfree relativistic radiating star, is undertaken. This is a highly nonlinear partial differential equation in general. We obtain the Lie point symmetries that leave the boundary condition invariant. Using a linear combination of the symmetries, we transform the junction condition into ordinary differential equations. We present several new exact solutions to the junction condition. In each case we can identify the exact solution with a Lie point generator. Some of the solutions obtained satisfy the linear barotropic equation of state. As a special case we regain the conformally flat models which were found previously. Our analysis highlights the interplay between Lie algebras, nonlinear differential equations and application to relativistic astrophysics.

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“…which is a self-similar solution for the master equation. It has been obtained previously by Abebe et al [23] when analyzing a conformally flat radiating star.…”

Section: Hence We Have the Potentialsmentioning

confidence: 60%

“…respectively. These solutions were previously obtained by Abebe et al [23] for a radiating star which has the property of conformal flatness.…”

Section: Class IIImentioning

confidence: 78%

A group theoretic approach to shear-free radiating stars

2015

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“…Hence we have shown that the mass flow rate is fundamentally affected by the two-fluid atmosphere with the generalised Vaidya metric since the null fluid density ρ is non-zero. Using the derivatives (22), (19) and (18) in the definitions (16) and (17) we generate the following expressions for the surface luminosity L and the asymptotic luminosity L ∞ , respectively:…”

Section: Luminosity and Gravitational Redshiftmentioning

confidence: 99%

“…Misthry et al [15] generated nonlinear exact models in the shear-free regime for relativistic stars with heat flow, using a group theoretic approach that involves the Lie symmetry analysis of the Santos junction condition. Following this, Abebe et al [16], employing the same technique, investigated the behaviour of radiating stars in conformally flat spacetime manifolds. Abebe et al [17,18] used Lie analysis to find radiating Euclidean stars with an equation of state.…”

Section: Introductionmentioning

confidence: 99%

The effect of a two-fluid atmosphere on relativistic stars

2015

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We model the physical behaviour at the surface of a relativistic radiating star in the strong gravity limit. The spacetime in the interior is taken to be spherically symmetrical and shear-free. The heat conduction in the interior of the star is governed by the geodesic motion of fluid particles and a non-vanishing radially directed heat flux. The local atmosphere in the exterior region is a two-component system consisting of standard pressureless (null) radiation and an additional null fluid with non-zero pressure and constant energy density. We analyse the generalised junction condition for the matter and gravitational variables on the stellar surface and generate an exact solution. We investigate the effect of the exterior energy density on the temporal evolution of the radiating fluid pressure, luminosity, gravitational redshift and mass flow at the boundary of the star. The influence of the density on the rate of gravitational collapse is also probed and the strong, dominant and weak energy conditions are also tested. We show that the presence of the additional null fluid has a significant effect on the dynamical evolution of the star.

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“…The Santos junction conditions leads to a differential equation governing the temporal behaviour of the model. Solutions of this junction condition included ad hoc assumptions of the gravitational potentials, applying the method of Lie symmetries and 'spotting' of particular solutions [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Radiating star with a time-dependent Karmarkar condition

Naidu

Govender

2018

Eur. Phys. J. C

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In this paper we employ the Karmarkar condition (Proc Indian Acad Sci A 27:56, 1948) to model a spherically symmetric radiating star undergoing dissipative gravitational collapse in the form of a radial heat flux. A particular solution of the boundary condition renders the Karmarkar condition independent of time which allows us to fully specify the spatial behaviour of the gravitational potentials. The interior solution is smoothly matched to Vaidya's outgoing solution across a time-like hypersurface which yields the temporal behaviour of the model. Physical analysis of the matter and thermodynamical variables show that the model is wellbehaved.

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Lie Symmetries for a Conformally Flat Radiating Star

Cited by 17 publications

References 34 publications

A group theoretic approach to shear-free radiating stars

A group theoretic approach to shear-free radiating stars

The effect of a two-fluid atmosphere on relativistic stars

Radiating star with a time-dependent Karmarkar condition

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