Thermal Evolution of a Radiating Anisotropic Star With Shear

A new model is proposed to a collapsing star consisting of an initial inhomogeneous energy density and anisotropic pressure fluid with shear, radial heat flow and outgoing radiation. In previous papers one of us has always assumed an initial star with homogeneous energy density. The aim of this work is to generalize the previous models by introducing an initial inhomogeneous energy density and compare it to the initial homogeneous energy density collapse model. We will show the differences between these models in the evolution of all physical quantities that characterizes the gravitational collapse. The behavior of the energy density, pressure, mass, luminosity and the effective adiabatic index is analyzed. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast of the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. In contrast of the former model where the luminosity also increases exponentially, reaching a maximum and after it decreases until the formation of the black hole. The effective adiabatic index is always positive without any discontinuity in contrast of the former model where there is a discontinuity around the time of maximum luminosity.

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“…From the junction conditions (23) and (24) we obtain the following results (see more details in [5][6][7][8][9])…”

Section: Junction Conditionsmentioning

confidence: 93%

“…Thus, it is interesting to study solutions that contains shear, because it plays a very important role in the study of gravitational collapse, as shown in [5][6][7][8][9]22,24,25] and in [19]. More recent studies on this subject with and without shear are also found in [11,16,21,23,26].…”

Section: Introductionmentioning

confidence: 98%

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

Pinheiro

Chan

2010

Gen Relativ Gravit

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“…This is a necessary condition that ensures continuity of the momentum flux across the boundary of the radiating star. The Santos junction conditions have been generalised to include shear [5,6], the cosmological constant as well as the electromagnetic field [7,8]. Since 1985 there has been a concerted effort in generating exact models of dissipative collapse with Herrera and co-workers establishing many of the fundamental results in terms of stability, energy conditions and thermodynamics of these models [9][10][11][12][13][14].…”

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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“…It is also well understood that the thermal evolution of the radiating fluid is crucial in any stellar model and the precise role of the relaxation and mean collision time were analysed by Martinez [20], Herrera and Santos [21] and Govender et al [22]. These ideas were further exploited in the more recent work of Naidu et al [23], Naidu and Govender [24] and Maharaj et al [25]. Attempts to model radiating stellar matter with a more realistic form, have been made by imposing either a barotropic or polytropic equation of state for the fluid distribution.…”

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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Thermal Evolution of a Radiating Anisotropic Star With Shear

Cited by 73 publications

References 27 publications

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

Radiating star with a time-dependent Karmarkar condition

The effect of a two-fluid atmosphere on relativistic stars

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