We study the effects of pressure anisotropy and heat dissipation in a spherically symmetric radiating star undergoing gravitational collapse. An exact solution of the Einstein field equations is presented in which the model has a Friedmann-like limit when the heat flux vanishes. The behaviour of the temperature profile of the evolving star is investigated within the framework of causal thermodynamics. In particular, we show that there are significant differences between the relaxation time for the heat flux and the relaxation time for the shear stress.

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.

Starting off with two distinct initially static stellar cores (i) Florides interior (constant density, vanishing radial pressure) and (ii) Wyman interior (constant density, nonvanishing radial pressure), we explore the dynamics of these two models once hydrostatic equilibrium is lost. We show that although the time of formation of horizon, evolution of the mass and proper radius are independent of the chosen initially static configurations, there is a significant difference in the temperature profiles of the radiating bodies as the collapse proceeds.

We investigate the role played by density inhomogeneities and dissipation on the final outcome of collapse of a self-gravitating sphere. By imposing a perturbative scheme on the thermodynamical variables and gravitational potentials we track the evolution of the collapse process starting off with an initially static perfect fluid sphere which is shear-free. The collapsing core dissipates energy in the form of a radial heat flux with the exterior spacetime being filled with a superposition of null energy and an anisotropic string distribution. The ensuing dynamical process slowly evolves into a shear-like regime with contributions from the heat flux and density fluctuations. We show that the anisotropy due to the presence of the strings drives the stellar fluid towards instability with this effect being enhanced by the density inhomogeneity. An interesting and novel consequence of this collapse scenario is the delay in the formation of the horizon. Keywords radiative collapse • anisotropic stresses • density inhomogeneities 1 Introduction Gravitational collapse is fundamental to the formation of the majority of stellar objects in the universe and thus one would expect that the study of this

We model a radiating star undergoing dissipative gravitational collapse in the form of radial heat flux. The exterior of the collapsing star is described by the generalised Vaidya solution representing a mixture of null radiation and strings. Our model generalises previously known results of constant string density atmosphere to include inhomogeneities in the exterior spacetime. By utilising a causal heat transport equation of the Maxwell-Cattaneo form we show that relaxational effects are enhanced in the presence of inhomogeneities due to the string density.Comment: 12 pages, 4 figure

We investigate the causal temperature profiles in a recent model of a radiating star undergoing dissipative gravitational collapse without the formation of an horizon. It is shown that this simple exact model provides a physically reasonable behaviour for the temperature profile within the framework of extended irreversible thermodynamics.

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