Thermal Behavior of Euclidean Stars

Abstract

A recent study of dissipative collapse considered a contracting sphere in which the areal and proper radii are equal throughout its evolution. The interior spacetime was matched to the exterior Vaidya spacetime which generated a temporal evolution equation at the boundary of the collapsing sphere. We present a solution of the boundary condition which allows the study of the gravitational and thermodynamical behaviour of this particular radiating model.

A general class of Euclidean stars

“…An interesting class of shearing, radiating stars was recently proposed by Herrera and Santos [10] in which the areal radius of the star is equal to its proper radius throughout the collapse process. An exact solution of the temporal evolution equation for these Euclidean stars was first presented by Govender et al [11]. This solution, although restricted, provided physically reasonable behaviours for the matter variables and the temperature profile for these radiating models.…”

Shearing radiative collapse with expansion and acceleration

“…Instead the boundary condition was analysed numerically to study the physical features of the model, producing a final state where the star has radiated away mass during collapse. By assuming a relation between the metric functions B and Y for Euclidean stars Govender et al 15 found particular models with shear. Our intention is to solve (10) exactly without restricting the functions.…”

“…The bracketed expressions in (15) contain the functions A, Y, and their derivatives. In spite of this difficulty it is possible to solve (15) and obtain B in general.…”

“…Nogueira and Chan, 13 modelling shear viscosity and bulk viscosity, attempted such a study but found that they needed to utilise numerical techniques to make progress. Some recent progress has been made in finding exact models for Euclidean stars by Herrera and Santos 14 and Govender et al 15 In Euclidean stars with shear the areal radius and proper radius are equal throughout the evolution of the radiating star. Our objective here is to show that it is possible to solve the relevant equations, for the general case, exactly in a systematic fashion.…”

Riccati equations for bounded radiating systems

“…However it is possible to solve the field equations and the boundary condition at the surface and generate closed form solutions. Exact models with acceleration, expansion and shear were presented by Thirukkanesh et al [6], Thirukkanesh and Govender [7], Herrera and Santos [8], Govender et al [9] and Govinder and Govender [10]. Abebe et al [11] obtained a generalized class of Euclidean stars, with a barotropic equation of state, using the method of Lie symmetries on differential equations.…”