Shearing radiative collapse with expansion and acceleration

Abstract

We investigate the behaviour of a relativistic spherically symmetric radiative star with an accelerating, expanding and shearing interior matter distribution in the presence of anisotropic pressures. The junction condition can be written in standard form in three cases: linear, Bernoulli and Riccati equations. We can integrate the boundary condition in each case and three classes of new solutions are generated. For particular choices of the metric we investigate the physical properties and consider the limiting behaviour for large values of time. The causal temperature can also be found explicitly.Comment: 16 pages, To appear in J. Math. Phy

Radiating star with a time-dependent Karmarkar condition

“…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].…”

Riccati equations for bounded radiating systems

“…It is important to observe that equation (8) is not equivalent to the original equation (6). The transformation (7), and consequently (8), is not valid for Y ′ = B orẎ = A.…”

“…It should be observed that the condition A =Ẏ is a special case of a relationship derived by Thirrukanesh et al [6] in their investigation of a radiating star. To solve (10) we follow their approach and assume Y is a separable function of the form…”

“…This is an equation with variables A, H and Y ; the potential B has been replaced by the new quantity H. It is clear that (8) is a simpler equation than (6). Equation (8) has been integrated for geodesic motion by Ivanov [14], and in particular cases with nongeodesic motion and shear in [13].…”

“…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.…”