Abstract
In this paper we study the junction conditions for a generalised matter distribution in a radiating star. The internal matter distribution is a composite distribution consisting of barotropic matter, null dust and a null string fluid in a shear-free spherical spacetime. The external matter distribution is a combination of a radiation field and a null string fluid. We find the boundary condition for the composite matter distribution at the stellar surface which reduces to the familiar Santos result with barotropic matter. Our result is extended to higher dimensions. We also find the boundary condition for the general spherical geometry in the presence of shear and anisotropy for a generalised matter distribution.
Highlights
We believe that the resulting boundary conditions, for our generalised matter distributions, will assist in analysing the radiative collapse dynamics of spacetimes with spherical topologies
We find that our approach does lead to a result which is a generalisation of the Santos [1] boundary condition with a clear physical interpretation
Which is a generalisation of the Santos [1] boundary condition, as well as the condition derived by Maharaj et al [32], with a clear physical interpretation
Summary
We believe that the resulting boundary conditions, for our generalised matter distributions, will assist in analysing the radiative collapse dynamics of spacetimes with spherical topologies. A recent example with spherical, toroidal and higher genus topologies in gravitational collapse including the formation of trapped surfaces was completed by Mena and Oliveira [30] Another interesting result is that of Charan et al [31] who described charged anisotropic spherical collapse in the presence of heat flow where the dynamics are reduced to an ordinary differential equation. We demonstrate the matching conditions for the two spacetimes and note the differences contained in the boundary conditions we derived, compared to those of Santos [1,32] These are extended to higher dimensions in Sect. 6 we consider a shearing and anisotropic interior with a composite matter field and we obtain the boundary conditions for its matching to the generalised Vaidya metric.
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