The effect of a two-fluid atmosphere on relativistic stars

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 nonvanishing 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 nonzero 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, luminosty, 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.Comment: 31 pages, Minor corrections implemente

Shear-free models for relativistic fluids with heat flow and pressure isotropy.

M. Sc. University of KwaZulu-Natal, Durban 2014.We model the interior dynamics of a relativistic radiating fuid in a nonstatic spher- ically symmetric spacetime. The matter distribution takes the form of an imperfect fuid with a nonvanishing radially directed heat flux. The fluid pressure is isotropic and the spherically symmetric spacetime manifold is described by a shear-free line el- ement. In our investigation, the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. We examine this governing equation by imposing vari- ous forms for these potentials and review classes of physically acceptable models that are applicable in relativistic astrophysics. Several new classes of new exact solutions to the condition of pressure isotropy are also found. A comparison of our solutions with earlier well known results is undertaken. A physical analysis of two of the new models is performed where the spatial and temporal evolution of the matter and grav- itational variables are probed. We demonstrate that the fluid pressure, energy density and heat flux are regular and well behaved for both models throughout the interior, and our results indicate that one of the models is consistent with the well established core-envelope framework for compact stellar scenarios. We also analyse the energy conditions for the radiating fluid and demonstrate consistent behaviour, with only the dominant condition being violated. Finally, an analysis of the relativistic thermody- namics of two solutions is undertaken in the Israel-Stewart theory and the temperature profiles for both the noncausal and causal cases are presented

Inhomogeneous and Radiating Composite Fluids

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems

Generalised radiating fields in Einstein–Gauss–Bonnet gravity

A five-dimensional spherically symmetric generalised radiating field is studied in Einstein–Gauss–Bonnet gravity. We assume the matter distribution is an extended Vaidya-like source and the resulting Einstein–Gauss–Bonnet field equations are solved for the matter variables and mass function. The evolution of the mass, energy density and pressure are then studied within the spacetime manifold. The effects of the higher order curvature corrections of Einstein–Gauss–Bonnet gravity are prevalent in the analysis of the mass function when compared to general relativity. The effects of diffusive transport are then considered and we derive the specific equation for which diffusive behaviour is possible. Gravitational collapse is then considered and we show that collapse ends with a weak and conical singularity for the generalised source, which is not the case in Einstein gravity

Radiating composite stars with electromagnetic fields

We derive the junction conditions for a general spherically symmetric radiating star with an electromagnetic field across a comoving surface. The interior consists of a charged composite field containing barotropic matter, a null dust and a null string fluid. The exterior atmosphere is described by the generalised Vaidya spacetime. We generate the boundary condition at the stellar surface showing that the pressure is determined by the interior heat flux, anisotropy, null density, charge distribution and the exterior null string density. A new physical feature that arises in our analysis is that the surface pressure depends on the internal charge distribution for generalised Vaidya spacetimes. It is only in the special case of charged Vaidya spacetimes that the matching interior charge distribution is equal to the exterior charge at the surface as measured by an external observer. Previous treatments, for neutral matter and charged matter, arise as special cases in our treatment of composite matter

Radiating stars with composite matter distributions

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

Charged radiation collapse in Einstein–Gauss–Bonnet gravity

We generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singularity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity separating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions $$N\ge 5$$, charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post collapse for all $$N\ge 6$$ and a weak conical singularity forms when $$N=5$$. A comparison with charged radiation collapse in general relativity is also given

Isotropic Perfect Fluids in Modified Gravity

We generate the Einstein–Gauss–Bonnet field equations in higher dimensions for a spherically symmetric static spacetime. The matter distribution is a neutral fluid with isotropic pressure. The condition of isotropic pressure, an Abel differential equation of the second kind, is transformed to a first order nonlinear canonical differential equation. This provides a mechanism to generate exact solutions systematically in higher dimensions. Our solution generating algorithm is a different approach from those considered earlier. We show that a specific choice of one potential leads to a new solution for the second potential for all spacetime dimensions. Several other families of exact solutions to the condition of pressure isotropy are found for all spacetime dimensions. Earlier results are regained from our treatments. The difference with general relativity is highlighted in our study