Mixed potentials in radiative stellar collapse

We study the behaviour of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational potentials or initially fixing the temporal evolution of the model unlike earlier treatments. A systematic approach enables us to write the junction condition as a Riccati equation which under particular conditions may be transformed into a separable equation. New classes of solutions are generated which allow for mixed spatial and temporal dependence in the metric functions. We regain particular models found previously from our general classes of solutions.Comment: 10 pages, To appear in J. Math. Phy

Charged analogue of Finch-Skea stars

We present solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes with a specified form of the electric field intensity. The condition of pressure isotropy yields three category of solutions. The first category is expressible in terms of elementary functions and does not have an uncharged limit. The second category is given in terms of Bessel functions of half-integer order. These charged solutions satisfy a barotropic equation of state and contain Finch-Skea uncharged stars. The third category is obtained in terms of modified Bessel functions of half-integer order and does not have an uncharged limit. The physical features of the charged analogue of the Finch-Skea stars are studied in detail. In particular the condition of causality is satisfied and the speed of sound does not exceed the speed of light. The physical analysis indicates that this analogue is a realistic model for static charged relativistic perfect fluid spheres.Comment: 17 pages, To appear in Int. J. Mod. Phys.

Compact anisotropic spheres with prescribed energy density

New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav., Vol 21, 899-905, 1989) and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav., Vol 26, 75-84, 1994) as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.Comment: 22 pages, 3 figures, to appear in Gen. Rel. Gra

A new algorithm for anisotropic solutions

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.Comment: 16 pages, to appear in Pramana - J. Phy

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy

Collapsing Spheres Satisfying An "Euclidean Condition"

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.Comment: 1o pages, Latex. Title changed and text shortened to fit the version to appear in Gen.Rel.Grav