Radiating relativistic matter in geodesic motion

We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find that Bernoulli, Riccati and confluent hypergeometric equations are possible. These admit solutions in terms of elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Our infinite family of solutions contains specific models found previously. For a particular metric we briefly investigate the physical features, derive the temperature profiles and plot the behaviour of the casual and acasual temperatures.Comment: 15 pages, to appear in J. Math. Phy

Conformal symmetries of spherical spacetimes

We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions. Previous results relating to static spacetimes are shown to be a special case of our solution. The general inheriting conformal symmetry vector, which maps fluid flow lines conformally onto fluid flow lines, is generated and the integrability conditions are shown to be satisfied. We show that there exists a hypersurface orthogonal conformal Killing vector in an exact solution of Einstein's equations for a relativistic fluid which is expanding, accelerating and shearing.Comment: 8 pages, To appear in Int. J. Theor. Phy

Anisotropic fluid spheres of embedding class one using Karmarkar condition

We obtain a new anisotropic solution for spherically symmetric spacetimes by analysing of the Karmarkar embedding condition. For this purpose we construct a suitable form of one of the gravitational potentials to obtain a closed form solution. This form of the remaining gravitational potential allows us to solve the embedding equation and integrate the field equations. The resulting new anisotropic solution is well behaved which can be utilized to construct realistic static fluid spheres. Also we estimated masses and radii of fluid spheres for LMC X-4 and EXO 1785-248 by using observational data sets values. The obtained masses and radii show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy.Comment: 16 pages, 11 figure

A class of charged relativistic spheres

We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular parameter values it is possible to find solutions in terms of elementary functions. Our results contain models found previously for uncharged neutron stars and charged isotropic spheres.Comment: 11 pages, To appear in Mathematical and Computational Application