%0 Journal Article
%T A Relativistic Algorithm with Isotropic Coordinates
%A S. A. Ngubelanga
%A S. D. Maharaj
%J Advances in Mathematical Physics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/905168
%X We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contain isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments. 1. Introduction We consider the interior of static perfect fluid spheres in general relativity with isotropic pressures. The predictions of general relativity have been shown to be consistent with observational data in relativistic astrophysics and cosmology. For a discussion of the physical features of a gravitating model, we require an exact solution to the Einstein field equations. Exact solutions are crucial in the description of dense relativistic astrophysical problems. Many solutions have been found in the past. For some comprehensive lists of known solutions to the field equations, refer to Delgaty and Lake [1], Finch and Skea [2], and Stephani et al. [3]. Many of these solutions are not physically reasonable. For physical reasonableness, we require that the gravitational potentials and matter variables are regular and well behaved, causality of the spacetime manifold is maintained and values for physical quantities, for example, the mass of a dense star, are consistent with observation. Solutions have been found in the past by making assumptions on the gravitational potentials, matter distribution, or imposing an equation of state. These particular approaches do yield models which have interesting properties. However in principle, it would be desirable to have a general method that produces exact solutions in a systematic manner. Some systematic methods generated in the past are those of Rahman and Visser [4], Lake [5], Martin and Visser [6], Boonserm et al. [7], Herrera et al. [8], Chaisi and Maharaj [9], and Maharaj and Chaisi [10]. In general relativity, we have the freedom of using any well-defined coordinate system. The references mentioned above mainly use canonical coordinates. The use of isotropic coordinates may provide new insights and possibly lead to new solutions. This is the approach that we follow in this paper. We generate a new algorithm producing a new solution, to Einstein field equations in isotropic coordinates. From a given solution we can
%U http://www.hindawi.com/journals/amp/2013/905168/