Abstract
The relationship between radiating stars in general relativity and Riccati equations is investigated for a general matter distribution including the electromagnetic field and the cosmological constant. A generalised transformation relating the gravitational potentials for a spherically symmetric relativistic gravitating fluid is introduced. This generates a new Riccati equation at the surface of the radiating star. Exact solutions to the boundary condition are found and the gravitational potentials are given explicitly. Some of the consistency conditions can be reduced to Bernoulli equations which admit exact solutions. We also demonstrate that the reduction of order allows us to write the boundary condition as a first order equation utilising the generalised transformation. Solutions obtained using the generalised transformation also admit a linear equation of state.
Highlights
The evolution of a radiating star is an interesting and long standing problem of interest in general relativity
We have introduced a generalised transformation relating the gravitational potential A, B and Y for a spherically symmetric relativistic fluid
The generalised transformation leads to a new form of the boundary condition at the surface of the relativistic radiating star
Summary
The evolution of a radiating star is an interesting and long standing problem of interest in general relativity. In analysing the physical features of the relativistic radiating star, including the various features mentioned above, it is necessary to solve the Santos junction condition at the surface of the star. A systematic approach is to apply the Lie group method of infinitesimal generators [20,21,22,23] which leads to new exact models Another approach is to write the junction condition as a Riccati equation which was first explored by Misthry et al [24], Thirukkanesh et al [25] and Rajah and Maharaj [26]. We show how second order derivative terms from the junction condition can be eliminated by placing restric-
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