Exact models for isotropic matter
Abstract
We study the EinsteinMaxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the EinsteinMaxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 April 2006
 DOI:
 10.1088/02649381/23/7/028
 arXiv:
 arXiv:grqc/0602082
 Bibcode:
 2006CQGra..23.2697T
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 14 pages, to appear in Class. Quantum Grav