Classes of exact Einstein Maxwell solutions
Abstract
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
 Publication:

General Relativity and Gravitation
 Pub Date:
 December 2007
 DOI:
 10.1007/s1071400705107
 arXiv:
 arXiv:0808.1998
 Bibcode:
 2007GReGr..39.2079K
 Keywords:

 Exact solutions;
 EinsteinMaxwell equations;
 Relativistic astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 16 pages, To appear in Gen. Relativ. Gravit