15 research outputs found
The Stability of an Isentropic Model for a Gaseous Relativistic Star
We show that the isentropic subclass of Buchdahl's exact solution for a
gaseous relativistic star is stable and gravitationally bound for all values of
the compactness ratio , where is the total mass and is
the radius of the configuration in geometrized units] in the range, , corresponding to the {\em regular} behaviour of the solution. This
result is in agreement with the expectation and opposite to the earlier claim
found in the literature.Comment: 9 pages (including 1 table); accepted for publication in GR
Classes of exact Einstein-Maxwell solutions
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.Comment: 16 pages, To appear in Gen. Relativ. Gravi