An exact isotropic solution

Details An exact isotropic solution An exact isotropic solution

2006-02-08

arxiv.org/abs/gr-qc/0602031v1

Nuovo Cim. B121 (2006) 27-33

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, to appear in Il Nuovo Cimento B

Scientific paper

10.1393/ncb/i2005-10179-y

The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the field equations corresponding to a static spherically symmetric gravitational potential in terms of elementary functions. The metric functions, the energy density and the pressure are continuous and well behaved which implies that this solution could be used to model the interior of a relativistic sphere. The model satisfies a barotropic equation of state in general which approximates a polytrope close to the stellar centre.

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