Since one semiaxis can be recovered from central section, we condition on the knowledge of its length and we are interested in the other semiaxis length, that is, A for prolate spheroids, C for oblate spheroids and D for profiles.
Similar result holds for the population of oblate spheroids.
n] be independent and identically distributed oblate spheroids with isotropic orientation.
Equation (20) is an approximate expression for the parameter [xi] of an oblate spheroid
to collapse to a black hole.
The covariant metric tensor in the gravitational field of a homogeneous oblate spheroid in oblate spheroidal coordinates (n, <p) has been obtained [4, 5] as;
0] is the uniform density of the oblate spheroid and a is a constant parameter.
We can now conveniently formulate astrophysical solutions for the equation in the next section; which are convergent in the exterior space time of a homogeneous massive oblate spheroid placed in empty space.
The gravitational scalar potential interior to a homogeneous oblate spheroid is well known  to be given as
2] (where c is the speed of light in vacuum) can be constructed in gravitational fields interior and exterior to static homogeneous oblate spheroids placed in empty space.
2 Metric tensor exterior to a homogeneous oblate spheroid
The gravitational scalar potential exterior to a homogeneous static oblate spheroid  is given as
This relation has been derived recently (Pabst and Berthold, 2007), using a modified Stokes law for oblate spheroids
and taking into account random orientation in the laser diffraction measurement via Cauchy's stereological theorem.