This solution do not exist in a closed form (for what I know). I've been studying the numerical approaches to this problem for some time. There are well know differential equations (and integral equations) that controls the possible solutions but these must be obtained numerically. But anyway...
I am working on writing a code to rotating compact objects. The process flows through a series of iterations, starting with a initial guess. I want to use the first guess as solution of Tolman-Oppenheimer-Volkoff (TOV) equations, for the spherical symmetric objects. But the transposition of this...
You mean that I could use a coordinate transformation for \theta like,
$$
d\theta=e^{-\alpha}d\theta,
$$
that could make the form of the metric equal?
The first expression was from Fridolin Weber's book "Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics, 1999" equation...
Hello. I expect this question is not repeated. I look from it in the forum but I found nothing.
I am confused on how an axisymmetric spacetime (generated by a rotating object) can manifest the spherically symmetric case. The axisymmetric spacetime should describe objects with any angular...