Buchdahl-Like Transformations in General Relativity

P. Boonserm, M. Visser

Abstract

Based on earlier work, we develop "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In addition, we now consider the situation in other coordinate systems: In particular, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation", while in other coordinate systems we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general relativistic static perfect fluid sphere.