2007/07/02 by Petarpa Boonserm, PETARPA BOONSERM, Matt Visser +1 · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1142/s0218271808011912
published as Int.J.Mod.Phys.D17:135-163,2008 · 23 pages
arxiv created 2007/07/02 · openalex publication_date 2008/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "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 the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) 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. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.