Misconceptions about general relativity in theoretical black hole astrophysics


E-mail: david.a.garofalo@jpl.nasa.gov


The fundamental role played by black holes in our study of microquasars, gamma-ray bursts and the outflows from active galactic nuclei requires an appreciation for, and at times some in-depth analysis of, curved space–time. We highlight misconceptions surrounding the notion of coordinate transformation in general relativity as applied to metrics for rotating black holes that are beginning to increasingly appear in the literature. We emphasize that there is no coordinate transformation that can turn the metric of a rotating space–time into that for a Schwarzschild space–time, or more generally, that no coordinate transformation exists that can diagonalize the metric for a rotating space–time. We caution against the notion of ‘local’ coordinate transformation, which is often incorrectly associated with a global analysis of the space–time.