Interpreting A and B metrics with Lambda as gravitational field of a tachyon in an (anti-)de Sitter universe
Abstract
We investigate the main properties and mutual relations of the so-called A and B metrics with any value of the cosmological constant. In particular, we explicitly show that both the All and BI metrics are, in fact, the famous Schwarzschild-(anti-)de Sitter spacetime (that is the AI metric) boosted to superluminal speed.
Together, they can be combined to form a complete gravitational field of a tachyon in an asymptotically Minkowski or (anti-)de Sitter background. The boundary separating the AII and BI regions is the MachCherenkov shockwave on which the curvature is unbounded.
We analyze various geometric features of such spacetimes, provide their natural physical interpretation, and visualize them using convenient background coordinates and embeddings.