Interpreting A and B-metrics with $\Lambda$ as gravitational field of a tachyon in (anti-)de Sitter universe

TL;DR

This paper explores the properties of A and B-metrics in (anti-)de Sitter space, revealing they represent boosted Schwarzschild-(anti-)de Sitter spacetimes and form the gravitational field of a tachyon, with a focus on their geometric and physical features.

Contribution

It demonstrates that AII and BI-metrics are boosted Schwarzschild-(anti-)de Sitter spacetimes, forming the gravitational field of a tachyon in (anti-)de Sitter universe, and analyzes their geometric structure.

Findings

AII and BI-metrics are Schwarzschild-(anti-)de Sitter spacetimes boosted to superluminal speeds.

The boundary between AII and BI regions is a Mach-Cherenkov shockwave with unbounded curvature.

The paper provides geometric interpretation and visualization of these spacetimes.

Abstract

We investigate 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 AII and BI-metrics are, in fact, the famous Schwarzschild-(anti-)de Sitter spacetime (that is the AI-metric) boosted to superluminal speed. Together they form the complete gravitational field of a tachyon in Minkowski or (anti-)de Sitter universe. The boundary separating the AII and BI regions is the Mach-Cherenkov shockwave on which the curvature is unbounded. We analyze various geometric features of such spacetimes, we provide their natural physical interpretation, and we visualize them using convenient background coordinates and embeddings.