Causal Behaviour on Carter spacetime

TL;DR

This paper investigates the causal properties of Carter spacetime, demonstrating that the Lorentzian distance between two points is infinite, which offers insights into the spacetime's causal structure and potential relaxations of causal conditions.

Contribution

The study proves that the Lorentzian distance in Carter spacetime is infinite, contributing to understanding its causal character and implications for spacetime characterization.

Findings

Lorentzian distance in Carter spacetime is infinite

Carter spacetime is not a counterexample for certain causal relaxations

Provides ideas for alternative approaches to causal characterization

Abstract

In this work we will focus on the causal character of Carter Spacetime (see B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971). The importance of this spacetime is the following: for the causally best well behaved spacetimes (the globally hyperbolic ones), there are several characterizations or alternative definitions. In some cases, it has been shown that some of the causal properties required in these characterizations can be weakened. But Carter spacetime provides a counterexample for an impossible relaxation in one of them. We studied the possibility of Carter spacetime to be a counterexample for impossible lessening in another characterization, based on the previous results. In particular, we will prove that the time-separation or Lorentzian distance between two chosen points in Carter spacetime is infinite. Although this spacetime turned out not to be the counterexample we were looking for, the found result is interesting per se and provides ideas for alternate approaches to the possibility of weakening the mentioned characterization.