A two-point boundary value problem on a Lorentz manifold arising in A. Poltorak's concept of reference frame

TL;DR

This paper investigates conditions under which events in a Lorentz manifold can be connected by time-like geodesics, based on Poltorak's reference frame concept in General Relativity, linking geometric properties to causal relations.

Contribution

It establishes geometric conditions for connecting events via time-like geodesics within Poltorak's reference frame framework in Lorentz manifolds.

Findings

Identifies conditions for events to be connected by time-like geodesics

Links geometric properties of the reference frame to causal relations in spacetime

Provides criteria for proper future relations in specific reference frames

Abstract

In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold equipped with a connection. The question under consideration here is whether it is possible to join two events in the space-time by a time-like geodesic if they are joined by a geodesic of the reference frame connection that has a time-like initial vector. This question is interpreted as whether an event belongs to the proper future of another event in the space-time in case it is so in the reference frame. For reference frames of two special types some geometric conditions are found under which the answer is positive.