Relativity theory in time-space

TL;DR

This paper generalizes the concept of space-time to time-space manifolds, redefining fundamental relativity concepts like curvature and Einstein equations within this broader framework.

Contribution

It introduces the notion of time-space manifolds and extends key relativity concepts to this new setting, broadening the theoretical foundation.

Findings

Defined time-space manifolds as differentiable manifolds with fixed time-space tangent structures

Reformulated affine connection, parallel transport, and curvature in the context of time-space

Extended Einstein equations to the general time-space manifold setting

Abstract

The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a differentiable manifold with such tangent spaces which have a certain fixed time-space structure. We redefine the fundamental concepts of global relativity theory with respect to this general situation. We study the concepts of affine connection, parallel transport, curvature tensor and Einstein equation, respectively.