Causal and Topological Aspects in Special and General Theory of Relativity

TL;DR

This paper reviews geometric and algebraic methods to analyze causal structures in special and general relativity, focusing on causal cones, transformations, and topologies of space-time.

Contribution

It provides a comprehensive review of causal cones, transformations, and topologies, integrating Lie group theory and domain theory in the context of relativity.

Findings

Relationship between causal cones and Lie groups elucidated

Comparison of causal relations with existing literature

Discussion of topologies arising from domain theory

Abstract

In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe Lie groups, especially matrix Lie groups, homogeneous and symmetric spaces and causal cones and certain implications of these concepts in special and general relativity, related to causal structure and topology of space-time. We compare and contrast the results on causal relations with those in the literature for general space-times and compare these relations with K-causal maps. We also describe causal orientations and their implications for space-time topology and discuss some more topologies on space-time which arise as an application of domain theory. For the sake of completeness, we reproduce proofs of certain theorems which we proved in our earlier work.