Causal Cones, Cone Preserving Transformations and Causal Structure in Special and General Theory of Relativity

TL;DR

This paper reviews the geometric and algebraic frameworks of causal cones and transformations, exploring their implications for the causal structure and topology of space-time in relativity theories.

Contribution

It provides a comprehensive overview of cone preserving transformations and their role in understanding causal structures in special and general relativity, including Lie groups and space-time topologies.

Findings

Analysis of causal cones and transformations in relativity

Comparison of causal relations with existing literature

Discussion of topologies arising from domain theory

Abstract

We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of 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 theory of 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.