Ecosystem for Closed Timelike Curves: An Energy Conditions Perspective

TL;DR

This paper investigates how energy condition violations relate to the existence of closed timelike curves in Kerr-Newman spacetimes, analyzing two models to understand their interplay from local and global perspectives.

Contribution

It introduces a correlation index linking energy conditions and closed timelike curves, and examines their relationship in non-commutative and Rastall Kerr-Newman spacetimes.

Findings

Violations of energy conditions can eliminate closed timelike curves.

Different spacetime models show contrasting roles of energy condition violations.

The analysis supports Hawking's chronology protection conjecture.

Abstract

In this article, we explore the relationship between the existence of closed timelike curves and energy conditions that occur in the Kerr-Newman spacetime. To quantify the dependence, we define a correlation index between energy conditions and closed timelike curves. Based on the inputs from Hawking's chronology protection conjecture, we analyze two popular variants of Kerr-Newman spacetime: Non-commutative and Rastall Kerr-Newman spacetimes. These two models provide complementary scenarios that aid in analyzing Hawking's statements regarding the correlation of closed timelike curves and energy conditions from a local and a global perspective. We report the results outlining the possible role played by violations of energy conditions in eliminating the closed timelike curves in two contrasting situations, namely in spacetimes with and without curvature singularities.