Angle of Null Energy Condition Lines in Critical Spacetimes

TL;DR

This paper discovers a new critical parameter called the NEC angle in Choptuik's gravitational collapse, linking null energy condition saturation lines with curvature regions and providing numerical and analytical results across dimensions.

Contribution

It introduces the NEC angle as a novel critical parameter and derives its analytical form for higher-dimensional spacetimes, expanding understanding of critical collapse phenomena.

Findings

NEC angle approximately 0.64 radians (37 degrees) in numerical simulations

Analytical derivation of NEC angle as 2 arccot(D-1) for D>3

NEC lines separate regions of positive and negative curvature in spacetime

Abstract

We identify a new critical parameter in Choptuik's gravitational collapse: the angle at which null energy condition (NEC) saturation lines intersect at the center of the critical spacetime. These NEC lines coincide with regions of vanishing curvature, dividing spacetime into stripes of positive and negative curvature. By numerically solving Choptuik's original system we find the NEC angle to be $\alpha\approx0.64$ ($\approx37^\circ$) and analytically derive $\alpha=2$arccot$(D-1)$ for any spacetime dimension $D>3$.