Angle of Null Energy Condition Lines in Critical Spacetimes

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 $D>3$.