In Choptuik critical collapse, the null energy condition saturation lines meet at the center with a universal angle α=2 arccot(D−1), numerically α≈0.64 in four dimensions.
Angle of Null Energy Condition Lines in Critical Spacetimes
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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 $D>3$.
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Angle of Null Energy Condition Lines in Critical Spacetimes
In Choptuik critical collapse, the null energy condition saturation lines meet at the center with a universal angle α=2 arccot(D−1), numerically α≈0.64 in four dimensions.