Angle of null energy condition lines in critical spacetimes

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>α</a:mi><a:mo>≈</a:mo><a:mn>0.64</a:mn></a:mrow></a:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>≈</c:mo><c:mn>3</c:mn><c:mn>7</c:mn><c:mi>°</c:mi></c:math>) and analytically derive <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>α</e:mi><e:mo>=</e:mo><e:mn>2</e:mn><e:mi>arccot</e:mi><e:mo stretchy="false">(</e:mo><e:mi>D</e:mi><e:mo>−</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:math> for any spacetime dimension <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>D</i:mi><i:mo>&gt;</i:mo><i:mn>3</i:mn></i:math>.