2025/07/14 by Christian Ecker, Florian Ecker, Daniel Grumiller · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Astrophysical Phenomena and Observations
paper · doi:10.1103/vpyn-b2fn
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>></i:mo> <i:mn>3</i:mn> </i:math> .