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  • Letter
  • Open Access

Angle of null energy condition lines in critical spacetimes

Christian Ecker1,*, Florian Ecker2,†, and Daniel Grumiller2,‡

  • 1Institute for Theoretical Physics, Goethe University, 60438, Frankfurt am Main, Germany
  • 2Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8–10/136, A-1040 Vienna, Austria

  • *Contact author: ecker@itp.uni-frankfurt.de
  • †Contact author: fecker@hep.itp.tuwien.ac.at
  • ‡Contact author: grumil@hep.itp.tuwien.ac.at
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Phys. Rev. D 112, L021505 – Published 31 July, 2025

DOI: https://doi.org/10.1103/vpyn-b2fn

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 α≈0.64 (≈37°) and analytically derive α=2arccot(D−1) for any spacetime dimension D>3.

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Phys. Rev. D 112, L021505– Published 31 July, 2025
  • Received 21 November 2024
  • Accepted 9 July 2025
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