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arXiv · 2506.10190

Dynamical Horizon Segments and Spacetime Isometries

Abhay Ashtekar·Badri Krishnan
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Abstract

Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $\xi^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$: Generically, $\xi^a$ can only be a rotational Killing field which, furthermore, leaves each marginally trapped 2-sphere cross-section $\mathcal{S}$ of $\mathscr{H}$ invariant. Finally, if $\xi^a$ happens to be hypersurface orthogonal near $\mathscr{H}$, then, not only the angular momentum but also all spin multipoles vanish on every $\mathcal{S}$; the entire spin structure of these DHSs is indistinguishable from that of spherically symmetric DHSs!

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Abhay Ashtekar, Badri Krishnan. 2025-06-11. Dynamical Horizon Segments and Spacetime Isometries. https://doi.org/10.1103/yxll-bvnm

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