Dynamical Horizon Segments and Spacetime Isometries

TL;DR

This paper investigates the constraints on spacetime symmetries near dynamical horizon segments, showing that such horizons typically admit only rotational Killing fields that leave each cross-section invariant, and that hypersurface orthogonal symmetries imply vanishing spin multipoles.

Contribution

It establishes strict limitations on Killing fields near dynamical horizons, revealing that they are mostly rotational and that hypersurface orthogonality leads to vanishing spin multipoles, resembling spherical symmetry.

Findings

Killing fields near DHS are mostly rotational.

Hypersurface orthogonal Killing fields imply zero spin multipoles.

DHSs with hypersurface orthogonal symmetries resemble spherically symmetric horizons.

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!