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Uniqueness and foliation-dependence of DHSs

Overcome current limitations on DHS uniqueness results by proving: (i) uniqueness statements when the null energy flux ๐”ˆ vanishes on open subsets of marginally trapped surfaces; (ii) relations among DHSs generated by suitably restricted classes of spacetime foliations; and (iii) constraints on multiple time-like DHSs representing the same dynamical phase.

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Background

Existing uniqueness results for regular, space-like DHSs assume global achronality and that ๐”ˆ is nowhere vanishing, and further address DHSs generated by a fixed foliation. Physically relevant configurations may violate these conditions (e.g., ๐”ˆ vanishing on sets of nonzero measure, or differing slicings).

Extending uniqueness to these cases and characterizing relations between DHSs from different foliations would reconcile mathematical theory with diverse numerical practices and improve physical interpretability.

References

Open Issue 6 (OI-6): Can these limitations be overcome? In the case of space-like DHSs, we are led to ask: (i) Are there interesting uniqueness statements that can be established for DHSs where \mathcal{E} vanishes on open regions of their MTSs?, and (ii) Are there results relating the DHSs of, say, the remnants that result from a suitably restricted class of foliations? In the case of time-like DHSs, what can we say about the possible DHSs representing the same dynamical phase of the BH?

— Quasi-Local Black Hole Horizons: Recent Advances (2502.11825 - Ashtekar et al., 17 Feb 2025) in Section 3.4