Preventing non‑radial matter accumulation at integrable singularities

Determine whether physically plausible dynamical mechanisms—such as isotropization or angular‑momentum dissipation—can prevent matter with non‑zero angular momentum from accumulating at r = 0 in static, spherically symmetric general‑relativistic spacetimes possessing integrable singularities (i.e., with Misner–Sharp mass behaving near the core as m(r) = m1 r + O(r^2)), thereby preserving the integrability condition and the continuity of the metric at the singularity.

Background

The paper studies black hole spacetimes with integrable singularities, where the metric remains continuous at r = 0 and tidal forces on radial geodesics are finite. A key integrability condition near the core is that the Misner–Sharp mass satisfies m(r) = m1 r + O(r^2).

Because all geodesics focus at r = 0, non‑radial geodesics cannot traverse the singularity and matter with angular momentum tends to accumulate at the core. The authors highlight that such accumulation threatens the maintenance of the integrability condition unless some process isotropizes or removes angular momentum before matter reaches r = 0.

They explicitly state that it remains unclear how to prevent this accumulation, motivating a concrete open question about the existence and nature of mechanisms that could preserve integrability under realistic matter infall.