Multi-horizon Angular Momentum Penrose inequality

Establish an inequality for initial data containing n disjoint marginally outer trapped surfaces Σ_i with areas A_i and Komar angular momenta J_i, showing that the ADM mass satisfies M_ADM ≥ Σ_{i=1}^n sqrt(A_i/(16π) + 4π J_i^2/A_i).

Background

The main theorem treats a single outermost stable MOTS and proves the angular momentum Penrose inequality. In many physical scenarios, multiple disjoint horizons can arise (e.g., multi–black hole configurations). The authors propose an additive lower bound mirroring known multi-horizon extensions in related contexts.

A resolution would clarify how area and angular momentum contributions from separate horizons aggregate to constrain the total ADM mass in axisymmetric settings.

References

Conjecture [Multi-Horizon Extension] For data with $n$ disjoint MOTS ${\Sigma_i}$ with areas $A_i$ and angular momenta $J_i$: \begin{equation} M_{ADM} \geq \sum_{i=1}n \sqrt{\frac{A_i}{16\pi} + \frac{4\pi J_i2}{A_i}. \end{equation}

— Angular Momentum Penrose Inequality (2512.06918 - Xu, 7 Dec 2025) in Section “Extensions and Open Problems”, Subsection “Multiple Horizons”