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arXiv · 2510.10306

Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers

Sven Hirsch·Lan-Hsuan Huang
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Abstract

We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed into strongly stationary vacuum spacetimes, thereby confirming the Bartnik stationary vacuum conjecture. A key ingredient is a new monotonicity formula for the Lorentzian length of a causal Killing vector field, which, among other applications, yields a strong maximum principle for the length.

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Sven Hirsch, Lan-Hsuan Huang. 2025-10-11. Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers. https://arxiv.org/abs/2510.10306

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