For stable MOTS with capillary boundary, equality in the area estimate forces the contact angle to 90 degrees and the ambient initial data set to split as a product, under stated energy assumptions.
A tilted spacetime positive mass theorem
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We show a spacetime positive mass theorem for asymptotically flat initial data sets with a noncompact boundary. We develop a mass type invariant and a boundary dominant energy condition. Our proof is based on spinors.
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Marginally outer trap surface with capillary boundary and rigidity of initial data sets
For stable MOTS with capillary boundary, equality in the area estimate forces the contact angle to 90 degrees and the ambient initial data set to split as a product, under stated energy assumptions.