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This paper introduces a new spinorial approach to establishing geometric inequalities related to the ADM mass of black holes in general relativity, utilizing a second-order elliptic equation for a Weyl spinor. The method allows for better specification of boundary conditions, leading to new inequalities that bound the mass from below based on an integral functional over a marginally outer trapped surface. The findings include a master inequality that can be used to derive various geometric inequalities, inc

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fauziyahnur374

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