Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow...
| Հիմնական հեղինակներ: | , , |
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| Ձևաչափ: | Journal article |
| Լեզու: | English |
| Հրապարակվել է: |
2006
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| Ամփոփում: | We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist. |
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