Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-04-11
J.Math.Phys.42:1779-1817,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
the discussion of our results includes now some solutions of Horowitz and Myers; typos corrected here and there; a shortened v
Scientific paper
10.1063/1.1340869
We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within (mainly) a conformal framework. We show connectedness of conformal infinity for appropriately regular such space-times. We give an explicit expression for the Hamiltonian mass of the (not necessarily static) metrics within the class considered; in the static case we show that they have a finite and well defined Hawking mass. We prove inequalities relating the mass and the horizon area of the (static) metrics considered to those of appropriate reference generalized Kottler metrics. Those inequalities yield an inequality which is opposite to the conjectured generalized Penrose inequality. They can thus be used to prove a uniqueness theorem for the generalized Kottler black holes if the generalized Penrose inequality can be established.
Chrusciel Piotr T.
Simon Walter
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