The area-angular momentum inequality for black holes in cosmological spacetimes
The area-angular momentum inequality for black holes in cosmological spacetimes
复制标题
宇宙时空中黑洞的面积角动量不等式
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
W. Simon
中科院分区：
文献类型：
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作者：
M. E. G. Clement;M. Reiris;W. Simon
For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant Λ > 0 ?> and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8 &pgr; ∣ J ∣ ≤ A ( 1 − Λ A / 4 &pgr; ) ( 1 − Λ A / 12 &pgr; ) ?> , which is saturated precisely for the extreme Kerr–de Sitter family of metrics. This result entails a universal upper bound ∣ J ∣ ≤ J max ≈ 0.17 / Λ ?> for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8 &pgr; ∣ J ∣ ≤ A ?> (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a ‘mass functional’, which is basically a suitably regularized harmonic map S 2 → H 2 . ?> However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized ‘Carter-identity’, and various techniques from variational calculus, including the mountain pass theorem.
