Causality and hyperbolicity of Lovelock theories
Causality and hyperbolicity of Lovelock theories
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DOI：
10.1088/0264-9381/31/20/205005
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发表时间：
2014-06
影响因子：
3.5
通讯作者：
H. Reall;Norihiro Tanahashi;Benson Way
中科院分区：
文献类型：
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作者：
H. Reall;Norihiro Tanahashi;Benson Way
在洛夫洛克理论中，引力可以比光传播得更快或更慢。因果结构由特征超曲面决定。我们推广了Izumi最近的一个结果，证明了对于Lovelock理论的所有引力自由度，任何杀戮视界都是一个特征超曲面。因此，引力信号无法从这样一个视界内的区域逃逸。我们通过确定不同背景下的特征超曲面来研究洛夫洛克理论的双曲性。首先我们考虑Ricci平面N型时空。我们证明了特征超曲面一般都是非零的，并且洛夫洛克理论在任何这样的时空中都是双曲的。接下来我们考虑洛夫洛克理论的静态、最大对称黑洞解。同样，特征曲面一般是非零的。对于一些小黑洞，双曲性在视界附近被打破。这意味着这类黑洞的稳定性不是一个适定的问题。
In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalize a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem.