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arXiv 2006.07338gr-qcastro-ph.HEhep-th
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修正引力理论中的最大力

Maximum Force in Modified Gravity Theories

John D. Barrow, Naresh Dadhich

摘要:

研究了视界接触的两个黑洞之间经典最大力束缚的存在性和性质。除了广义相对论,最大力界与黑洞质量无关的只有莫法特理论、Brans Dicke理论(与爱因斯坦的真空理论相同)和爱因斯坦理论的高维推广,即纯Lovelock引力,其特征在于Lovelock多项式中只有一个$n$阶项,作用量中没有低阶项之和。此外,如果这个边界存在于更高的维度中,并且完全取决于光速和引力常量,那么它必须是唯一的纯洛夫洛克引力。在纯洛夫洛克引力中,最大力界存在于所有的$3n$ -空间维度中,其值为$c^4/4G_n$,其中$G_n$是相应的引力常量.在最大力界中没有质量依赖性可能与裸奇点的形成有关。

英文摘要:

We investigate the existence and nature of classical maximum force bound between two black holes with touching horizons. Besides general relativity, the maximum force bound is independent of black hole masses only in Moffat's theory, Brans Dicke theory (which is the same as Einstein's for vacuum) and the higher dimensional generalization of Einstein's theory, pure Lovelock gravity which is characterised by having single $n$th order term in Lovelock polynomial without sum over lower orders in the action. Further if the bound is to exist in higher dimensions and is entirely in terms of the velocity of light and the gravitational constant, it has uniquely to be pure Lovelock gravity. In pure Lovelock gravity, the maximum force bound exists in all $3n$-space dimensions and has the value, $c^4/4G_n$ where $G_n$ is the corresponding gravitational constant. The absence of mass dependence in the maximum force bound may have relevance for the formation of naked singularities.

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