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arXiv 1802.09499gr-qchep-th
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超越广义相对论的Raychaudhuri方程

Towards the Raychaudhuri Equation Beyond General Relativity

Daniel J Burger, Saurya Das, S. Shajidul Haque, Nathan Moynihan, Bret Underwood

摘要:

在广义相对论中,引力是普遍吸引的,这一特征体现在雷乔杜里方程中,该方程要求测地线的同余的展开总是不增加的,只要物质服从强或弱能量条件。测地线的这种行为是奇点定理的一般证明中的一个重要组成部分,它表明许多时空在测地线不完备的意义上是奇点,并暗示广义相对论本身是不完备的。在某种程度上可以简化为广义相对论的其他引力理论也可能解决这些奇异性,因此考虑如何在这些框架中修改测地线的行为是很有意义的。我们计算的主要修正Raychaudhuri方程的膨胀由于模型在弦论,膜世界引力,$f(R)$理论,圈量子宇宙学,宇宙学和黑洞的背景下,并表明,虽然在大多数情况下测地线收敛加强,在少数情况下表示排斥出现,削弱测地线收敛,从而奇异性定理的结论。

英文摘要:

In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak energy conditions. This behavior of geodesics is an important ingredient in general proofs of singularity theorems, which show that many spacetimes are singular in the sense of being geodesically incomplete and suggest that General Relativity is itself incomplete. It is possible that alternative theories of gravity, which reduce to General Relativity in some limit, can resolve these singularities, so it is of interest to consider how the behavior of geodesics is modified in these frameworks. We compute the leading corrections to the Raychaudhuri equation for the expansion due to models in string theory, braneworld gravity, $f(R)$ theories, and Loop Quantum Cosmology, for cosmological and black hole backgrounds, and show that while in most cases geodesic convergence is reinforced, in a few cases terms representing repulsion arise, weakening geodesic convergence and thereby the conclusions of the singularity theorems.

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