arXiv 2103.009292021-03-26gr-qchep-th

广义相对论与一类Hoelava引力理论的关系

The relation between general relativity and a class of Hořava gravity theories

Nicola Franchini, Mario Herrero-Valea, Enrico Barausse

备注：: 15 pages, no figures. Ancillary files with field equations in Mathematica available. Accepted for publication in PRD
发表信息：: Phys. Rev. D 103, (2021) 084012
DOI：: 10.1103/PhysRevD.103.084012

摘要：

洛伦兹（特别是助推）不变性的破坏可以使引力在紫外线下重新归一化，正如霍洛维茨娃最初指出的那样，但在红外线下越来越受到限制。在低能量下，Hoelava引力的特征是三个无量纲耦合，$α$，$β$和$λ$，在广义相对论极限下消失。太阳系和引力波实验将其中两个耦合（$α$和$β$）限制在很小的值，但第三个耦合（$0\leqλ\lesssim 0.01-0.1$）相对不受限制。此外，要求（缓慢移动的）黑洞解规则地远离中心奇点，需要$α$和$β$ { \it精确地}为零。虽然正则约束分析表明，从这些约束（$α=β=0$和$λ\neq0$）产生的类khronometric理论不能等同于广义相对论，即使在真空中，以前的计算的动力学的太阳系，双星和引力波的产生显示出完美的协议与广义相对论。在这里，我们分析了球形坍缩和计算黑洞的准正规模，并再次发现，它们的行为{ \it完全}在广义相对论，只要{ \it观测}预测有关。然而，我们发现，球形坍缩导致形成一个规则的{ \it universal}视界，即任意传播速度的信号的因果边界，在通常的事件视界内的物质和张量引力子。我们的分析还证实，附加的标量自由度存在于广义相对论的自旋2引力子旁边，即使在弯曲的背景下，在低能量下也保持强耦合。这些令人困惑的结果表明，对霍拉瓦引力的任何进一步的限制都可能来自宇宙学。

英文摘要：

Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Hořava, but are increasingly constrained in the infrared. At low energies, Hořava gravity is characterized by three dimensionless couplings, $α$, $β$ and $λ$, which vanish in the general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings ($α$ and $β$) to tiny values, but the third remains relatively unconstrained ($0\leqλ\lesssim 0.01-0.1$). Moreover, demanding that (slowly moving) black-hole solutions are regular away from the central singularity requires $α$ and $β$ to vanish {\it exactly}. Although a canonical constraint analysis shows that the class of khronometric theories resulting from these constraints ($α=β=0$ and $λ\neq0$) cannot be equivalent to General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary pulsars and gravitational-wave generation show perfect agreement with General Relativity. Here, we analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave {\it exactly} as in General Relativity, as far as {\it observational} predictions are concerned. Nevertheless, we find that spherical collapse leads to the formation of a regular {\it universal} horizon, i.e. a causal boundary for signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons. Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2 graviton of General Relativity remains strongly coupled at low energies, even on curved backgrounds. These puzzling results suggest that any further bounds on Hořava gravity will probably come from cosmology.

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