arXiv 2110.045362021-10gr-qchep-thquant-ph

引力子凝聚的红外定标

Infrared scaling for a graviton condensate

Sougato Bose, Anupam Mazumdar, Marko Toroš

备注：: 10 pages
发表信息：: Nucl. Phys. B 976 (2022), 115730
DOI：: 10.1016/j.nuclphysb.2022.115730

摘要：

引力和物质之间的耦合为爱因斯坦-希尔伯特作用量及更大范围内的引力理论提供了一个有趣的红外尺度。特别是，我们将表明，这样的红外长度尺度是由引力子的数量$N_{g}\gg1$与一个给定的质量在非相对论性的限制。通过对物质自由度的追踪，发现引力子真空处于一个位移真空中，引力子占据数为$N_{g}\gg1$。在红外线中，长度标度似乎是$L=\sqrt{N_{g}}\ell_{p}$，其中$L$是新的红外线长度标度，而$\ell_{p}$是普朗克长度。在一个具体的例子中，我们发现，对于一个缓慢移动的物质薄壳，红外长度尺度大于史瓦西半径。我们将论证，在更高曲率的引力理论中，例如在二次和三次曲率的引力理论中，这样的红外长度尺度的出现也是可以预期的。此外，我们将表明，重力是从根本上不同于电磁相互作用的光子数，$N_{p}$，是跟踪电子波函数后的精细结构常数。

英文摘要：

The coupling between gravity and matter provides an intriguing length scale in the infrared for theories of gravity within Einstein-Hilbert action and beyond. In particular, we will show that such an infrared length scale is determined by the number of gravitons $N_{g}\gg1$ associated to a given mass in the non-relativistic limit. After tracing out the matter degrees of freedom, the graviton vacuum is found to be in a displaced vacuum with an occupation number of gravitons $N_{g}\gg1$. In the infrared, the length scale appears to be $L=\sqrt{N_{g}}\ell_{p}$, where $L$ is the new infrared length scale, and $\ell_{p}$ is the Planck length. In a specific example, we have found that the infrared length scale is greater than the Schwarzschild radius for a slowly moving in-falling thin shell of matter. We will argue that the appearance of such an infrared length scale in higher curvature theories of gravity, such as in quadratic and cubic curvature theories of gravity, is also expected. Furthermore, we will show that gravity is fundamentally different from the electromagnetic interaction where the number of photons, $N_{p}$, is the fine structure constant after tracing out an electron wave function.

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