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A hairy box in three dimensions
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-07-13 , DOI: 10.1016/j.nuclphysb.2020.115115
Chethan Krishnan , Rohit Shekhar , P.N. Bala Subramanian

In this short note, we consider the phases of gravity coupled to a U(1) gauge field and charged scalar in 2+1 dimensions without a cosmological constant, but with box boundary conditions. This is an extension of the results in arXiv:1609.01208, but unlike in higher dimensions, here the physics has sharp differences from the corresponding AdS problem. This is because Einstein-Maxwell black holes cease to exist when the cosmological constant goes to zero. We show that hairy black holes also do not exist in the flat 2+1 dimensional box under some assumptions, but hairy boson stars do. There is a second order phase transition from the empty box to the boson star phase at a charge density larger than some critical value. We find various new features in the phase diagram which were absent in 3+1 dimensions. Our explicit calculations assume radial symmetry, but we also note that the absence of black holes is more general. It is a trivial consequence of a 2+1 dimensional version of Hawking's horizon topology argument from 3+1 dimensions, and relies on the Dominant Energy Condition, which is violated when (e.g.) there is a negative cosmological constant.



中文翻译:

三维毛状盒子

在本简短说明中,我们考虑了与 ü1个2 + 1维中的标量场和带电标量,没有宇宙学常数,但具有框边界条件。这是arXiv:1609.01208中结果的扩展,但与更高维度不同,此处的物理学与相应的AdS问题有着明显的差异。这是因为当宇宙常数变为零时,爱因斯坦-麦克斯韦黑洞不再存在。我们表明,在某些假设下,平坦的2 + 1维盒中也不存在毛状黑洞,但毛状玻色子星确实存在。从空盒到玻色子星相有一个二阶相变,其电荷密度大于一些临界值。我们在相图中发现了3 + 1尺寸所缺少的各种新功能。我们的显式计算假定径向对称,但是我们也注意到不存在黑洞更为普遍。

更新日期:2020-07-15
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