Krishnan, C and Shekhar, R and Subramanian, PNB (2020) A hairy box in three dimensions. In: Nuclear Physics B, 958 .

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Abstract
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 EinsteinMaxwell 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.
Item Type:  Journal Article 

Publication:  Nuclear Physics B 
Publisher:  Elsevier B.V. 
Additional Information:  Copy right for this article belongs to Elsevier B.V. 
Department/Centre:  Division of Physical & Mathematical Sciences > Centre for High Energy Physics 
Date Deposited:  20 Oct 2020 09:51 
Last Modified:  20 Oct 2020 09:51 
URI:  http://eprints.iisc.ac.in/id/eprint/66086 
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