Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational solitons, hairy black holes and phase transitions in BHT
  massive gravity   Hairy black holes and gravitational solitons in three dimensions for the new
massive gravity theory proposed by Bergshoeff, Hohm and Townsend (BHT) are
considered at the special case when there is a unique maximally symmetric
solution. Following the Brown-York approach with suitable counterterms, it is
shown that the soliton possesses a fixed negative mass which coincides with the
one of AdS spacetime regardless the value of the integration constant that
describes it. Hence, the soliton can be naturally regarded as a degenerate
ground state labeled by a single modulus parameter. The Euclidean action,
endowed with suitable counterterms, is shown to be finite and independent of
modulus and hair parameters for both classes of solutions, and in the case of
hairy black holes the free energy in the semiclassical approximation is
reproduced. Modular invariance allows to show that the gravitational hair turns
out to be determined by the modulus parameter. According to Cardy's formula, it
is shown that the semiclassical entropy agrees with the microscopic counting of
states provided the modulus parameter of the ground state is spontaneously
fixed, which suggests that the hairy black hole is in a broken phase of the
theory. Indeed, it is found that there is a critical temperature characterizing
a first order phase transition between the static hairy black hole and the
soliton which, due to the existence of gravitational hair, can take place in
the semiclassical regime.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th