508 research outputs found
Minimal Log Gravity
Minimal Massive Gravity (MMG) is an extension of three-dimensional
Topologically Massive Gravity that, when formulated about Anti-de Sitter space,
accomplishes to solve the tension between bulk and boundary unitarity that
other models in three dimensions suffer from. We study this theory at the
chiral point, i.e. at the point of the parameter space where one of the central
charges of the dual conformal field theory vanishes. We investigate the
non-linear regime of the theory, meaning that we study exact solutions to the
MMG field equations that are not Einstein manifolds. We exhibit a large class
of solutions of this type, which behave asymptotically in different manners. In
particular, we find analytic solutions that represent two-parameter
deformations of extremal Banados-Teitelboim-Zanelli (BTZ) black holes. These
geometries behave asymptotically as solutions of the so-called Log Gravity,
and, despite the weakened falling-off close to the boundary, they have finite
mass and finite angular momentum, which we compute. We also find time-dependent
deformations of BTZ that obey Brown-Henneaux asymptotic boundary conditions.
The existence of such solutions show that Birkhoff theorem does not hold in MMG
at the chiral point. Other peculiar features of the theory at the chiral point,
such as the degeneracy it exhibits in the decoupling limit of the Cotton
tensor, are discussed.Comment: 13 pages. v2 minor typos corrected. Accepted for publication in Phys.
Rev.
About the coordinate time for photons in Lifshitz Space-times
In this paper we studied the behavior of radial photons from the point of
view of the coordinate time in (asymptotically) Lifshitz space-times, and we
found a generalization to the result reported in previous works by Cruz et. al.
[Eur. Phys. J. C {\bf 73}, 7 (2013)], Olivares et. al. [Astrophys. Space Sci.
{\bf 347}, 83-89 (2013)], and Olivares et. al. [arXiv: 1306.5285]. We
demonstrate that all asymptotically Lifshitz space-times characterized by a
lapse funcion which tends to one when , present the
same behavior, in the sense that an external observer will see that photons
arrive at spatial infinity in a finite coordinate time. Also, we show that
radial photons in the proper system cannot determine the presence of the black
hole in the region , because the proper time results to be
independent of the lapse function .Comment: 5 pages, 4 figures, accepted for publication on EPJ
AdS and Lifshitz black hole solutions in conformal gravity sourced with a scalar field
In this paper we obtain exact asymptotically anti-de Sitter black hole
solutions and asymptotically Lifshitz black hole solutions with dynamical
exponents and of four-dimensional conformal gravity coupled with a
self-interacting conformally invariant scalar field. Then, we compute their
thermodynamical quantities, such as the mass, the Wald entropy and the Hawking
temperature. The mass expression is obtained by using the generalized off-shell
Noether potential formulation. It is found that the anti-de Sitter black holes
as well as the Lifshitz black holes with have zero mass and zero entropy,
although they have non-zero temperature. A similar behavior has been observed
in previous works, where the integration constant is not associated with a
conserved charge, and it can be interpreted as a kind of gravitational hair. On
the other hand, the Lifshitz black holes with dynamical exponent have
non-zero conserved charges, and the first law of black hole thermodynamics
holds. Also, we analyze the horizon thermodynamics for the Lifshitz black holes
with , and we show that the first law of black hole thermodynamics arises
from the field equations evaluated on the horizon. Furthermore, we study the
propagation of a conformally coupled scalar field on these backgrounds and we
find the quasinormal modes analytically in several cases. We find that for
anti-de Sitter black holes and Lifshitz black holes with , there is a
continuous spectrum of frequencies for Dirichlet boundary condition; however,
we show that discrete sets of well defined quasinormal frequencies can be
obtained by considering Neumann boundary conditions
Dirac Quasinormal Modes of New Type Black Holes in New Massive Gravity
We study new type black holes in three-dimensional New Massive Gravity and we
calculate analytically the quasinormal modes for fermionic perturbations for
some special cases. Then, we show that for these cases the new type black holes
are stable under fermionic field perturbations.Comment: improved version. arXiv admin note: text overlap with
arXiv:1306.5974, arXiv:1404.317
Nonsoluble Length Of Finite Groups with Commutators of Small Order
Let p be a prime. Every finite group G has a normal series each of whose
quotients either is p-soluble or is a direct product of nonabelian simple
groups of orders divisible by p. The non-p-soluble length of G is defined as
the minimal number of non-p-soluble quotients in a series of this kind.
We deal with the question whether, for a given prime p and a given proper
group variety V, there is a bound for the non-p-soluble length of finite groups
whose Sylow p-subgroups belong to V. Let the word w be a multilinear
commutator. In the present paper we answer the question in the affirmative in
the case where p is odd and the variety is the one of groups in which the
w-values have orders dividing a fixed number
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