44 research outputs found
G\"odel Type Metrics in Three Dimensions
We show that the G{\" o}del type Metrics in three dimensions with arbitrary
two dimensional background space satisfy the Einstein-perfect fluid field
equations. There exists only one first order partial differential equation
satisfied by the components of fluid's velocity vector field. We then show that
the same metrics solve the field equations of the topologically massive gravity
where the two dimensional background geometry is a space of constant negative
Gaussian curvature. We discuss the possibility that the G{\" o}del Type Metrics
to solve the Ricci and Cotton flow equations. When the vector field
is a Killing vector field we finally show that the stationary G{\" o}del Type
Metrics solve the field equations of the most possible gravitational field
equations where the interaction lagrangian is an arbitrary function of the
electromagnetic field and the curvature tensors.Comment: 17 page
Nonpropagation of massive mode on AdS2 in topologically massive gravity
Making use of Achucarro-Ortiz (AO) type of dimensional reduction, we study
the topologically massive gravity with a negative cosmological constant on AdS2
spacetimes. For a constant dilaton, this two-dimensional model also admits
three AdS2 vacuum solutions, which are related to two AdS3 and warped AdS3
backgrounds with an identification upon uplifting three dimensions. We carry
out the perturbation analysis around these backgrounds to find what is a
physically propagating field. However, it turns out that there is no
propagating massive mode on AdS2 background, in contrast to the Kaluza-Klein
(KK) type of dimensional reduction. We note that two dimensionally reduced
actions are different and thus, the non-equivalence of their on-shell
amplitudes is obtained.Comment: 19 pages, version to appear in EPJ
Chiral Topologically Massive Gravity and Extremal B-F Scalars
At a critical ``chiral'' coupling, topologically massive gravity with a
negative cosmological constant exhibits several unusual features, including the
emergence of a new logarithmic branch of solutions and a linearization
instability for certain boundary conditions. I show that at this coupling, the
linearized theory may be parametrized by a free scalar field at the
Breitenlohner-Freedman bound, and use this description to investigate these
features.Comment: 16 pages; v2: added references, typos correcte
Absorption cross section in the topologically massive gravity at the critical point
The absorption cross section for the the warped AdS black hole background
shows that it is larger than the area even if the s-wave limit is considered.
It raises some question whether the deviation from the areal cross section is
due to the warped configuration of the geometry or the rotating coordinate
system, where these two effects are mixed up in the warped AdS black hole.
So, we study the low-frequency scattering dynamics of propagating scalar fields
under the warped AdS background at the critical point which reduces to the
BTZ black hole in the rotating frame without the warped factor, which shows
that the deformation effect at the critical point does not appear.Comment: 12 pages, LaTe
Quasi-normal modes of warped black holes and warped AdS/CFT correspondence
We analytically calculate the quasi-normal modes of various perturbations of
spacelike stretched and null warped black holes. From AdS/CFT
correspondence, these quasi-normal modes are expected to appear as the poles in
momentum space of retarded Green functions of dual operators in CFT at finite
temperature. We find that this is indeed the case, after taking into account of
the subtle identification of quantum numbers. The subtlety comes from the fact
that only after appropriate coordinate transformation the asymptotic geometries
of warped black holes are the same as the ones of warped spacetimes. We
show that in general the quasi-normal modes are in good agreement with the
prediction of the warped AdS/CFT correspondence, up to a constant factor. As a
byproduct, we compute the conformal dimensions of boundary operators dual to
the perturbations. Our result gives strong support to the conjectured warped
AdS/CFT correspondence.Comment: 26 pages; typos corrected, references added; more clarifications,
match the version to appear in JHE
Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
We propose a set of consistent boundary conditions containing the spacelike
warped black holes solutions of Topologically Massive Gravity. We prove that
the corresponding asymptotic charges whose algebra consists in a Virasoro
algebra and a current algebra are finite, integrable and conserved. A similar
analysis is performed for the timelike warped AdS_3 spaces which contain a
family of regular solitons. The energy of the boundary Virasoro excitations is
positive while the current algebra leads to negative (for the spacelike warped
case) and positive (for the timelike warped case) energy boundary excitations.
We discuss the relationship with the Brown-Henneaux boundary conditions.Comment: 16 pages, ESI proceedings, v2: typos corrected, published versio
Topologically Massive Gravity and the AdS/CFT Correspondence
We set up the AdS/CFT correspondence for topologically massive gravity (TMG)
in three dimensions. The first step in this procedure is to determine the
appropriate fall off conditions at infinity. These cannot be fixed a priori as
they depend on the bulk theory under consideration and are derived by solving
asymptotically the non-linear field equations. We discuss in detail the
asymptotic structure of the field equations for TMG, showing that it contains
leading and subleading logarithms, determine the map between bulk fields and
CFT operators, obtain the appropriate counterterms needed for holographic
renormalization and compute holographically one- and two-point functions at and
away from the 'chiral point' (mu = 1). The 2-point functions at the chiral
point are those of a logarithmic CFT (LCFT) with c_L = 0, c_R = 3l/G_N and b =
-3l/G_N, where b is a parameter characterizing different c = 0 LCFTs. The bulk
correlators away from the chiral point (mu \neq 1) smoothly limit to the LCFT
ones as mu \to 1. Away from the chiral point, the CFT contains a state of
negative norm and the expectation value of the energy momentum tensor in that
state is also negative, reflecting a corresponding bulk instability due to
negative energy modes.Comment: 54 pages, v2: added comments and reference
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Topologically massive gravity on AdS spacetimes
We study the topologically massive gravity with a negative cosmological
constant on AdS spacetimes by making use of dimensional reduction. For a
constant dilaton, this two-dimensional model admits three AdS vacuum
solutions, which are related to AdS and warped AdS with an
identification upon uplifting three dimensions. We carry out the perturbation
analysis around these backgrounds to find what is a physically propagating
field. It turns out that a mode of is merely a redundant
field of dilaton in the absence of Chern-Simons terms, while it
becomes a massive scalar in the presence of Chern-Simons terms. This shows
clearly that the proper number of physically propagating degrees of freedom is
one for the topologically massive gravity. Moreover, at the points of
, becomes a massless scalar which implies that there is no
physically propagating degrees of freedom at the chiral point.Comment: 24 pages, 3 figures, added appendix, version to appear in JHE
Chiral Gravity in Three Dimensions
Three dimensional Einstein gravity with negative cosmological constant
-1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient
1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate
unitary or positivity for generic \mu due to negative-energy massive gravitons.
However at the critical value \mu\ell=1, the massive gravitons disappear and
BTZ black holes all have mass and angular momentum related by \ell M=J. The
corresponding chiral quantum theory of gravity is conjectured to exist and be
dual to a purely right-moving boundary CFT with central charges
(c_L,c_R)=(0,3\ell /G).Comment: 21 pages, published version, typos corrected, more reference adde