16 research outputs found
Gravitational non-commutativity and G\"odel-like spacetimes
We derive general conditions under which geodesics of stationary spacetimes
resemble trajectories of charged particles in an electromagnetic field. For
large curvatures (analogous to strong magnetic fields), the quantum
mechanicical states of these particles are confined to gravitational analogs of
{\it lowest Landau levels}. Furthermore, there is an effective
non-commutativity between their spatial coordinates. We point out that the
Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of
the above type and compute the effective non-commutativities that they induce.
We show that the non-commutativity for G\"odel spacetime is identical to that
on the fuzzy sphere. Finally, we show how the star product naturally emerges in
Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the
star product). 10 pages, Revtex. To appear in General Relativity and
Gravitatio
The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity
We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de
Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized
two-particle Calogero-Sutherland model. This correspondence is established by
formulating the JT model of (A)dS gravity in two dimensions as a topological
gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the
boundary of (A)dS space. The appearance of cyclic coordinates allows then a
further reduction to the Calogero-Sutherland quantum mechanical model.Comment: 16 pages, LaTeX, no figures, uses JHEP.cls. v2: Some references and
comments added. v3: Minor errors correcte
Holography: 2-D or not 2-D?
As was recently pointed out by Cadoni, a certain class of two-dimensional
gravitational theories will exhibit (black hole) thermodynamic behavior that is
reminiscent of a free field theory. In the current letter, a direct
correspondence is established between these two-dimensional models and the
strongly curved regime of (arbitrary-dimensional) anti-de Sitter gravity. On
this basis, we go on to speculatively argue that two-dimensional gravity may
ultimatley be utilized for identifying and perhaps even understanding
holographic dualities.Comment: 8 pages, Revtex; (v2) references and footnote added; (v3) discussion
on page 5 revise
Gravitational lensing by a charged black hole of string theory
We study gravitational lensing by the
Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole of
heterotic string theory and obtain the angular position and magnification of
the relativistic images. Modeling the supermassive central object of the galaxy
as a GMGHS black hole, we estimate the numerical values of different
strong-lensing parameters. We find that there is no significant string effect
present in the lensing observables in the strong-gravity scenario.Comment: 6 page
Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch
We consider a self-interacting scalar field whose mass saturates the
Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a
negative cosmological constant in D \geq 3 dimensions. It is shown that the
asymptotic behavior of the metric has a slower fall-off than that of pure
gravity with a localized distribution of matter, due to the back-reaction of
the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln
r for large radius r.
We find the asymptotic conditions on the fields which are invariant under the
same symmetry group as pure gravity with negative cosmological constant
(conformal group in D-1 dimensions). The generators of the asymptotic
symmetries are finite even when the logarithmic branch is considered but
acquire, however, a contribution from the scalar field.Comment: 7 pages, CECS style, references adde
Black hole mass and angular momentum in 2+1 gravity
We propose a new definition for the mass and angular momentum of neutral or
electrically charged black holes in 2+1 gravity with two Killing vectors. These
finite conserved quantities, associated with the SL(2,R) invariance of the
reduced mechanical system, are shown to be identical to the quasilocal
conserved quantities for an improved gravitational action corresponding to
mixed boundary conditions. They obey a general Smarr-like formula and, in all
cases investigated, are consistent with the first law of black hole
thermodynamics. Our framework is applied to the computation of the mass and
angular momentum of black hole solutions to several field-theoretical models.Comment: 23 pages, 3 references added, to be published in Physical Review
Relativistic Electromagnetic Mass Models: Charged Dust Distribution in Higher Dimensions
Electromagnetic mass models are proved to exist in higher dimensional theory
of general relativity corresponding to charged dust distribution. Along with
the general proof a specific example is also sited as a supporting candidate.Comment: Latex, 7 pages. Accepted in Astrophysics and Space Scienc
Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
General matterless--theories in 1+1 dimensions include dilaton gravity,
Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion
and higher power gravity, and even models of spherically symmetric d = 4
General Relativity. Their recent identification as special cases of
'Poisson--sigma--models' with simple general solution in an arbitrary gauge,
allows a comprehensive discussion of the relation between the known absolutely
conserved quantities in all those cases and Noether charges, resp. notions of
quasilocal 'energy--momentum'. In contrast to Noether like quantities,
quasilocal energy definitions require some sort of 'asymptotics' to allow an
interpretation as a (gauge--independent) observable. Dilaton gravitation,
although a little different in detail, shares this property with the other
cases. We also present a simple generalization of the absolute conservation law
for the case of interactions with matter of any type.Comment: 21 pages, LaTeX-fil
Holographic Central Charge for 2-Dimensional de Sitter Space
Recently, investigations have begun into a holographic duality for
two-dimensional de Sitter space. In this paper, we evaluate the associated
central charge, using a modified version of the canonical Hamiltonian method
that was first advocated by Catelani {\it et al}. Our computation agrees with
that of a prior work (Cadoni {\it et al}), but we argue that the method used
here is, perhaps, aesthetically preferable on holographic grounds. We also
confirm an agreement between the Cardy and thermodynamic entropy, thus
providing further support for the conjectured two-dimensional de
Sitter/conformal field theory correspondence.Comment: 19 pages, Latex; discussion (Section 4) and references adde
Near-Horizon Conformal Symmetry and Black Hole Entropy in Any Dimension
Recently, Carlip proposed a derivation of the entropy of the two-dimensional
dilatonic black hole by investigating the Virasoro algebra associated with a
newly introduced near-horizon conformal symmetry. We point out not only that
the algebra of these conformal transformations is not well defined on the
horizon, but also that the correct use of the eigenvalue of the operator
yields vanishing entropy. It has been shown that these problems can be resolved
by choosing a different basis of the conformal transformations which is regular
even at the horizon. We also show the generalization of Carlip's derivation to
any higher dimensional case in pure Einstein gravity. The entropy obtained is
proportional to the area of the event horizon, but it also depends linearly on
the product of the surface gravity and the parameter length of a horizon
segment in consideration. We finally point out that this derivation of black
hole entropy is quite different from the ones proposed so far, and several
features of this method and some open issues are also discussed.Comment: 14 pages, no figur