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 $L_0$ 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