Lower bound on the spectral dimension near a black hole

We consider an evaporating Schwarzschild black hole in a framework in which the spectral dimension of spacetime varies continuously from four at large distances to a number smaller than three at small distances, as suggested by various approaches to quantum gravity. We demonstrate that the evaporation stops when the horizon radius reaches a scale at which spacetime becomes effectively 3-dimensional, and argue that an observer remaining outside the horizon cannot probe the properties of the black hole at smaller scales. This result is universal in the sense that it does not depend on the details of the effective dimension as a function of the diffusion time. Observers falling into the black hole can resolve smaller scales, as can external observers in the presence of a cosmological constant. Even in these cases, though, we obtain an absolute bound D>2 on the effective dimension that can be seen in any such attempt to measure the properties of the black hole.Comment: 6 pp, 2 eps fig

Poisson-sigma model for 2D gravity with non-metricity

We present a Poisson-sigma model describing general 2D dilaton gravity with non-metricity, torsion and curvature. It involves three arbitrary functions of the dilaton field, two of which are well-known from metric compatible theories, while the third one characterizes the local strength of non-metricity. As an example we show that alpha' corrections in 2D string theory can generate (target space) non-metricity.Comment: 9 page

A note on dilaton gravity with non-smooth potentials

Recent interest in brane world models motivates the investigation of generic first order dilaton gravity actions, with potentials having some non-smoothness. We consider two different types of \delta-like contributions in the action and analyse their effects on the solutions. Furthermore a second source of non-smoothness arises due to the remaining ambiguities in the solutions in the separated smooth patches, after fixing all other constants by matching and asymptotic conditions. If moreover staticity is assumed, we explicitly construct exact solutions. With the methods described, for example models with point like sources or brane world models (where the second source of non-smoothness becomes crucial), can now be treated as non-smooth dilaton gravity theories.Comment: 10 pages, 1 table; two new references, some typos corrected, Dedicated to Wolfgang Kummer at the occasion of his Emeritierun

Black holes as boundaries in 2D dilaton supergravity

We discuss 2D dilaton supergravity in the presence of boundaries. Generic ones lead to results different from black hole horizon boundaries. In particular, the respective numbers of physical degrees of freedom differ, thus generalizing the bosonic results of hep-th/0512230.Comment: 6 pages; to appear in the proceedings of the Eleventh Marcel Grossman Meetin

Kaluza-Klein reduction of conformally flat spaces

Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions. The corresponding equations are particularly elegant for the reduction from four to three dimensions. Assuming circular symmetry leads to explicit solutions which also arise from specific two-dimensional dilaton gravity actions.Comment: 19 pages, invited contribution to IJMPD, v2: corrected sign in Eq. (48), final versio

Canonical bifurcation in higher derivative, higher spin, theories

We present a non-perturbative canonical analysis of the D=3 quadratic-curvature, yet ghost-free, model to exemplify a novel, "constraint bifurcation", effect. Consequences include a jump in excitation count: a linearized level gauge variable is promoted to a dynamical one in the full theory. We illustrate these results with their concrete perturbative counterparts. They are of course mutually consistent, as are perturbative findings in related models. A geometrical interpretation in terms of propagating torsion reveals the model's relation to an (improved) version of Einstein-Weyl gravity at the linearized level. Finally, we list some necessary conditions for triggering the bifurcation phenomenon in general interacting gauge systems.Comment: 10 pages, v2: typos corrected, v3: new title to reflect greatly expanded version, to appear in special issue of J Phys A (eds, M Vasiliev & M Gaberdiel

Unitarity in three-dimensional flat space higher spin theories

We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean $W_4^{(2-1-1)}$ algebra. We extend this no-go result to rule out unitary "multi-graviton" theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.Comment: 34 pp, v2: added two paragraphs in section 5.3 + minor change