676 research outputs found

    Lower bound on the spectral dimension near a black hole

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    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

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    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

    Path integral for half-binding potentials as quantum mechanical analog for black hole partition functions

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    The semi-classical approximation to black hole partition functions is not well-defined, because the classical action is unbounded and the first variation of the uncorrected action does not vanish for all variations preserving the boundary conditions. Both problems can be solved by adding a Hamilton-Jacobi counterterm. I show that the same problem and solution arises in quantum mechanics for half-binding potentials.Comment: 6 pages, proceedings contribution to "Path integrals - New Trends and Perspectives", Dresden, September 200

    Centrifugal deformations of the gravitational kink

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    The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.Comment: 8 pages, no figure

    The Volume of 2D Black Holes

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    It is shown that the definition for the volume of stationary black holes advocated in hep-th/0508108 readily generalizes to the case of dilaton gravity in D=2. The dilaton field is included as part of the measure. A feature observed in D=3 and 4 has been the impossibility to obtain infinite volume while retaining finite area without encountering some kind of pathology. It is demonstrated that this also holds in D=2. Consistency with spherically reduced gravity is shown. For the Witten black hole it is found that the area is proportional to the volume.Comment: 9 pages, 3 figures, uses iopart_mod.cl

    A note on dilaton gravity with non-smooth potentials

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    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
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