8,336 research outputs found

    Stationary Black Holes in a Generalized Three-Dimensional Theory of Gravity

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    We consider a generalized three-dimensional theory of gravity which is specified by two fields, the graviton and the dilaton, and one parameter. This theory contains, as particular cases, three-dimensional General Relativity and three-dimensional String Theory. Stationary black hole solutions are generated from the static ones using a simple coordinate transformation. The stationary black holes solutions thus obtained are locally equivalent to the corresponding static ones, but globally distinct. The mass and angular momentum of the stationary black hole solutions are computed using an extension of the Regge and Teitelboim formalism. The causal structure of the black holes is described.Comment: 12 pages, Late

    Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

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    It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.Comment: 6 pages, no figures, Revtex4. Some discussions on the physical nature of the interior solution and on the omega->infinity limit and some references added. Version to appear in Phys. Rev.

    BLACK HOLES IN THREE-DIMENSIONAL DILATON GRAVITY THEORIES

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    Three dimensional black holes in a generalized dilaton gravity action theory are analysed. The theory is specified by two fields, the dilaton and the graviton, and two parameters, the cosmological constant and the Brans-Dicke parameter. It contains seven different cases, of which one distinguishes as special cases, string theory, general relativity and a theory equivalent to four dimensional general relativity with one Killing vector. We study the causal structure and geodesic motion of null and timelike particles in the black hole geometries and find the ADM masses of the different solutions.Comment: 19 pages, latex, 4 figures as uuencoded postscript file

    The Two-Dimensional Analogue of General Relativity

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    General Relativity in three or more dimensions can be obtained by taking the limit ω\omega\rightarrow\infty in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit ω\omega\rightarrow\infty of the two-dimensional Brans-Dicke theory.Comment: 8 pages, LaTeX, preprint DF/IST-17.9

    The Three-Dimensional BTZ Black Hole as a Cylindrical System in Four-Dimensional General Relativity

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    It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.Comment: Latex, 9 page

    Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes

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    A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti-de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recovers the usual form of the Virasoro algebra, obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzero central charge c. The entropy is then obtained via the Cardy formula.Comment: 21 page

    Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop and cosmic censorship conjectures

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    Gravitational collapse of radiation in an anti-de Sitter background is studied. For the spherical case, the collapse proceeds in much the same way as in the Minkowski background, i.e., massless naked singularities may form for a highly inhomogeneous collapse, violating the cosmic censorship, but not the hoop conjecture. The toroidal, cylindrical and planar collapses can be treated together. In these cases no naked singularity ever forms, in accordance with the cosmic censorship. However, since the collapse proceeds to form toroidal, cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter spacetime is violated.Comment: 4 pages, Revtex Journal: to appear in Physical Review

    A sufficient optimality condition for delayed state-linear optimal control problems

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    We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear optimal control problem to an equivalent non-delayed problem. This allows us to use a well-known theorem that ensures a sufficient optimality condition for non-delayed state-linear optimal control problems. An example is given in order to illustrate the obtained result.Comment: This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series B' (DCDS-B), ISSN 1531-3492, eISSN 1553-524X, available at [http://www.aimsciences.org/journal/1531-3492]. Paper Submitted 31/Dec/2017; Revised 13/April/2018; Accepted 11/Jan/201

    Thermodynamics of the two-dimensional black hole in the Teitelboim-Jackiw theory

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    The two-dimensional theory of Teitelboim and Jackiw has constant and negative curvature. In spite of this, the theory admits a black hole solution with no singularities. In this work we study the thermodynamics of this black hole using York's formalism.Comment: 16 pages, Late
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