Two-Dimensional Black Holes and Planar General Relativity

The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.Comment: 11 pages, plainte

Fast method for the determination of short-chain-length polyhydroxyalkanoates (scl-PHAs) in bacterial samples by In Vial-Thermolysis (IVT)

none8siA new method based on the GC–MS analysis of thermolysis products obtained by treating bacterial samples at a high temperature (above 270 C) has been developed. This method, here named “In-Vial- Thermolysis” (IVT), allowed for the simultaneous determination of short-chain-length polyhydrox- yalkanoates (scl-PHA) content and composition. The method was applied to both single strains and microbial mixed cultures (MMC) fed with different carbon sources. The IVT procedure provided similar analytical performances compared to previous Py-GC–MS and Py- GC-FID methods, suggesting a similar application for PHA quantitation in bacterial cells. Results from the IVT procedure and the traditional methanolysis method were compared; the correlation between the two datasets was fit for the purpose, giving a R2 of 0.975. In search of further simplification, the rationale of IVT was exploited for the development of a “field method” based on the titration of thermolyzed samples with sodium hydrogen carbonate to quantify PHA inside bacterial cells. The accuracy of the IVT method was fit for the purpose. These results lead to the possibility for the on-line measurement of PHA productivity. Moreover, they allow for the fast and inexpensive quantification/characterization of PHA for biotechnological process control, as well as investigation over various bacterial communities and/or feeding strategies.mixedF. Abbondanzi; G. Biscaro; G. Carvalho; L. Favaro; P. Lemos; M. Paglione; C. Samorì; C. TorriF. Abbondanzi; G. Biscaro; G. Carvalho; L. Favaro; P. Lemos; M. Paglione; C. Samorì; C. Torr

The Two-Dimensional Analogue of General Relativity

General Relativity in three or more dimensions can be obtained by taking the limit $\omega\rightarrow\infty$ 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 $\omega\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.Comment: 8 pages, LaTeX, preprint DF/IST-17.9

BLACK HOLES IN THREE-DIMENSIONAL DILATON GRAVITY THEORIES

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

Thermodynamics of toroidal black holes

The thermodynamical properties of toroidal black holes in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and specific heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, as the one encountered for spherical black holes.Comment: 11 pages, 2 eps figures, revte

Exact General Relativistic Perfect Fluid Disks with Halos

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic coordinates. The same method is applied to different exactsolutions to the Einstein'sequations that represent static spheres of perfect fluids. We construct several models of disks with axially symmetric perfect fluid halos. All disks have some common features: surface energy density and pressures decrease monotonically and rapidly with radius. As the ``cut'' parameter $a$ decreases, the disks become more relativistic, with surface energy density and pressure more concentrated near the center. Also regions of unstable circular orbits are more likely to appear for high relativistic disks. Parameters can be chosen so that the sound velocity in the fluid and the tangential velocity of test particles in circular motion are less then the velocity of light. This tangential velocity first increases with radius and reaches a maximum.Comment: 22 pages, 25 eps.figs, RevTex. Phys. Rev. D to appea

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

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

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

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

Gravitational collapse to toroidal, cylindrical and planar black holes

Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to form a toroidal black hole. According to the analytical model presented, the collapsing matter absorbs energy in the form of radiation (be it scalar, neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon decompactification of one or two coordinates of the torus one gets collapsing solutions of cylindrical or planar matter onto black strings or black membranes, respectively. The results have implications on the hoop conjecture.Comment: 6 pages, Revtex, modifications in the title and in the interpretation of some results, to appear in Physical Review