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

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

Charged Lifshitz black holes from general covariance breaking

In this work we use a general covariance breaking method to obtain a class of topological charged black holes whose background geometry asymptotically approaches Lifshitz spacetimes. We discuss how this mechanism affects Einstein's equations and explore the thermodynamics and critical behavior of the solution found.Comment: 9 pages, 4 figure

Rotating Relativistic Thin Disks

Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to the geometric mean of the prograde and retrograde geodesic circular velocities of test particles moving on the disk. We also found that for generic disks we can have zones with heat flow. For the two families of models studied the boundaries that separate the zones with and without heat flow are not stable against radial perturbations (ring formation).Comment: 18 eps figures, to be published PR

Relativistic Static Thin Disks with Radial Stress Suport

New solutions for static non-rotating thin disks of finite radius with nonzero radial stress are studied. A method to introduce either radial pressure or radial tension is presented. The method is based on the use of conformal transformations.Comment: 19 pages, LaTeX, 7 figures, submitted to Class. Quan. Gra

Relativistic Static Thin Disks: The Counter-Rotating Model

A detailed study of the Counter-Rotating Model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, there is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities and stable against radial perturbations. The CRM obtained are in agree with the strong energy condition, but there are regions of the disks with negative energy density, in violation of the weak energy condition.Comment: 19 pages, 6 figures. Submitted to Physical Review

Architectural mismatch tolerance

The integrity of complex software systems built from existing components is becoming more dependent on the integrity of the mechanisms used to interconnect these components and, in particular, on the ability of these mechanisms to cope with architectural mismatches that might exist between components. There is a need to detect and handle (i.e. to tolerate) architectural mismatches during runtime because in the majority of practical situations it is impossible to localize and correct all such mismatches during development time. When developing complex software systems, the problem is not only to identify the appropriate components, but also to make sure that these components are interconnected in a way that allows mismatches to be tolerated. The resulting architectural solution should be a system based on the existing components, which are independent in their nature, but are able to interact in well-understood ways. To find such a solution we apply general principles of fault tolerance to dealing with arch itectural mismatche

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

Exact General Relativistic Disks with Magnetic Fields

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bicak, Lynden-Bell and Katz [Phys. Rev. D47, 4334, 1993] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.Comment: 21 pages, 11 figures, uses package graphics, accepted in PR

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