Patricio S. Letelier

Exact self‐gravitating disks and rings: A solitonic approach

The Belinsky–Zakharov version of the inverse scattering method is used to generate a large class of solutions to the vacuum Einstein equations representing uniformly accelerating and rotating disks and rings. The solutions studied are generated from a simple class of static disks and rings that can be expressed in a simple form using suitable complex functions of the usual cylindrical coordinates.

Superposition of Morgan and Morgan discs with a Schwarzschild black hole

The exact superposition of a black hole and a thin disc is considered. The disc is made of counter-rotating particles and belongs to the Morgan and Morgan family (1969). There are three parameters to play with, the black hole mass, and the disc mass and radius. The superposed exact solution comprehends several configurations, some yield mass ratios in conformity with the usual accretion discs. There is also a remarkable configuration of a black hole surrounded by a disc made of pure superluminal matter up to the edge, which is at the photonic orbit.

Fractal basins in Hénon–Heiles and other polynomial potentials

Abstract The dynamics of several Hamiltonian systems of two degrees of freedom with polynomial potentials is examined. All these systems present unbounded trajectories escaping along different routes. The motion in these open systems is characterized by a fractal boundary (and its corresponding fractal dimension) separating the basins of the escape routes. The fractal (basin boundary) dimensions for these systems are studied in some detail.

Galaxy rotation curves from general relativity with renormalization group corrections

We consider the application of quantum corrections computed using renormalization group arguments in the astrophysical domain and show that, for the most natural interpretation of the renormalization group scale parameter, a gravitational coupling parameter G varying 10−7 of its value across a galaxy (which is roughly a variation of 10−12 per light-year) is sufficient to generate galaxy rotation curves in agreement with the observations. The quality of the resulting fit is similar to the Isothermal profile quality once both the shape of the rotation curve and the mass-to-light ratios are considered for evaluation. In order to perform the analysis, we use recent high quality data from nine regular disk galaxies. For the sake of comparison, the same set of data is modeled also for the Modified Newtonian Dynamics (MOND) and for the recently proposed Scalar Tensor Vector Gravity (STVG). At face value, the model based on quantum corrections clearly leads to better fits than these two alternative theories.

Relativistic and Newtonian Core-Shell Models: Analytical and Numerical Results

We make a detailed analysis of the exact relativistic core-shell models recently proposed to describe a black hole or neutron star surrounded by an axially symmetric, hollow halo of matter and in a seminal sense also galaxies, since there are massive shell-like structures—as, for example, rings and shells—surrounding many of them and also evidence for many galactic nuclei hiding black holes. We discuss the unicity of the models in relation to their analyticity at the black hole horizon and to the full elimination of axial (conical) singularities. We also consider Newtonian and linearized core-shell models, on their own to account for dust shells and rings around galaxies and supernovae and star remnants around their centers, and also as limiting cases of the corresponding relativistic models to gain physical insight. Second, these models are generic enough to numerically study the role played by the presence/lack of discrete reflection symmetries about planes, i.e., the presence/lack of equatorial planes, in the chaotic behavior of the orbits. This is to be contrasted with the almost universal acceptance of reflection symmetries as default assumptions in galactic modeling. We also compare the related effects if we change a true central black hole by a Newtonian central mass. Our main numerical findings are as follows: (1) The breakdown of the reflection symmetry about the equatorial plane in both Newtonian and relativistic core-shell models (a) enhances in a significant way the chaotic behavior of orbits in reflection symmetric oblate shell models and (b) inhibits significantly also the occurrence of chaos in reflection symmetric prolate shell models. In particular, in the prolate case the lack of the reflection symmetry provides the phase space with a robust family of regular orbits that is otherwise not found at higher energies. (2) The relative extents of the chaotic regions in the relativistic cases (i.e., with a true central black hole) are significantly larger than in the corresponding Newtonian ones (which have just a -1/r central potential).

Static and stationary multiple soliton solutions to the Einstein equations

The application of the Belinsky–Zakharov solution‐generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd‐number soliton solutions is investigated. These solutions represent solitonic perturbations of Euclidean metrics. The possibility of using instantons as seed solutions is also investigated. The one‐ and two‐soliton solutions generated from a diagonal seed solution are studied. As an application, a unified derivation of some well‐known static solutions, like the Schwarzschild metric and the Chazy–Curzon metric, as well as other new metrics is presented. By using these metrics as seed solutions, some known stationary solutions, like the Kerr‐NUT metric, the double Kerr metric, and the rotating Weyl C‐metric, as well as other new metrics are also derived in a unified way.

Relativistic static thin discs with radial stress support

New solutions for static non-rotating thin discs of finite radius with non-zero 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.

TWO FAMILIES OF EXACT DISKS WITH A CENTRAL BLACK HOLE

The gravitational field of a configuration formed by a static disk and a Schwarzschild black hole is analysed for two families of disks. The matter of the disks is made of counter-rotating particles with as many particles rotating to one side as to the other, in such a way that the net angular momentum is zero and the disk is static. The first family consists of peculiar disks, in the sense that they are generated by two opposite dipoles. The particles of the disk have no pressure or centrifugal support. However, when there is a central black hole, centrifugal balance in the form of counter-rotation appears. The second family is a one parameter family of self-similar disks which includes at one end a Newtonian disk, and at the other a topological defect of spacetime. The presence of the black hole impresses more rotational velocity to the particles. These two families are of infinite extent. Some interesting physical effects are studied.

Double Kerr-NUT spacetimes: spinning strings and spinning rods

Abstract The spinning conic singularities necessary to equilibrate two collinear Kerr-NUT black holes are studied in some detail. We find that the generic case is represented by two black holes kept apart by infinitely long spinning strings. Particular cases can also be equilibrated with spinning rods.

Space–time defects

The theory of distributions in Riemannian spaces due to Lichnerowicz is used to obtain exact solutions to the Einstein equations for space–times that have null Riemann–Christoffel curvature tensors everywhere except on a hypersurface. The cases of spherically, cylindrically, plane, and axially symmetric space–times in which the matter content of the singular surfaces can be described by a barotropic equation of state are treated in some detail. Solutions with null curvature tensor, except on (a) concentric spheres, (b) concentric cylinders, (c) parallel planes, and (d) parallel discs, are exhibited and studied.