MaxEnt and dynamical information

The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we show both theoretically and numerically that power laws and power laws with exponential cut-offs emerge as equilibrium densities in proportional and other dynamics

No-horizon theorem for vacuum gravity with spacelike G1 isometry groups

We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.Comment: 6 pages, revtex4; published in Phys. Rev. D Rapid Com

Complex Kerr Geometry and Nonstationary Kerr Solutions

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in PRD), added the relation to twistors and algorithm of numerical computations, English is correcte

Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"

The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove this result we first describe a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering, in a gauge characterized by the introduction of a double null cone foliation of the spacetime. Then we prove that the existence region for the analytic solutions can be extended to a larger region which depends only on the validity of the apriori estimates for the Weyl equations, associated to the "Bel-Robinson norms". In particular if the initial data are sufficiently small we show that the analytic solution is global. Before showing how to extend the existence region we describe the same result in the case of the Burger equation, which, even if much simpler, nevertheless requires analogous logical steps required for the general proof. Due to length of this work, in this paper we mainly concentrate on the definition of the gauge we use and on writing in a "geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski theorem is adapted to the characteristic problem for the Einstein equations and we describe how the existence region can be extended in the case of the Burger equation. Finally we describe the structure of the extension proof in the case of the Einstein equations. The technical parts of this last result is the content of a second paper.Comment: 68 page

Electrodynamic Radiation Reaction and General Relativity

We argue that the well-known problem of the instabilities associated with the self-forces (radiation reaction forces) in classical electrodynamics are possibly stabilized by the introduction of gravitational forces via general relativity

Hamiltonian dynamics for Einstein's action in G→\rightarrow0 limit

The Hamiltonian analysis for the Einstein's action in $G\to 0$ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $Gto 0$ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis

Fate of Zero-Temperature Ising Ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically ``blinking'' metastable states.Comment: 4 pages in column format, 6 figure

Rotating metrics admitting non-perfect fluids in General Relativity

In this paper, by applying Newman-Janis algorithm in spherical symmetric metrics, a class of embedded rotating solutions of field equations is presented. These solutions admit non-perfect fluidsComment: LaTex, 39 page

Angular momentum of isolated systems

Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with different cuts of scri can be identified as manifolds (but not as vector spaces). The result is a well-defined, Bondi-Metzner-Sachs-invariant notion of angular momentum in a radiating space-time; the difficulties and ambiguities previously encountered are attached to attempts to express this in special-relativistic terms, and in particular to attempts to identify a single Minkowski space of origins. Unlike the special-relativistic case, the angular momentum cannot be represented by a purely j=1 quantity M_{ab}, but has higher-j contributions as well. Applying standard kinematic prescriptions, these higher-j contributions are shown to correspond precisely to the shear. Thus it appears that shear and angular momentum should be regarded as different aspects of a single unified concept.Comment: 23 pages, to appear in GR

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

Observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are black holes. As observations improve, it becomes possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or with gravitational-waves) and to test whether they have the characteristics of black hole orbits in general relativity. Such measurements can be used to map the spacetime of a massive compact object, testing whether the object's multipoles satisfy the strict constraints of the black hole hypothesis. Such a test requires that we compare against objects with the ``wrong'' multipole structure. In this paper, we present tools for constructing bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. The spacetimes which we present are good deep into the strong field of the object -- we do not use a large r expansion, except to make contact with weak field intuition. Also, our spacetimes reduce to the black hole spacetimes of general relativity when the ``bumpiness'' is set to zero. We propose bumpy black holes as the foundation for a null experiment: if black hole candidates are the black holes of general relativity, their bumpiness should be zero. By comparing orbits in a bumpy spacetime with those of an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are the black holes of general relativity. (Abridged)Comment: 16 pages + 2 appendices + 3 figures. Submitted to PR