Extended 2d generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2d relativity principle, which introduces a non-trivial center in the 2d Poincare algebra. Then we work out the reduced phase-space of the anomaly-free 2d relativistic particle, in order to show that it lives in a noncommutative 2d Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well-defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2d generalized dilaton gravity models by a specific Maxwell component, which gauges the extra symmetry associated with the center of the 2d Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of space-time. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved space-time, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides a strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.Comment: 21 pages, IOP LaTeX2e preprint classfile, Improved discussions, Minor corrections, More didactic, More self-contained, New results concerning noncommutativity in curved space-time, Accepted for publication in Classical and Quantum Gravity on 02 Jul 200

Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure

Resonant Orbits in Triaxial Galaxies

Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form l\omega_1 +m\omega_2+n\omega_3=0 between the three fundamental frequencies. Resonant orbits are confined to a membrane; they play roughly the same role, in three dimensions, that closed orbits play in two. Stable resonant orbits avoid the center of the potential; orbits that are thick enough to pass near the center are typically stochastic. Very near the center, where the gravitational potential is dominated by the black hole, resonant orbits continue to exist, including at least one family whose elongation is parallel to the long axes of the triaxial figure.Comment: 20 Latex pages, 11 Postscript figures. Submitted to The Astronomical Journa

The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang

We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe. The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations without invoking superluminal expansion (inflation). The scenario relies, instead, on physical phenomena that arise naturally in theories based on extra dimensions and branes. As an example, we present our scenario predominantly within the context of heterotic M-theory. A prediction that distinguishes this scenario from standard inflationary cosmology is a strongly blue gravitational wave spectrum, which has consequences for microwave background polarization experiments and gravitational wave detectors.Comment: 67 pages, 4 figures. v2,v3: minor corrections, references adde

The Cardy-Verlinde equation in a spherical symmetric gravitational collapse

The Cardy-Verlinde formula is analyzed in the contest of the gravitational collapse. Starting from the holographic principle, we show how the equations for a homogeneous and isotropic gravitational collapse describe the formation of the black hole entropy. Some comments on the role of the entangled entropy and the connection with the c-theorem are made

Dissipative motion in galaxies with non-axisymmetric potentials

Due to the clumpy nature of the self gravitating gas composing the interstellar medium, it is not clear whether galactic gas dynamics can be discussed in terms of standard hydrodynamics. Nevertheless, it is clear that certain generic properties related to orbital structure in a given potential and the effect of dissipation can be used to qualitatively understand gas motion in galaxies. The effect of dissipation is examined in triaxial galaxy potentials with and without rotating time dependent components. In the former case, dissipative trajectories settle around closed loop orbits when these exist. When they do not, e.g., inside a constant density core, then the only attractor is the centre and this leads to mass inflow. This provides a self regulating mechanism for accession of material towards the centre --- since the formation of a central masses destroys the central density core and eventually stops the accession. In the case when a rotating bar is present, there are usually several types of attractors, including those on which long lived chaotic motion can occur (strange attractors). Motion on these is erratic with large radial and vertical oscillations.Comment: Contibution to the conference on ``Astrophysical Fluids: From Atomic Nuclei to Stars and Galaxies'' (in honour of Giora Shaviv's 60 th birthday). To appear in Physics Report

Black Hole Information and Thermodynamics

This SpringerBrief is based on a masters course on black hole thermodynamics and the black hole information problem taught by Dieter L\"ust during the summer term 2017 at the Ludwig-Maximilians-Universit\"at in Munich; it was written by Ward Vleeshouwers. It provides a short introduction to general relativity, which describes gravity in terms of the curvature of space-time, and examines the properties of black holes. These are central objects in general relativity which arise when sufficient energy is compressed into a finite volume, so that even light cannot escape its gravitational pull. We will see that black holes exhibit a profound connection with thermodynamic systems. Indeed, by quantizing a field theory on curved backgrounds, one can show that black holes emit thermal (Hawking) radiation, so that the connection with thermodynamics is more than a formal similarity. Hawking radiation gives rise to an apparent conflict between general relativity and quantum mechanics known as the black hole information problem. If a black hole formed from a pure quantum state evaporates to form thermal radiation, which is in a mixed state, then the unitarity postulate of quantum mechanics is violated. We will examine the black hole information problem, which has plagued the physics community for over four decades, and consider prominent examples of proposed solutions, in particular, the string theoretical construction of the Tangherlini black hole, and the infinite number of asymptotic symmetries given by BMS-transformations.Comment: Revised version with typos correcte

NGC 1300 Dynamics: I. The gravitational potential as a tool for detailed stellar dynamics

In a series of papers we study the stellar dynamics of the grand design barred-spiral galaxy NGC~1300. In the first paper of this series we estimate the gravitational potential and we give it in a form suitable to be used in dynamical studies. The estimation is done directly from near-infrared observations. Since the 3D distribution of the luminous matter is unknown, we construct three different general models for the potential corresponding to three different assumptions for the geometry of the system, representing limiting cases. A pure 2D disc, a cylindrical geometry (thick disc) and a third case, where a spherical geometry is assumed to apply for the major part of the bar. For the potential of the disc component on the galactic plane a Fourier decomposition method is used, that allows us to express it as a sum of trigonometric terms. Both even and odd components are considered, so that the estimated potential accounts also for the observed asymmetries in the morphology. For the amplitudes of the trigonometric terms a smoothed cubic interpolation scheme is used. The total potential in each model may include two additional terms (Plummer spheres) representing a central mass concentration and a dark halo component, respectively. In all examined models, the relative force perturbation points to a strongly nonlinear gravitational field, which ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being the most nonlinear one. We present the topological distributions of the stable and unstable Lagrangian points as a function of the pattern speed $(\Omega_p)$. In all three models there is a range of $\Omega_p$ values, where we find multiple stationary points whose stability affects the overall dynamics of the system.Comment: 14 pages, 11 figures, published in MNRA

Stochastic Growth Equations and Reparametrization Invariance

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail.Comment: 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phy