52 research outputs found
Perturbation theory for self-gravitating gauge fields I: The odd-parity sector
A gauge and coordinate invariant perturbation theory for self-gravitating
non-Abelian gauge fields is developed and used to analyze local uniqueness and
linear stability properties of non-Abelian equilibrium configurations. It is
shown that all admissible stationary odd-parity excitations of the static and
spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have
total angular momentum number , and are characterized by
non-vanishing asymptotic flux integrals. Local uniqueness results with respect
to non-Abelian perturbations are also established for the Schwarzschild and the
Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly
stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable
modes with are also excluded for the static and spherically
symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure
The generalization of the Regge-Wheeler equation for self-gravitating matter fields
It is shown that the dynamical evolution of perturbations on a static
spacetime is governed by a standard pulsation equation for the extrinsic
curvature tensor. The centerpiece of the pulsation equation is a wave operator
whose spatial part is manifestly self-adjoint. In contrast to metric
formulations, the curvature-based approach to gravitational perturbation theory
generalizes in a natural way to self-gravitating matter fields. For a certain
relevant subspace of perturbations the pulsation operator is symmetric with
respect to a positive inner product and therefore allows spectral theory to be
applied. In particular, this is the case for odd-parity perturbations of
spherically symmetric background configurations. As an example, the pulsation
equations for self-gravitating, non-Abelian gauge fields are explicitly shown
to be symmetric in the gravitational, the Yang Mills, and the off-diagonal
sector.Comment: 4 pages, revtex, no figure
An alternative approach to the galactic dark matter problem
We discuss scenarios in which the galactic dark matter in spiral galaxies is
described by a long range coherent field which settles in a stationary
configuration that might account for the features of the galactic rotation
curves. The simplest possibility is to consider scalar fields, so we discuss in
particular, two mechanisms that would account for the settlement of the scalar
field in a non-trivial configuration in the absence of a direct coupling of the
field with ordinary matter: topological defects, and spontaneous scalarization.Comment: 36 pages, 12 figures, Revtex, a brief discussion added, accepted for
publication in PR
Non-minimally coupled scalar fields and isolated horizons
The isolated horizon framework is extended to include non-minimally coupled
scalar fields. As expected from the analysis based on Killing horizons, entropy
is no longer given just by (a quarter of) the horizon area but also depends on
the scalar field. In a subsequent paper these results will serve as a point of
departure for a statistical mechanical derivation of entropy using quantum
geometry.Comment: 14 pages, 1 figure, revtex4. References and minor clarifications
adde
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters and of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner.
The classical Hamiltonian written in terms of these variables and their
conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian
operator, and an eigenvalue equation for the ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity are of the form , where
is an integer. It turns out that this result is closely related to
Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local in time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity which offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure are given. A conjectural picture of the
asymptotic behaviour of general cosmological solutions of the Einstein
equations is built up. Some miscellaneous topics connected with the main theme
are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit
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