33 research outputs found
Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below
corrected, references and Note added; to appear in Class. Quantum Gra
Generalized 2d dilaton gravity with matter fields
We extend the classical integrability of the CGHS model of 2d dilaton gravity
[1] to a larger class of models, allowing the gravitational part of the action
to depend more generally on the dilaton field and, simultaneously, adding
fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we
provide the complete solution of the most general dilaton-dependent 2d gravity
action coupled to chiral fermions. The latter analysis is generalized to a
chiral fermion multiplet with a non-abelian gauge symmetry as well as to the
(anti-)self-dual sector df = *df (df = -*df) of a scalar field f.Comment: 37 pages, Latex; typos and Eqs. (44,45) corrected; paragraph on p.
26, referring to a work of S. Solodukhin, reformulated; references adde
Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology
All global solutions of arbitrary topology of the most general 1+1
dimensional dilaton gravity models are obtained. We show that for a generic
model there are globally smooth solutions on any non-compact 2-surface. The
solution space is parametrized explicitly and the geometrical significance of
continuous and discrete labels is elucidated. As a corollary we gain insight
into the (in general non-trivial) topology of the reduced phase space.
The classification covers basically all 2D metrics of Lorentzian signature
with a (local) Killing symmetry.Comment: 39 pages, 22 figures, uses AMSTeX, extended version of former chapter
7 (Gravitational Kinks) now available as gr-qc/9707053, problem with figure 6
fixe
Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
We provide a concise approach to generalized dilaton theories with and
without torsion and coupling to Yang-Mills fields. Transformations on the space
of fields are used to trivialize the field equations locally. In this way their
solution becomes accessible within a few lines of calculation only. In this
first of a series of papers we set the stage for a thorough global
investigation of classical and quantum aspects of more or less all available 2D
gravity-Yang-Mills models.Comment: 24 pages, no figures, some sign errors in Eqs. 52--59 have been
corrected (according to the Erratum
On the Canonical Reduction of Spherically Symmetric Gravity
In a thorough paper Kuchar has examined the canonical reduction of the most
general action functional describing the geometrodynamics of the maximally
extended Schwarzschild geometry. This reduction yields the true degrees of
freedom for (vacuum) spherically symmetric general relativity. The essential
technical ingredient in Kuchar's analysis is a canonical transformation to a
certain chart on the gravitational phase space which features the Schwarzschild
mass parameter , expressed in terms of what are essentially
Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we
discuss the geometric interpretation of Kuchar's canonical transformation in
terms of the theory of quasilocal energy-momentum in general relativity given
by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent
boost to the rest frame," where the ``rest frame'' is defined by vanishing
quasilocal momentum. Furthermore, our formalism is general enough to cover the
case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing
Kucha\v{r}'s original work for Schwarzschild black holes from the framework of
hyperbolic geometry, we present new results concerning the canonical reduction
of Witten-black-hole geometrodynamics.Comment: Revtex, 35 pages, no figure
Virtual black hole phenomenology from 2d dilaton theories
Equipped with the tools of (spherically reduced) dilaton gravity in first
order formulation and with the results for the lowest order S-matrix for s-wave
gravitational scattering (P. Fischer, D. Grumiller, W. Kummer, and D.
Vassilevich, gr-qc/0105034) new properties of the ensuing cross-section are
discussed. We find CPT invariance, despite of the non-local nature of our
effective theory and discover pseudo-self-similarity in its kinematic sector.
After presenting the Carter-Penrose diagram for the corresponding virtual
black hole geometry we encounter distributional contributions to its
Ricci-scalar and a vanishing Einstein-Hilbert action for that configuration.
Finally, a comparison is done between our (Minkowskian) virtual black hole and
Hawking's (Euclidean) virtual black hole bubbles.Comment: 17 pages, 13 figure
Quantization of Two-Dimensional Gravity with Dynamical Torsion
We consider two-dimensional gravity with dynamical torsion in the Batalin -
Vilkovisky and Batalin - Lavrov - Tyutin formalisms of gauge theories
quantization as well as in the background field method.Comment: 12 pages, LaTe
Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
Euclidean dilaton gravity in two dimensions is studied exploiting its
representation as a complexified first order gravity model. All local classical
solutions are obtained. A global discussion reveals that for a given model only
a restricted class of topologies is consistent with the metric and the dilaton.
A particular case of string motivated Liouville gravity is studied in detail.
Path integral quantisation in generic Euclidean dilaton gravity is performed
non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot