2,378 research outputs found
Absolute conservation law for black holes
In all 2d theories of gravity a conservation law connects the (space-time
dependent) mass aspect function at all times and all radii with an integral of
the matter fields. It depends on an arbitrary constant which may be interpreted
as determining the initial value together with the initial values for the
matter field. We discuss this for spherically reduced Einstein-gravity in a
diagonal metric and in a Bondi-Sachs metric using the first order formulation
of spherically reduced gravity, which allows easy and direct fixations of any
type of gauge. The relation of our conserved quantity to the ADM and Bondi mass
is investigated. Further possible applications (ideal fluid, black holes in
higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.
Convex algebraic geometry of curvature operators
We study the structure of the set of algebraic curvature operators satisfying a sectional curvature bound under the light of the emerging field of Convex Algebraic Geometry. More precisely, we determine in which dimensions this convex semialgebraic set is a spectrahedron or a spectrahedral shadow; in particular, for , these give new counter-examples to the Helton--Nie Conjecture. Moreover, efficient algorithms are provided if to test membership in such a set. For , algorithms using semidefinite programming are obtained from hierarchies of inner approximations by spectrahedral shadows and outer relaxations by spectrahedra
Universal conservation law and modified Noether symmetry in 2d models of gravity with matter
It is well-known that all 2d models of gravity---including theories with
nonvanishing torsion and dilaton theories---can be solved exactly, if matter
interactions are absent. An absolutely (in space and time) conserved quantity
determines the global classification of all (classical) solutions. For the
special case of spherically reduced Einstein gravity it coincides with the mass
in the Schwarzschild solution. The corresponding Noether symmetry has been
derived previously by P. Widerin and one of the authors (W.K.) for a specific
2d model with nonvanishing torsion. In the present paper this is generalized to
all covariant 2d theories, including interactions with matter. The related
Noether-like symmetry differs from the usual one. The parameters for the
symmetry transformation of the geometric part and those of the matterfields are
distinct. The total conservation law (a zero-form current) results from a two
stage argument which also involves a consistency condition expressed by the
conservation of a one-form matter ``current''. The black hole is treated as a
special case.Comment: 3
Comment on: ``Trace anomaly of dilaton coupled scalars in two dimensions''
The trace anomaly for nonminimally coupled scalars in spherically reduced
gravity obtained by Bousso and Hawking (hep-th/9705236) is incorrect. We
explain the reasons for the deviations from our correct (published) result
which is supported by several other recent papers.Comment: 2 page
Symmetries in two-dimensional dilaton gravity with matter
The symmetries of generic 2D dilaton models of gravity with (and without)
matter are studied in some detail. It is shown that , one of the
symmetries of the matterless models, can be generalized to the case where
matter fields of any kind are present. The general (classical) solution for
some of these models, in particular those coupled to chiral matter, which
generalizes the Vaidya solution of Einstein Gravity, is also given.Comment: Minor changes have been made; the references have been updated and
some added; 11 pages. To appear in Phys. Rev.
Constraints, gauge symmetries, and noncommutative gravity in two dimensions
After an introduction into the subject we show how one constructs a canonical
formalism in space-time noncommutative theories which allows to define the
notion of first-class constraints and to analyse gauge symmetries. We use this
formalism to perform a noncommutative deformation of two-dimensional string
gravity (also known as Witten black hole).Comment: Based on lectures given at IFSAP-2004 (St.Petersburg), to be
submitted to Theor. Math. Phys., dedicated to Yu.V.Novozhilov on the occasion
of his 80th birthda
Quantum corrections for (anti)-evaporating black hole
In this paper we analyse the quantum correction for Schwarzschild black hole
in the Unruh state in the framework of spherically symmetric gravity (SSG)
model. SSG is a two-dimensional dilaton model which is obtained by spherically
symmetric reduction from the four-dimensional theory. We find the one-loop
geometry of the (anti)-evaporating black hole and corrections for mass, entropy
and apparent horizon.Comment: 16 pages, Latex, no figure
The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle
Recently an alternative description of 2d supergravities in terms of graded
Poisson-Sigma models (gPSM) has been given. As pointed out previously by the
present authors a certain subset of gPSMs can be interpreted as "genuine"
supergravity, fulfilling the well-known limits of supergravity, albeit deformed
by the dilaton field. In our present paper we show that precisely that class of
gPSMs corresponds one-to-one to the known dilaton supergravity superfield
theories presented a long time ago by Park and Strominger. Therefore, the
unique advantages of the gPSM approach can be exploited for the latter: We are
able to provide the first complete classical solution for any such theory. On
the other hand, the straightforward superfield formulation of the point
particle in a supergravity background can be translated back into the gPSM
frame, where "supergeodesics" can be discussed in terms of a minimal set of
supergravity field degrees of freedom. Further possible applications like the
(almost) trivial quantization are mentioned.Comment: 48 pages, 1 figure. v3: after final version, typos correcte
Area spectrum in Lorentz covariant loop gravity
We use the manifestly Lorentz covariant canonical formalism to evaluate
eigenvalues of the area operator acting on Wilson lines. To this end we modify
the standard definition of the loop states to make it applicable to the present
case of non-commutative connections. The area operator is diagonalized by using
the usual shift ambiguity in definition of the connection. The eigenvalues are
then expressed through quadratic Casimir operators. No dependence on the
Immirzi parameter appears.Comment: 12 pages, RevTEX; improved layout, typos corrected, references added;
changes in the discussion in sec. IIIB and
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
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