688 research outputs found
Noncommutative Einstein-Maxwell pp-waves
The field equations coupling a Seiberg-Witten electromagnetic field to
noncommutative gravity, as described by a formal power series in the
noncommutativity parameters , is investigated. A large
family of solutions, up to order one in , describing
Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be
viewed as providing noncommutative corrections to pp-waves. In our solutions,
noncommutativity enters the spacetime metric through a conformal factor and is
responsible for dilating/contracting the separation between points in the same
null surface. The noncommutative corrections to the electromagnetic waves,
while preserving the wave null character, include constant polarization, higher
harmonic generation and inhomogeneous susceptibility. As compared to pure
noncommutative gravity, the novelty is that nonzero corrections to the metric
already occur at order one in .Comment: 19 revtex pages. One refrence suppressed, two references added. Minor
wording changes in the abstract, introduction and conclusio
Natural extension of the Generalised Uncertainty Principle
We discuss a gedanken experiment for the simultaneous measurement of the
position and momentum of a particle in de Sitter spacetime. We propose an
extension of the so-called generalized uncertainty principle (GUP) which
implies the existence of a minimum observable momentum. The new GUP is directly
connected to the nonzero cosmological constant, which becomes a necessary
ingredient for a more complete picture of the quantum spacetime.Comment: 4 pages, 1 figure, v2 with added references, revised and extended as
published in CQ
New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors
A new first integral for the equations corresponding to twisting type-N
vacuum gravitational fields with two non-commuting Killing vectors is
introduced. A new reduction of the problem to a complex second-order ordinary
differential equation is given. Alternatively, the mentioned first integral can
be used in order to provide a first integral of the second-order complex
equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in
Class. Quantum Gra
Local freedom in the gravitational field revisited
Maartens {\it et al.}\@ gave a covariant characterization, in a 1+3 formalism
based on a perfect fluid's velocity, of the parts of the first derivatives of
the curvature tensor in general relativity which are ``locally free'', i.e. not
pointwise determined by the fluid energy momentum and its derivative. The full
decomposition of independent curvature derivative components given in earlier
work on the spinor approach to the equivalence problem enables analogous
general results to be stated for any order: the independent matter terms can
also be characterized. Explicit relations between the two sets of results are
obtained. The 24 Maartens {\it et al.} locally free data are shown to
correspond to the quantities in the spinor approach, and the
fluid terms are similarly related to the remaining 16 independent quantities in
the first derivatives of the curvature.Comment: LaTeX. 13 pp. To be submitted to Class. Quant. Gra
Brans-Dicke cylindrical wormholes
Static axisymmetric thin-shell wormholes are constructed within the framework
of the Brans-Dicke scalar-tensor theory of gravity. Examples of wormholes
associated with vacuum and electromagnetic fields are studied. All
constructions must be threaded by exotic matter, except in the case of
geometries with a singularity of finite radius, associated with an electric
field, which can have a throat supported by ordinary matter. These results are
achieved with any of the two definitions of the flare-out condition considered.Comment: 11 pages, 3 figures; v3: corrected version, conclusions unchange
Jacobi multipliers, non-local symmetries and nonlinear oscillators
Constants of motion, Lagrangians and Hamiltonians admitted by a family of
relevant nonlinear oscillators are derived using a geometric formalism. The
theory of the Jacobi last multiplier allows us to find Lagrangian descriptions
and constants of the motion. An application of the jet bundle formulation of
symmetries of differential equations is presented in the second part of the
paper. After a short review of the general formalism, the particular case of
non-local symmetries is studied in detail by making use of an extended
formalism. The theory is related to some results previously obtained by
Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local
symmetries for such two nonlinear oscillators is proved.Comment: 20 page
Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity
In the context of a noncommutative model of coordinate coherent states, we
present a Schwarzschild-like metric for a Vaidya solution instead of the
standard Eddington-Finkelstein metric. This leads to the appearance of an exact
dependent case of the metric. We analyze the resulting metric in
three possible causal structures. In this setup, we find a zero remnant mass in
the long-time limit, i.e. an instable black hole remnant. We also study the
tunneling process across the quantum horizon of such a Vaidya black hole. The
tunneling probability including the time-dependent part is obtained by using
the tunneling method proposed by Parikh and Wilczek in terms of the
noncommutative parameter . After that, we calculate the entropy
associated to this noncommutative black hole solution. However the corrections
are fundamentally trifling; one could respect this as a consequence of quantum
inspection at the level of semiclassical quantum gravity.Comment: 19 pages, 5 figure
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