9,862 research outputs found
On Property (FA) for wreath products
We characterize permutational wreath products with Property (FA). For
instance, the standard wreath product A wr B of two nontrivial countable groups
A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely
generated group with finite abelianisation. We also prove an analogous result
for hereditary Property (FA). On the other hand, we prove that many wreath
products with hereditary Property (FA) are not quotients of finitely presented
groups with the same property.Comment: 12 pages, 0 figur
Geometry of deformations of branes in warped backgrounds
The `braneworld' (described by the usual worldvolume action) is a D
dimensional timelike surface embedded in a N dimensional () warped,
nonfactorisable spacetime. We first address the conditions on the warp factor
required to have an extremal flat brane in a five dimensional background.
Subsequently, we deal with normal deformations of such extremal branes. The
ensuing Jacobi equations are analysed to obtain the stability condition. It
turns out that to have a stable brane, the warp factor should have a minimum at
the location of the brane in the given background spacetime. To illustrate our
results we explicitly check the extremality and stability criteria for a few
known co-dimension one braneworld models. Generalisations of the above
formalism for the cases of (i) curved branes (ii) asymmetrical warping and
(iii) higher co-dimension braneworlds are then presented alongwith some typical
examples for each. Finally, we summarize our results and provide perspectives
for future work along these lines.Comment: 21 pages. Version matching final version. Accepted for publication in
Class. Quant. Gra
Gravitational amplitudes in black-hole evaporation: the effect of non-commutative geometry
Recent work in the literature has studied the quantum-mechanical decay of a
Schwarzschild-like black hole, formed by gravitational collapse, into
almost-flat space-time and weak radiation at a very late time. The relevant
quantum amplitudes have been evaluated for bosonic and fermionic fields,
showing that no information is lost in collapse to a black hole. On the other
hand, recent developments in noncommutative geometry have shown that, in
general relativity, the effects of noncommutativity can be taken into account
by keeping the standard form of the Einstein tensor on the left-hand side of
the field equations and introducing a modified energy-momentum tensor as a
source on the right-hand side. The present paper, relying on the recently
obtained noncommutativity effect on a static, spherically symmetric metric,
considers from a new perspective the quantum amplitudes in black hole
evaporation. The general relativity analysis of spin-2 amplitudes is shown to
be modified by a multiplicative factor F depending on a constant
non-commutativity parameter and on the upper limit R of the radial coordinate.
Limiting forms of F are derived which are compatible with the adiabatic
approximation here exploited. Approximate formulae for the particle emission
rate are also obtained within this framework.Comment: 14 pages, 2 figures, Latex macros. In the final version, section 5
has been amended, the presentation has been improved, and References 21-24
have been added. Last misprints amended in Section 5 and Ref. 2
Local simulation of singlet statistics for restricted set of measurement
The essence of Bell's theorem is that, in general, quantum statistics cannot
be reproduced by local hidden variable (LHV) model. This impossibility is
strongly manifested while analyzing the singlet state statistics for Bell-CHSH
violations. In this work, we provide various subsets of two outcome POVMs for
which a local hidden variable model can be constructed for singlet state.Comment: 2 column, 5 pages, 4 figures, new references, abstract modified,
accepted in JP
Kinematics of flows on curved, deformable media
In this article, we first investigate the kinematics of specific geodesic
flows on two dimensional media with constant curvature, by explicitly solving
the evolution (Raychaudhuri) equations for the expansion, shear and rotation
along the flows. We point out the existence of singular (within a finite value
of the time parameter) and non-singular solutions and illustrate our results
through a `phase' diagram. This diagram demonstrates under which initial
conditions (or combinations thereof) we end up with a singularity in the
congruence and when, if at all, we encounter non--singular solutions for the
kinematic variables. Our analysis illustrates the differences which arise due
to a positive or negative value of the curvature. Subsequently, we move on to
geodesic flows on two dimensional spaces with varying curvature. As an example,
we discuss flows on a torus, where interesting oscillatory features of the
expansion, shear and rotation emerge, which are found to depend on the ratio of
the radii of the torus. The singular (within a finite time)/non--singular
nature of the solutions are also discussed. Finally, we arrive at some general
statements and point out similarities or dissimilarities that arise in
comparison to our earlier work on media in flat space.Comment: Corrections in some equations and in one figure
Exact solutions in two-dimensional string cosmology with back reaction
We present analytic cosmological solutions in a model of two-dimensional
dilaton gravity with back reaction. One of these solutions exhibits a graceful
exit from the inflationary to the FRW phase and is nonsingular everywhere. A
duality related second solution is found to exist only in the ``pre-big-bang''
epoch and is singular at . In either case back reaction is shown to
play a crucial role in determining the specific nature of these geometries.Comment: Shortened slightly, references added, to appear in Physical Review D
(Rapid Communications). 16 pages, RevTex, 3 PostScript figure
A river model of space
Within the theory of general relativity gravitational phenomena are usually
attributed to the curvature of four-dimensional spacetime. In this context we
are often confronted with the question of how the concept of ordinary physical
three-dimensional space fits into this picture. In this work we present a
simple and intuitive model of space for both the Schwarzschild spacetime and
the de Sitter spacetime in which physical space is defined as a specified set
of freely moving reference particles. Using a combination of orthonormal basis
fields and the usual formalism in a coordinate basis we calculate the physical
velocity field of these reference particles. Thus we obtain a vivid description
of space in which space behaves like a river flowing radially toward the
singularity in the Schwarzschild spacetime and radially toward infinity in the
de Sitter spacetime. We also consider the effect of the river of space upon
light rays and material particles and show that the river model of space
provides an intuitive explanation for the behavior of light and particles at
and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure
Convergent variational calculation of positronium-hydrogen-atom scattering lengths
We present a convergent variational basis-set calculational scheme for
elastic scattering of positronium atom by hydrogen atom in S wave. Highly
correlated trial functions with appropriate symmetry are needed for achieving
convergence. We report convergent results for scattering lengths in atomic
units for both singlet () and triplet () states.Comment: 11 pages, 1 postscript figure, Accepted in J. Phys. B (Letter
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