5,595 research outputs found
Renormings of
We investigate the best order of smoothness of . We prove in
particular that there exists a -smooth bump function on if
and only if and are both even integers and is a multiple of .Comment: 18 pages; AMS-Te
An effective quantum mechanism for mass generation in diffeomorphism-invariant theories
We propose a scenario for particle-mass generation, assuming the existence of
a physical regime where, firstly, physical particles can be considered as
point-like objects moving in a background space-time and, secondly, their mere
presence spoils the invariance under the local diffeomorphism group, resulting
in an anomalous realization of the latter. Under these hypotheses, we describe
mass generation starting from the massless free theory. The mechanism is not
sensitive to the detailed description of the underlying theory at higher
energies, leaning only on general structural features of it, specifically
diffeomorphism invariance.Comment: 8 pages, LaTeX, no figures; version accepted for publication in MPL
Numerical simulation of random paths with a curvature dependent action
We study an ensemble of closed random paths, embedded in R^3, with a
curvature dependent action. Previous analytical results indicate that there is
no crumpling transition for any finite value of the curvature coupling.
Nevertheless, in a high statistics numerical simulation, we observe two
different regimes for the specific heat separated by a rather smooth structure.
The analysis of this fact warns us about the difficulties in the interpretation
of numerical results obtained in cases where theoretical results are absent and
a high statistics simulation is unreachable. This may be the case of random
surfaces.Comment: 9 pages, LaTeX, 4 eps figures. Final version to appear in Mod. Phys.
Lett.
Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes
The qualitative and quantitative understanding of near-horizon gravitational
dynamics in the strong-field regime represents a challenge both at a
fundamental level and in astrophysical applications. Recent advances in
numerical relativity and in the geometric characterization of black hole
horizons open new conceptual and technical avenues into the problem. We discuss
here a research methodology in which spacetime dynamics is probed through the
cross-correlation of geometric quantities constructed on the black hole horizon
and on null infinity. These two hypersurfaces respond to evolving gravitational
fields in the bulk, providing canonical "test screens" in a "scattering"-like
perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial
Value Problem approach to the construction of generic spacetimes and discuss
the role and properties of dynamical trapping horizons as canonical inner
"screens" in this context. We apply these ideas and techniques to the study of
the recoil dynamics in post-merger binary black holes, an important issue in
supermassive galactic black hole mergers.Comment: 16 pages, 5 figures, contribution to the proceedings volume of the
Spanish Relativity Meeting ERE2011: "Towards new paradigms", Madrid, Spain,
29 Aug-2 Sep 201
A class of Hamilton-Jacobi equations on Banach-Finsler manifolds
The concept of subdifferentiability is studied in the context of
Finsler manifolds (modeled on a Banach space with a Lipschitz bump
function). A class of Hamilton-Jacobi equations defined on Finsler
manifolds is studied and several results related to the existence and
uniqueness of viscosity solutions are obtained.Comment: 24 page
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