4,292 research outputs found
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
Bounds on area and charge for marginally trapped surfaces with cosmological constant
We sharpen the known inequalities and between the area and the electric charge of a stable marginally
outer trapped surface (MOTS) of genus g in the presence of a cosmological
constant . In particular, instead of requiring stability we include
the principal eigenvalue of the stability operator. For we obtain a lower and an upper bound for in terms of as well as the upper bound for the charge, which reduces to in the stable case . For
there remains only a lower bound on . In the spherically symmetric, static,
stable case one of the area inequalities is saturated iff the surface gravity
vanishes. We also discuss implications of our inequalities for "jumps" and
mergers of charged MOTS.Comment: minor corrections to previous version and to published versio
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
An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
We present an introduction to dynamical trapping horizons as quasi-local
models for black hole horizons, from the perspective of an Initial Value
Problem approach to the construction of generic black hole spacetimes. We focus
on the geometric and structural properties of these horizons aiming, as a main
application, at the numerical evolution and analysis of black hole spacetimes
in astrophysical scenarios. In this setting, we discuss their dual role as an
"a priori" ingredient in certain formulations of Einstein equations and as an
"a posteriori" tool for the diagnosis of dynamical black hole spacetimes.
Complementary to the first-principles discussion of quasi-local horizon
physics, we place an emphasis on the "rigidity" properties of these
hypersurfaces and their role as privileged geometric probes into near-horizon
strong-field spacetime dynamics.Comment: 37 pages, 5 figures. Notes prepared for the course at the 2011
Shanghai Asia-Pacific School and Workshop on Gravitation (Shanghai Normal
University, February 10-14, 2011
Black-hole horizons as probes of black-hole dynamics II: geometrical insights
In a companion paper [1], we have presented a cross-correlation approach to
near-horizon physics in which bulk dynamics is probed through the correlation
of quantities defined at inner and outer spacetime hypersurfaces acting as test
screens. More specifically, dynamical horizons provide appropriate inner
screens in a 3+1 setting and, in this context, we have shown that an
effective-curvature vector measured at the common horizon produced in a head-on
collision merger can be correlated with the flux of linear Bondi-momentum at
null infinity. In this paper we provide a more sound geometric basis to this
picture. First, we show that a rigidity property of dynamical horizons, namely
foliation uniqueness, leads to a preferred class of null tetrads and Weyl
scalars on these hypersurfaces. Second, we identify a heuristic horizon
news-like function, depending only on the geometry of spatial sections of the
horizon. Fluxes constructed from this function offer refined geometric
quantities to be correlated with Bondi fluxes at infinity, as well as a contact
with the discussion of quasi-local 4-momentum on dynamical horizons. Third, we
highlight the importance of tracking the internal horizon dual to the apparent
horizon in spatial 3-slices when integrating fluxes along the horizon. Finally,
we discuss the link between the dissipation of the non-stationary part of the
horizon's geometry with the viscous-fluid analogy for black holes, introducing
a geometric prescription for a "slowness parameter" in black-hole recoil
dynamics.Comment: Final version published on PR
Extended diffeomorphism algebras in (quantum) gravitational physics
We construct an explicit representation of the algebra of local
diffeomorphisms of a manifold with realistic dimensions. This is achieved in
the setting of a general approach to the (quantum) dynamics of a physical
system which is characterized by the fundamental role assigned to a basic
underlying symmetry. The developed mathematical formalism makes contact with
the relevant gravitational notions by means of the addition of some extra
structure. The specific manners in which this is accomplished, together with
their corresponding physical interpretation, lead to different gravitational
models. Distinct strategies are in fact briefly outlined, showing the
versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure
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