22,032 research outputs found
Gravitational energy of rotating black holes
In the teleparallel equivalent of general relativity the energy density of
asymptotically flat gravitational fields can be naturaly defined as a scalar
density restricted to a three-dimensional spacelike hypersurface .
Integration over the whole yields the standard ADM energy. After
establishing the reference space with zero gravitational energy we obtain the
expression of the localized energy for a Kerr black hole. The expression of the
energy inside a surface of constant radius can be explicitly calculated in the
limit of small , the specific angular momentum. Such expression turns out to
be exactly the same as the one obtained by means of the method preposed
recently by Brown and York. We also calculate the energy contained within the
outer horizon of the black hole for {\it any} value of . The result is
practically indistinguishable from , where is the
irreducible mass of the black hole.Comment: 18 pages, LaTex file, one figur
Uniqueness of the Fisher-Rao metric on the space of smooth densities
MB was supported by ‘Fonds zur F¨orderung der wissenschaftlichen Forschung, Projekt P 24625’
Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics
We show for a certain class of operators and holomorphic functions
that the functional calculus is holomorphic. Using this result
we are able to prove that fractional Laplacians depend real
analytically on the metric in suitable Sobolev topologies. As an
application we obtain local well-posedness of the geodesic equation for
fractional Sobolev metrics on the space of all Riemannian metrics.Comment: 31 page
Probing the gluon density of the proton in the exclusive photoproduction of vector mesons at the LHC: A phenomenological analysis
The current uncertainty on the gluon density extracted from the global parton
analysis is large in the kinematical range of small values of the Bjorken -
variable and low values of the hard scale . An alternative to reduces this
uncertainty is the analysis of the exclusive vector meson photoproduction in
photon - hadron and hadron - hadron collisions. This process offers a unique
opportunity to constrain the gluon density of the proton, since its cross
section is proportional to the gluon density squared. In this paper we consider
current parametrizations for the gluon distribution and estimate the exclusive
vector meson photoproduction cross section at HERA and LHC using the leading
logarithmic formalism. We perform a fit of the normalization of the
cross section and the value of the hard scale for the process and demonstrate
that the current LHCb experimental data are better described by models that
assume a slow increasing of the gluon distribution at small - and low
.Comment: 8 pages, 6 figures, 1 table. Version published in European Physical
Journal
Curved Graphene Nanoribbons: Structure and Dynamics of Carbon Nanobelts
Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect
ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into
spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect
ratio. In this work we investigated the energetics and dynamical aspects of
CNBs formed from rolling up CNRs. We have carried out molecular dynamics
simulations using reactive empirical bond-order potentials. Our results show
that similarly to CNSs, CNBs formation is dominated by two major energy
contribution, the increase in the elastic energy due to the bending of the
initial planar configuration (decreasing structural stability) and the
energetic gain due to van der Waals interactions of the overlapping surface of
the rolled layers (increasing structural stability). Beyond a critical diameter
value these scrolled structures can be even more stable (in terms of energy)
than their equivalent planar configurations. In contrast to CNSs that require
energy assisted processes (sonication, chemical reactions, etc.) to be formed,
CNBs can be spontaneously formed from low temperature driven processes. Long
CNBs (length of 30.0 nm) tend to exhibit self-folded racket-like
conformations with formation dynamics very similar to the one observed for long
carbon nanotubes. Shorter CNBs will be more likely to form perfect scrolled
structures. Possible synthetic routes to fabricate CNBs from graphene membranes
are also addressed
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