13,512 research outputs found
Generalized Dirac operators on Lorentzian manifolds and propagation of singularities
We survey the correct definition of a generalized Dirac operator on a
Space--Time and the classical result about propagation of singularities. This
says that light travels along light--like geodesics. Finally we show this is
also true for generalized Dirac operators
On the distribution of stellar remnants around massive black holes: slow mass segregation, star cluster inspirals and correlated orbits
We study the long term dynamical evolution of stellar mass black holes (BHs)
at the Galactic center (GC) and put constraints on their number and central
mass distribution. Models of the GC are considered that have not yet achieved a
steady state under the influence of random gravitational encounters. Contrary
to some recent claims that mass-segregation can rapidly rebuild a density cusp
in the stars, we find that time scales associated with cusp regrowth are longer
than the Hubble time. These results cast doubts on standard models that
postulate high densities of BHs near the GC and motivate studies that start
from initial conditions which correspond to well-defined physical models. For
the first time, we consider the distribution of BHs in a dissipationless
formation model for the Milky Way nuclear cluster (NC), in which massive
stellar clusters merge in the GC to form a nucleus. We simulate the successive
inspiral of massive clusters containing an inner dense cluster of BHs. The
pre-existing mass segregation is not completely erased as the clusters are
disrupted by the massive black hole tidal field. As a result, after 12 inspiral
events a NC forms in which the BHs have higher central densities than the
stars. After evolving the model for 5-10 Gyr, the BHs do form a steep central
cusp, while the stellar distribution maintains properties that resemble those
of the Milky Way NC. Finally, we investigate the effect of BH perturbations on
the motion of the GC S-stars, as a means of constraining the number of the
perturbers. We find that reproducing the S-star orbital distribution requires
>~1000 BHs within 0.1 pc of Sgr A*. A dissipationless formation scenario for
the Milky Way NC is consistent with this lower limit and therefore could
reconcile the need for high central densities of BHs (to explain the orbits of
the S-stars), with the missing-cusp problem of the GC giant star population.Comment: 23 pages, 21 Figures. Accepted for publication in Ap
The Calderon projection over C* algebras
We construct the Calderon projection on the space of Cauchy datas for a
twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus
for operators acting on bundles of finitely generated --Hilbert modules on
a compact manifold with boundary. In particular an invertible double is
constructed generalizing the classical result
Dynamical friction and the evolution of Supermassive Black hole Binaries: the final hundred-parsec problem
The supermassive black holes originally in the nuclei of two merging galaxies
will form a binary in the remnant core. The early evolution of the massive
binary is driven by dynamical friction before the binary becomes "hard" and
eventually reaches coalescence through gravitational wave emission. { We
consider the dynamical friction evolution of massive binaries consisting of a
secondary hole orbiting inside a stellar cusp dominated by a more massive
central black hole.} In our treatment we include the frictional force from
stars moving faster than the inspiralling object which is neglected in the
standard Chandrasekhar's treatment. We show that the binary eccentricity
increases if the stellar cusp density profile rises less steeply than
. In cusps shallower than the
frictional timescale can become very long due to the deficit of stars moving
slower than the massive body. Although including the fast stars increases the
decay rate, low mass-ratio binaries () in sufficiently
massive galaxies have decay timescales longer than one Hubble time. During such
minor mergers the secondary hole stalls on an eccentric orbit at a distance of
order one tenth the influence radius of the primary hole (i.e., for massive ellipticals). We calculate the expected number of
stalled satellites as a function of the host galaxy mass, and show that the
brightest cluster galaxies should have of such satellites orbiting
within their cores. Our results could provide an explanation to a number of
observations, which include multiple nuclei in core ellipticals, off-center
AGNs and eccentric nuclear disks.Comment: 18 pages, 13 Figures. Accepted for publication in Ap
Massive binary star mergers in galactic nuclei: implications for blue stragglers, binary S-stars and gravitational waves
Galactic nuclei are often found to contain young stellar populations and, in
most cases, a central supermassive black hole (SMBH). Most known massive stars
are found in binaries or higher-multiplicity systems, and in a galactic nucleus
the gravitational interaction with the SMBH can affect their long-term
evolution. In this paper, we study the orbital evolution of stellar binaries
near SMBHs using high precision -body simulations, and including tidal
forces and Post-Newtonian corrections to the motion. We focus on the
Lidov-Kozai (LK) effect induced by the SMBH on massive star binaries. We
investigate how the properties of the merging binaries change with varying the
SMBH mass, the slope of the initial mass function, the distributions of the
binary orbital parameters and the efficiency in energy dissipation in
dissipative tides. We find that the fraction of merging massive binary stars is
in the range -- regardless of the details of the initial
distributions of masses and orbital elements. For a Milky Way-like nucleus, we
find a typical rate of binary mergers
yr. The merger products of massive binaries can be rejuvenated
blue-straggler stars, more massive than each of their original progenitors, and
G2-like objects. Binary systems that survive the LK cycles can be source of
X-rays and gravitational waves, observable with present and upcoming
instruments.Comment: 13 pages, 7 figures, 1 table, accepted by MNRA
From conjecture generation by maintaining dragging to proof
In this paper we propose a hypothesis about how different uses of maintaining
dragging, either as a physical tool in a dynamic geometry environment or as a
psychological tool for generating conjectures can influence subsequent
processes of proving. Through two examples we support the hypothesis that using
maintaining dragging as a physical tool may foster cognitive rupture between
the conjecturing phase and the proof, while using it as a psychological tool
may foster cognitive unity between them.Comment: Research report at the 40th PME conference, Hungar
Maintaining dragging and the pivot invariant in processes of conjecture generation
In this paper, we analyze processes of conjecture generation in the context
of open problems proposed in a dynamic geometry environment, when a particular
dragging modality, maintaining dragging, is used. This involves dragging points
while maintaining certain properties, controlling the movement of the figures.
Our results suggest that the pragmatic need of physically controlling the
simultaneous movements of the different parts of figures can foster the
production of two chains of successive properties, hinged together by an
invariant that we will call pivot invariant. Moreover, we show how the
production of these chains is tied to the production of conjectures and to the
processes of argumentation through which they are generated.Comment: Research report at the 40th PME Conference, Hungar
- …