148 research outputs found
Lectures on Linear Stability of Rotating Black Holes
These lecture notes are concerned with linear stability of the non-extreme
Kerr geometry under perturbations of general spin. After a brief review of the
Kerr black hole and its symmetries, we describe these symmetries by Killing
fields and work out the connection to conservation laws. The Penrose process
and superradiance effects are discussed. Decay results on the long-time
behavior of Dirac waves are outlined. It is explained schematically how the
Maxwell equations and the equations for linearized gravitational waves can be
decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky
equation can be fully separated to a system of coupled ordinary differential
equations. Linear stability of the non-extreme Kerr black hole is stated as a
pointwise decay result for solutions of the Cauchy problem for the Teukolsky
equation. The stability proof is outlined, with an emphasis on the underlying
ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in
July 2018, minor improvements (published version
Combustion in thermonuclear supernova explosions
Type Ia supernovae are associated with thermonuclear explosions of white
dwarf stars. Combustion processes convert material in nuclear reactions and
release the energy required to explode the stars. At the same time, they
produce the radioactive species that power radiation and give rise to the
formation of the observables. Therefore, the physical mechanism of the
combustion processes, as reviewed here, is the key to understand these
astrophysical events. Theory establishes two distinct modes of propagation for
combustion fronts: subsonic deflagrations and supersonic detonations. Both are
assumed to play an important role in thermonuclear supernovae. The physical
nature and theoretical models of deflagrations and detonations are discussed
together with numerical implementations. A particular challenge arises due to
the wide range of spatial scales involved in these phenomena. Neither the
combustion waves nor their interaction with fluid flow and instabilities can be
directly resolved in simulations. Substantial modeling effort is required to
consistently capture such effects and the corresponding techniques are
discussed in detail. They form the basis of modern multidimensional
hydrodynamical simulations of thermonuclear supernova explosions. The problem
of deflagration-to-detonation transitions in thermonuclear supernova explosions
is briefly mentioned.Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A.
Alsabti and P. Murdin, Springer. 24 pages, 4 figure
Plasma Perturbations and Cosmic Microwave Background Anisotropy in the Linearly Expanding Milne-like Universe
We expose the scenarios of primordial baryon-photon plasma evolution within
the framework of the Milne-like universe models. Recently, such models find a
second wind and promise an inflation-free solution of a lot of cosmological
puzzles including the cosmological constant one. Metric tensor perturbations
are considered using the five-vectors theory of gravity admitting the Friedmann
equation satisfied up to some constant. The Cosmic Microwave Background (CMB)
spectrum is calculated qualitatively.Comment: 20 page
Rotational superradiant scattering in a vortex flow
When an incident wave scatters off of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance 1, 2, 3, 4. We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole 5, 6, 7, 8, 9, 10, as well as to hydrodynamics, due to the close relation to over-reflection instabilities 11, 12, 13
Black Hole Models of Quasars
Observations of active galactic nuclei are interpreted in terms of a theoretical model involving accretion onto a massive black hole. Optical quasars and Seyfert galaxies are associated with holes accreting near the Eddington rate and radio galaxies with sub-critical accretion. It is argued that magnetic fields are largely responsible for extracting energy and angular momentum from black holes and disks. Recent studies of electron-positron pair plasmas and their possible role in establishing the emergent X-ray spectrum are reviewed. The main evolutionary properties of active galactic nuclei can be interpreted in terms of a simple model in which black holes accrete gas at a rate dictated by the rate of gas supply which decreases with cosmic time. It may be worth searching for eclipsing binary black holes in lower power Seyferts
Small Scale Structure and High Redshift HI
Cosmological simulations with gas dynamics suggest that the Lyman-alpha
forest is produced mainly by "small scale structure" --- filaments and sheets
that are the high redshift analog of today's galaxy superclusters. There is no
sharp distinction between Lyman-alpha clouds and "Gunn-Peterson" absorption
produced by the fluctuating IGM -- the Lyman-alpha forest {\it is} the
Gunn-Peterson effect. Lyman limit and damped Lyman-alpha absorption arises in
the radiatively cooled gas of forming galaxies. At , most of the gas is
in the photoionized, diffuse medium associated with the Lyman-alpha forest, but
most of the {\it neutral} gas is in damped Lyman-alpha systems. We discuss
generic evolution of cosmic gas in a hierarchical scenario of structure
formation, with particular attention to the prospects for detecting 21cm
emission from high redshift HI. A scaling argument based on the present-day
cluster mass function suggests that objects with M_{HI} >~ 5e11 h^{-1} \msun
should be extremely rare at , so detections with existing instruments will
be difficult. An instrument like the proposed Square Kilometer Array could
detect individual damped Lyman-alpha systems at high redshift, making it
possible to map structure in the high redshift universe in much the same way
that today's galaxy redshift surveys map the local large scale structure.Comment: 15 pages, latex w/ crckapb & epsf macros, ps figures; get ps version
with all figures from ftp://bessel.mps.ohio-state.edu/pub/dhw/Preprints To
appear in Cold Gas at High Redshift, eds. M. Bremer et al. (Kluwer, 1996
Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene
The remarkable electronic properties of graphene have fueled the vision of a
graphene-based platform for lighter, faster and smarter electronics and
computing applications. One of the challenges is to devise ways to tailor its
electronic properties and to control its charge carriers. Here we show that a
single atom vacancy in graphene can stably host a local charge and that this
charge can be gradually built up by applying voltage pulses with the tip of a
scanning tunneling microscope (STM). The response of the conduction electrons
in graphene to the local charge is monitored with scanning tunneling and Landau
level spectroscopy, and compared to numerical simulations. As the charge is
increased, its interaction with the conduction electrons undergoes a transition
into a supercritical regime 6-11 where itinerant electrons are trapped in a
sequence of quasi-bound states which resemble an artificial atom. The
quasi-bound electron states are detected by a strong enhancement of the density
of states (DOS) within a disc centered on the vacancy site which is surrounded
by halo of hole states. We further show that the quasi-bound states at the
vacancy site are gate tunable and that the trapping mechanism can be turned on
and off, providing a new mechanism to control and guide electrons in grapheneComment: 18 pages and 5 figures plus 14 pages and 15 figures of supplementary
information. Nature Physics advance online publication, Feb 22 (2016
Characteristic Energy of the Coulomb Interactions and the Pileup of States
Tunneling data on crystals confirm
Coulomb interaction effects through the dependence of the
density of states. Importantly, the data and analysis at high energy, E, show a
pileup of states: most of the states removed from near the Fermi level are
found between ~40 and 130 meV, from which we infer the possibility of universal
behavior. The agreement of our tunneling data with recent photoemission results
further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR
Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme
We discuss the numerical solution of nonlinear parabolic partial differential
equations, exhibiting finite speed of propagation, via a strongly implicit
finite-difference scheme with formal truncation error . Our application of interest is the spreading of
viscous gravity currents in the study of which these type of differential
equations arise. Viscous gravity currents are low Reynolds number (viscous
forces dominate inertial forces) flow phenomena in which a dense, viscous fluid
displaces a lighter (usually immiscible) fluid. The fluids may be confined by
the sidewalls of a channel or propagate in an unconfined two-dimensional (or
axisymmetric three-dimensional) geometry. Under the lubrication approximation,
the mathematical description of the spreading of these fluids reduces to
solving the so-called thin-film equation for the current's shape . To
solve such nonlinear parabolic equations we propose a finite-difference scheme
based on the Crank--Nicolson idea. We implement the scheme for problems
involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or
spherically-symmetric three-dimensional currents) on an equispaced but
staggered grid. We benchmark the scheme against analytical solutions and
highlight its strong numerical stability by specifically considering the
spreading of non-Newtonian power-law fluids in a variable-width confined
channel-like geometry (a "Hele-Shaw cell") subject to a given mass
conservation/balance constraint. We show that this constraint can be
implemented by re-expressing it as nonlinear flux boundary conditions on the
domain's endpoints. Then, we show numerically that the scheme achieves its full
second-order accuracy in space and time. We also highlight through numerical
simulations how the proposed scheme accurately respects the mass
conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements
and corrections; to appear as a contribution in "Applied Wave Mathematics II
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