1,743 research outputs found
On Toroidal Horizons in Binary Black Hole Inspirals
We examine the structure of the event horizon for numerical simulations of
two black holes that begin in a quasicircular orbit, inspiral, and finally
merge. We find that the spatial cross section of the merged event horizon has
spherical topology (to the limit of our resolution), despite the expectation
that generic binary black hole mergers in the absence of symmetries should
result in an event horizon that briefly has a toroidal cross section. Using
insight gained from our numerical simulations, we investigate how the choice of
time slicing affects both the spatial cross section of the event horizon and
the locus of points at which generators of the event horizon cross. To ensure
the robustness of our conclusions, our results are checked at multiple
numerical resolutions. 3D visualization data for these resolutions are
available for public access online. We find that the structure of the horizon
generators in our simulations is consistent with expectations, and the lack of
toroidal horizons in our simulations is due to our choice of time slicing.Comment: Submitted to Phys. Rev.
Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure
The Self-Dual String and Anomalies in the M5-brane
We study the anomalies of a charge self-dual string solution in the
Coulomb branch of M5-branes. Cancellation of these anomalies allows us to
determine the anomaly of the zero-modes on the self-dual string and their
scaling with and . The dimensional reduction of the five-brane
anomalous couplings then lead to certain anomalous couplings for D-branes.Comment: 13 pages, Harvmac, refs adde
Spin-dependent scattering in a silicon transistor
The scattering of conduction electrons off neutral donors depends sensitively
on the relative orientation of their spin states. We present a theory of
spin-dependent scattering in the two dimensional electron gas (2DEG) of field
effect transistors. Our theory shows that the scattering mechanism is dominated
by virtual transitions to negatively ionized donor levels. This effect
translates into a source-drain current that always gets reduced when donor
spins are at resonance with a strong microwave field. We propose a model for
donor impurities interacting with conduction electrons in a silicon transistor,
and compare our explicit numerical calculations to electrically detected
magnetic resonance (EDMR) experiments. Remarkably, we show that EDMR is optimal
for donors placed into a sweet spot located at a narrow depth window quite far
from the 2DEG interface. This allows significant optimization of spin signal
intensity for the minimal number of donors placed into the sweet spot, enabling
the development of single spin readout devices. Our theory reveals an
interesting dependence on conduction electron spin polarization p_c. As p_c
increases upon spin injection, the EDMR amplitude first increases as p_{c}^{2},
and then saturates when a polarization threshold p_T is reached. These results
show that it is possible to use EDMR as an in-situ probe of carrier spin
polarization in silicon and other materials with weak spin-orbit coupling
Post-Newtonian Approximation in Maxwell-Like Form
The equations of the linearized first post-Newtonian approximation to general
relativity are often written in "gravitoelectromagnetic" Maxwell-like form,
since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a
side issue in their complex but elegant papers on relativistic celestial
mechanics) have expressed the first post-Newtonian approximation, including all
nonlinearities, in Maxwell-like form. This paper summarizes that DSX
Maxwell-like formalism (which is not easily extracted from their celestial
mechanics papers), and then extends it to include the post-Newtonian
(Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e.
gravitational stress tensor) and law of momentum conservation in Maxwell-like
form. The authors and their colleagues have found these Maxwell-like momentum
tools useful for developing physical intuition into numerical-relativity
simulations of compact binaries with spin.Comment: v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated
in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added
references. Changed definitions & convention
Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure
Momentum flow in black-hole binaries: II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins
Research on extracting science from binary-black-hole (BBH) simulations has
often adopted a "scattering matrix" perspective: given the binary's initial
parameters, what are the final hole's parameters and the emitted gravitational
waveform? In contrast, we are using BBH simulations to explore the nonlinear
dynamics of curved spacetime. Focusing on the head-on plunge, merger, and
ringdown of a BBH with transverse, antiparallel spins, we explore numerically
the momentum flow between the holes and the surrounding spacetime. We use the
Landau-Lifshitz field-theory-in-flat-spacetime formulation of general
relativity to define and compute the density of field energy and field momentum
outside horizons and the energy and momentum contained within horizons, and we
define the effective velocity of each apparent and event horizon as the ratio
of its enclosed momentum to its enclosed mass-energy. We find surprisingly good
agreement between the horizons' effective and coordinate velocities. To
investigate the gauge dependence of our results, we compare pseudospectral and
moving-puncture evolutions of physically similar initial data; although
spectral and puncture simulations use different gauge conditions, we find
remarkably good agreement for our results in these two cases. We also compare
our simulations with the post-Newtonian trajectories and near-field
energy-momentum. [Abstract abbreviated; full abstract also mentions additional
results.]Comment: Submitted to Phys. Rev.
Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
When one splits spacetime into space plus time, the Weyl curvature tensor
(vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free
(STF) tensors: (i) the Weyl tensor's so-called "electric" part or tidal field,
and (ii) the Weyl tensor's so-called "magnetic" part or frame-drag field. Being
STF, the tidal field and frame-drag field each have three orthogonal
eigenvector fields which can be depicted by their integral curves. We call the
integral curves of the tidal field's eigenvectors tendex lines, we call each
tendex line's eigenvalue its tendicity, and we give the name tendex to a
collection of tendex lines with large tendicity. The analogous quantities for
the frame-drag field are vortex lines, their vorticities, and vortexes. We
build up physical intuition into these concepts by applying them to a variety
of weak-gravity phenomena: a spinning, gravitating point particle, two such
particles side by side, a plane gravitational wave, a point particle with a
dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a
slow-motion binary system made of nonspinning point particles. [Abstract is
abbreviated; full abstract also mentions additional results.]Comment: 25 pages, 20 figures, matches the published versio
Gravitational waveforms for neutron star binaries from binary black hole simulations
Gravitational waves from binary neutron star (BNS) and black-hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of
the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the non-tidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of < 1 radian over ~ 15 orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter â‹‹
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