1,749 research outputs found
A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
The motion of a small compact object in a background spacetime is
investigated in the context of a model nonlinear scalar field theory. This
model is constructed to have a perturbative structure analogous to the General
Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the
effective field theory approach to this model and calculate the finite part of
the self force on the small compact object through third order in the ratio of
the size of the compact object to the curvature scale of the background (e.g.,
black hole) spacetime. We use well-known renormalization methods and
demonstrate the consistency of the formalism in rendering the self force finite
at higher orders within a point particle prescription for the small compact
object. This nonlinear scalar model should be useful for studying various
aspects of higher-order self force effects in EMRIs but within a comparatively
simpler context than the full gravitational case. These aspects include
developing practical schemes for higher order self force numerical
computations, quantifying the effects of transient resonances on EMRI waveforms
and accurately modeling the small compact object's motion for precise
determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure
Radiation reaction at 3.5 post-Newtonian order in effective field theory
We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of Hamilton’s variational principle that rigorously extends the usual Lagrangian and Hamiltonian formalisms to dissipative systems, including the inspiral of a compact binary from the emission of gravitational waves. We find agreement with previous results, which thus provides a non-trivial confirmation of the extended variational principle. The results from this work nearly complete the equations of motion for the generic inspiral of a compact binary with spinning constituents through 3.5 post-Newtonian order, as derived entirely with effective field theory, with only the spin-orbit corrections to the potential at 3.5 post-Newtonian remaining
Coalescing Binary Neutron Stars
Coalescing compact binaries with neutron star or black hole components
provide the most promising sources of gravitational radiation for detection by
the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact
has motivated several different theoretical studies of the inspiral and
hydrodynamic merging of compact binaries. Analytic analyses of the inspiral
waveforms have been performed in the Post-Newtonian approximation. Analytic and
numerical treatments of the coalescence waveforms from binary neutron stars
have been performed using Newtonian hydrodynamics and the quadrupole radiation
approximation. Numerical simulations of coalescing black hole and neutron star
binaries are also underway in full general relativity. Recent results from each
of these approaches will be described and their virtues and limitations
summarized.Comment: Invited Topical Review paper to appear in Classical and Quantum
Gravity, 35 pages, including 5 figure
The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
On September 14, 2015, the newly upgraded Laser Interferometer
Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW)
signal, emitted a billion light-years away by a coalescing binary of two
stellar-mass black holes. The detection was announced in February 2016, in time
for the hundredth anniversary of Einstein's prediction of GWs within the theory
of general relativity (GR). The signal represents the first direct detection of
GWs, the first observation of a black-hole binary, and the first test of GR in
its strong-field, high-velocity, nonlinear regime. In the remainder of its
first observing run, LIGO observed two more signals from black-hole binaries,
one moderately loud, another at the boundary of statistical significance. The
detections mark the end of a decades-long quest, and the beginning of GW
astronomy: finally, we are able to probe the unseen, electromagnetically dark
Universe by listening to it. In this article, we present a short historical
overview of GW science: this young discipline combines GR, arguably the
crowning achievement of classical physics, with record-setting, ultra-low-noise
laser interferometry, and with some of the most powerful developments in the
theory of differential geometry, partial differential equations,
high-performance computation, numerical analysis, signal processing,
statistical inference, and data science. Our emphasis is on the synergy between
these disciplines, and how mathematics, broadly understood, has historically
played, and continues to play, a crucial role in the development of GW science.
We focus on black holes, which are very pure mathematical solutions of
Einstein's gravitational-field equations that are nevertheless realized in
Nature, and that provided the first observed signals.Comment: 41 pages, 5 figures. To appear in Bulletin of the American
Mathematical Societ
Judiciously distributing laser emitters to shape the desired far field patterns
The far-field pattern of a simple one-dimensional laser array of emitters
radiating into free space is considered. In the path of investigating the
inverse problem for their near fields leading to a target beam form,
surprisingly we found that the result is successful when the matrix of the
corresponding linear system is not well-scaled. The essence of our numerical
observations is captured by an elegant inequality defining the functional range
of the optical distance between two neighboring emitters. Our finding can
restrict substantially the parametric space of integrated photonic systems and
simplify significantly the subsequent optimizations
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