2,565 research outputs found
Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
We compute the conservative piece of the gravitational self-force (GSF)
acting on a particle of mass m_1 as it moves along an (unstable) circular
geodesic orbit between the innermost stable circular orbit (ISCO) and the light
ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we
construct the function h_{uu}(x) = h_{\mu\nu} u^{\mu} u^{\nu} (related to
Detweiler's gauge-invariant "redshift" variable), where h_{\mu\nu} is the
regularized metric perturbation in the Lorenz gauge, u^{\mu} is the
four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)\Omega]^{2/3} is an invariant
coordinate constructed from the orbital frequency \Omega. In particular, we
explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where
the circular orbit becomes null. Using the recently discovered link between
h_{uu} and the piece a(u), linear in the symmetric mass ratio \nu, of the main
radial potential A(u,\nu) of the Effective One Body (EOB) formalism, we compute
a(u) over the entire domain 0<u<1/3. We find that a(u) diverges at the
light-ring as ~0.25 (1-3u)^{-1/2}, explain the physical origin of this
divergence, and discuss its consequences for the EOB formalism. We construct
accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and
possibly beyond), and give accurate numerical estimates of the values of a(u)
and its first 3 derivatives at the ISCO, as well as the O(\nu) shift in the
ISCO frequency. In previous work we used GSF data on slightly eccentric orbits
to compute a certain linear combination of a(u) and its first two derivatives,
involving also the O(\nu) piece \bar d(u) of a second EOB radial potential
{\bar D}(u,\nu). Combining these results with our present global analytic
representation of a(u), we numerically compute {\bar d}(u)$ on the interval
0<u\leq 1/6.Comment: 44 pages, 8 figures. Extended discussion in Section V and minor
typographical corrections throughout. Version to be published in PR
Introductory lectures on the Effective One Body formalism
The Effective One Body (EOB) formalism is an analytical approach which aims
at providing an accurate description of the motion and radiation of coalescing
binary black holes. We present a brief review of the basic elements of this
approach.Comment: 22 pages, 3 figures, lectures given at the Second ICRANet
Stueckelberg Workshop on Relativistic Field Theories (Pescara, Italy,
September 3-8, 2007); to be published in the International Journal of Modern
Physics
Constraints on the variability of quark masses from nuclear binding
Based on recent work on nuclear binding, we update and extend the anthropic
constraints on the light quark masses, with results that are more tightly
constrained than previously obtained. We find that heavy nuclei would fall
apart (because the attractive nuclear central potential becomes too weak) if
the sum of the light quark masses m_u+m_d would exceed their physical values by
64% (at 95% confidence level). We summarize the anthropic constraints that
follow from requiring the existence both of heavy atoms and of hydrogen. With
the additional assumption that the quark Yukawa couplings do not vary, these
constraints provide a remarkably tight anthropic window for the Higgs vacuum
expectation value: 0.39 < v/v_physical < 1.64.Comment: 21 pages, 7 figure
Photon rockets and gravitational radiation
The absence of gravitational radiation in Kinnersley's ``photon rocket''
solution of Einstein's equations is clarified by studying the mathematically
well-defined problem of point-like photon rockets in Minkowski space (i.e.
massive particles emitting null fluid anisotro\-pically and accelerating
because of the recoil). We explicitly compute the (uniquely defined) {\it
linearized} retarded gravitational waves emitted by such objects, which are the
coherent superposition of the gravitational waves generated by the motion of
the massive point-like rocket and of those generated by the energy-momentum
distribution of the photon fluid. In the special case (corresponding to
Kinnersley's solution) where the anisotropy of the photon emission is purely
dipolar we find that the gravitational wave amplitude generated by the
energy-momentum of the photons exactly cancels the usual gravitational
wave amplitude generated by the accelerated motion of the rocket. More general
photon anisotropies would, however, generate genuine gravitational radiation at
infinity. Our explicit calculations show the compatibility between the
non-radiative character of Kinnersley's solution and the currently used
gravitational wave generation formalisms based on post-Minkowskian perturbation
theory.Comment: 21 pages, LATEX, submitted to Class. Quant. Gra
Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries
The coalescences of binary black hole (BBH) systems, here taken to be
non-spinning, are among the most promising sources for gravitational wave (GW)
ground-based detectors, such as LIGO and Virgo. To detect the GW signals
emitted by BBHs, and measure the parameters of the source, one needs to have in
hand a bank of GW templates that are both effectual (for detection), and
accurate (for measurement). We study the effectualness and the accuracy of the
two types of parametrized banks of templates that are directly defined in the
frequency-domain by means of closed-form expressions, namely 'post-Newtonian'
(PN) and 'phenomenological' models. In absence of knowledge of the exact
waveforms, our study assumes as fiducial, target waveforms the ones generated
by the most accurate version of the effective one body (EOB) formalism. We find
that, for initial GW detectors the use, at each point of parameter space, of
the best closed-form template (among PN and phenomenological models) leads to
an effectualness >97% over the entire mass range and >99% in an important
fraction of parameter space; however, when considering advanced detectors, both
of the closed-form frequency-domain models fail to be effectual enough in
significant domains of the two-dimensional [total mass and mass ratio]
parameter space. Moreover, we find that, both for initial and advanced
detectors, the two closed-form frequency-domain models fail to satisfy the
minimal required accuracy standard in a very large domain of the
two-dimensional parameter space. In addition, a side result of our study is the
determination, as a function of the mass ratio, of the maximum frequency at
which a frequency-domain PN waveform can be 'joined' onto a NR-calibrated EOB
waveform without undue loss of accuracy.Comment: 29 pages, 8 figures, 1 table. Accepted for publication in Phys. Rev.
Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
Using the Effective One Body approach, that includes nonperturbative resummed
estimates for the damping and conservative parts of the compact binary
dynamics, we compute the recoil during the late inspiral and the subsequent
plunge of non-spinning black holes of comparable masses moving in
quasi-circular orbits. Further, using a prescription that smoothly connects the
plunge phase to a perturbed single black hole, we obtain an estimate for the
total recoil associated with the binary black hole coalescence. We show that
the crucial physical feature which determines the magnitude of the terminal
recoil is the presence of a ``burst'' of linear momentum flux emitted slightly
before coalescence. When using the most natural expression for the linear
momentum flux during the plunge, together with a Taylor-expanded
correction factor, we find that the maximum value of the terminal recoil is
km/s and occurs for a mass ratio . We comment,
however, on the fact that the above `best bet estimate' is subject to strong
uncertainties because the location and amplitude of the crucial peak of linear
momentum flux happens at a moment during the plunge where most of the
simplifying analytical assumptions underlying the Effective One Body approach
are no longer justified. Changing the analytical way of estimating the linear
momentum flux, we find maximum recoils that range between 49 and 172 km/s.
(Abridged)Comment: 46 pages, new figures and discussions, to appear in PR
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