37 research outputs found
Accurate and realistic initial data for black hole-neutron star binaries
This paper is devoted to the computation of compact binaries composed of one
black hole and one neutron star. The objects are assumed to be on exact
circular orbits. Standard 3+1 decomposition of Einstein equations is performed
and the conformal flatness approximation is used. The obtained system of
elliptic equations is solved by means of multi-domain spectral methods. Results
are compared with previous work both in the high mass ratio limit and for one
neutron star with very low compactness parameter. The accuracy of the present
code is shown to be greater than with previous codes. Moreover, for the first
time, some sequences containing one neutron star of realistic compactness are
presented and discussed.Comment: Version including the erratum to be published in Phys. Rev.
Fully consistent rotating black holes in the cubic Galileon theory
Configurations of rotating black holes in the cubic Galileon theory are
computed by means of spectral methods. The equations are written in the 3+1
formalism and the coordinates are based on the maximal slicing condition and
the spatial harmonic gauge. The black holes are described as apparent horizons
in equilibrium. It enables the first fully consistent computation of rotating
black holes in this theory. Several quantities are extracted from the
solutions. In particular, the vanishing of the mass is confirmed. A link is
made between that and the fact that the solutions do not obey the zeroth-law of
black hole thermodynamics
Self-gravitating scalar breathers with negative cosmological constant
Breather-type (time-periodic and spatially localized) solutions with
spherical symmetry are investigated in a massless scalar field theory coupled
to Einstein's gravity with cosmological constant in spatial dimensions
imposing anti de Sitter (AdS) asymptotics on space-time. Using a code
constructed with the Kadath library that enables the use of spectral methods,
the phase space of breather solutions is explored in detail for and
. It is found that there are discrete families of solutions indexed by an
integer and by their frequency. Using a time evolution code these AdS breathers
are found to be stable for up to a critical central density, in analogy to
boson stars. Using an analytical perturbative expansion small amplitude
breathers are worked out for arbitrary dimensions .Comment: 24 pages, 13 figures, one figure and references added, version
accepted for Phys. Rev.
Scalar field breathers on anti-de Sitter background
We study spatially localized, time-periodic solutions (breathers) of scalar
field theories with various self-interacting potentials on Anti-de Sitter (AdS)
spacetimes in dimensions. A detailed numerical study of spherically
symmetric configurations in dimensions is carried out, revealing a rich
and complex structure of the phase-space (bifurcations, resonances). Scalar
breather solutions form one-parameter families parametrized by their amplitude,
, while their frequency, , is a
function of the amplitude. The scalar breathers on AdS we find have a small
amplitude limit, tending to the eigenfunctions of the linear Klein-Gordon
operator on AdS. Importantly most of these breathers appear to be generically
stable under time evolution.Comment: 30 pages, 22 figure
High precision numerical sequences of rotating hairy black holes
We analyze numerically the existence of regular stationary rotating hairy
black holes within the framework of general relativity, which are the result of
solving the Einstein-Klein-Gordon system for a complex-valued scalar field
under suitable boundary (regularity and asymptotically flat) conditions. To
that aim we solve the corresponding system of elliptic partial differential
equations using spectral methods which are specially suited for such a
numerical task. In order to obtain such system of equations we employ a
parametrization for the metric that corresponds to quasi-isotropic coordinates
(QIC) that have been used in the past for analyzing different kinds of
stationary rotating relativistic systems. Our findings are in agreement with
those reported originally by Herdeiro \& Radu ite{Herdeiro2014,Herdeiro2015}.
The method is submitted to several analytic and numerical tests, which include
the recovery of the Kerr solution in QIC and the cloud solutions in the Kerr
background. We report different global quantities that allow us to determine
the contribution of the boson hair to the spacetime, as well as relevant
quantities at the horizon, like the surface gravity. The latter indicates to
what extent the hairy solutions approach the extremal limit, noting that for
this kind of solutions the ratio of the angular momentum per squared mass
can be larger than unity due to the contribution of
the scalar hair, a situation which differs from the Kerr metric where this
parameter is bounded according to with the upper bound
corresponding to the extremal case.Comment: 28 pages, 36 figure
Numerical simulation of oscillatons: extracting the radiating tail
Spherically symmetric, time-periodic oscillatons -- solutions of the
Einstein-Klein-Gordon system (a massive scalar field coupled to gravity) with a
spatially localized core -- are investigated by very precise numerical
techniques based on spectral methods. In particular the amplitude of their
standing-wave tail is determined. It is found that the amplitude of the
oscillating tail is very small, but non-vanishing for the range of frequencies
considered. It follows that exactly time-periodic oscillatons are not truly
localized, and they can be pictured loosely as consisting of a well
(exponentially) localized nonsingular core and an oscillating tail making the
total mass infinite. Finite mass physical oscillatons with a well localized
core -- solutions of the Cauchy-problem with suitable initial conditions -- are
only approximately time-periodic. They are continuously losing their mass
because the scalar field radiates to infinity. Their core and radiative tail is
well approximated by that of time-periodic oscillatons. Moreover the mass loss
rate of physical oscillatons is estimated from the numerical data and a
semi-empirical formula is deduced. The numerical results are in agreement with
those obtained analytically in the limit of small amplitude time-periodic
oscillatons.Comment: 22 figures, accepted for publication in PR
Searching for Gravitational Waves from the Inspiral of Precessing Binary Systems: New Hierarchical Scheme using "Spiky" Templates
In a recent investigation of the effects of precession on the anticipated
detection of gravitational-wave inspiral signals from compact object binaries
with moderate total masses, we found that (i) if precession is ignored, the
inspiral detection rate can decrease by almost a factor of 10, and (ii)
previously proposed ``mimic'' templates cannot improve the detection rate
significantly (by more than a factor of 2). In this paper we propose a new
family of templates that can improve the detection rate by factors of 5--6 in
cases where precession is most important. Our proposed method for these new
``mimic'' templates involves a hierarchical scheme of efficient, two-parameter
template searches that can account for a sequence of spikes that appear in the
residual inspiral phase, after one corrects for the any oscillatory
modification in the phase. We present our results for two cases of compact
object masses (10 and 1.4 solar masses and 7 and 3 solar masses) as a function
of spin properties. Although further work is needed to fully assess the
computational efficiency of this newly proposed template family, we conclude
that these ``spiky templates'' are good candidates for a family of precession
templates used in realistic searches, that can improve detection rates of
inspiral events.Comment: 17 pages, 22 figures, version accepted by PRD. Minor revision
Kadath: a spectral solver for theoretical physics
Kadath is a library that implements spectral methods in a very modular
manner. It is designed to solve a wide class of problems that arise in the
context of theoretical physics. Several types of coordinates are implemented
and additional geometries can be easily encoded. Partial differential equations
of various types are discretized by means of spectral methods. The resulting
system is solved using a Newton-Raphson iteration. Doing so, Kadath is able to
deal with strongly non-linear situations. The algorithms are validated by
applying the library to four different problems of contemporary physics, in the
fields of gauge field theory and general relativityComment: Accepted to Journal of Computational Physic
Searching for Gravitational Waves from the Inspiral of Precessing Binary Systems: Astrophysical Expectations and Detection Efficiency of "Spiky'' Templates
Relativistic spin-orbit and spin-spin couplings has been shown to modify the
gravitational waveforms expected from inspiraling binaries with a black hole
and a neutron star. As a result inspiral signals may be missed due to
significant losses in signal-to-noise ratio, if precession effects are ignored
in gravitational-wave searches. We examine the sensitivity of the anticipated
loss of signal-to-noise ratio on two factors: the accuracy of the precessing
waveforms adopted as the true signals and the expected distributions of
spin-orbit tilt angles, given the current understanding of their physical
origin. We find that the results obtained using signals generated by
approximate techniques are in good agreement with the ones obtained by
integrating the 2PN equations. This shows that a complete account of all
high-order post-Newtonian effects is usually not necessary for the
determination of detection efficiencies. Based on our current astrophysical
expectations, large tilt angles are not favored and as a result the decrease in
detection rate varies rather slowly with respect to the black hole spin
magnitude and is within 20--30% of the maximum possible values.Comment: 7 fig., accepted by Phys. Rev. D Minor modification
A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
We propose a new formulation for 3+1 numerical relativity, based on a
constrained scheme and a generalization of Dirac gauge to spherical
coordinates. This is made possible thanks to the introduction of a flat
3-metric on the spatial hypersurfaces t=const, which corresponds to the
asymptotic structure of the physical 3-metric induced by the spacetime metric.
Thanks to the joint use of Dirac gauge, maximal slicing and spherical
components of tensor fields, the ten Einstein equations are reduced to a system
of five quasi-linear elliptic equations (including the Hamiltonian and momentum
constraints) coupled to two quasi-linear scalar wave equations. The remaining
three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows
a direct computation of the spherical components of the conformal metric from
the two scalar potentials which obey the wave equations. We present some
numerical evolution of 3-D gravitational wave spacetimes which demonstrates the
stability of the proposed scheme.Comment: Difference w.r.t. v1: Major revision: improved presentation of the
tensor wave equation and addition of the first results from a numerical
implementation; w.r.t. v2: Minor changes: improved conclusion and figures;
w.r.t. v3: Minors changes, 1 figure added; 25 pages, 13 figures, REVTeX,
accepted for publication in Phys. Rev.