||Chair: L. Rezzolla
Numerical Stability of a conformal decomposition of Z4
I will briefly summarize the motivation for the use of different
formulations of GR in numerical relativity. I will then present a
conformal decomposition of the Z4 formulation, Z4c, and discuss
issues relating to stability in numerical approximation. The
discussion will include a presentation of the apples with apples
tests, comparing results obtained with BSSNOK and Z4c.
Constraint damping for the Z4 formulation of general relativity
The Z4 formulation of general relativity provides a build in damping scheme
which promises to damp away constraint violations during free evolutions.
In this talk I present the results of a numerical study of the damping
system in Z4c, a conformal decomposition of Z4. I will dicuss the effect
of the damping on low-frequency and on high-amplitude perturbations
of flat space-time as well and on the long-term dynamics of puncture and
compact star initial data in the context of spherical symmetry.
Gravitational waves in the Fully Constrained Formulation
The Fully Constrained Formulation (FCF) of General Relativity is a novel
framework introduced as an alternative to the hyperbolic formulations
traditionally used in numerical relativity. The FCF equations form a hybrid
elliptic-hyperbolic system of equations including explicitly the constraints.
We present an implicit-explicit numerical algorithm to solve the hyperbolic
part, whereas the elliptic sector shares the form and properties with the well
known Conformally Flat Condition (CFC) approximation. We show the stability and
convergence properties of the numerical scheme with numerical simulations of
vacuum solutions. We have performed the first numerical evolutions of the
coupled system of hydrodynamics and Einstein equations within FCF. We apply
this formalism to extract gravitational waves from compact objects.
||Chair: U. Sperhake
A new approach to the Newman-Penrose formalism
The Newman-Penrose formalism is widely used in the areas of numerical relativity
and perturbation theory as the quantities introduced by the formalism are coordinate
independent and therefore give a gauge invariant description of the physical properties
of the space-time under study, among which its gravitational wave content. Perturbation theory
for a rotating black hole is introduced within this formalism, through the Teukolsky equation.
However, the full set of equations introduced by the formalism is not yet fully understood,
and even the mechanism that allows the decoupling of the Teukolsky equation is not yet fully
clear. Understanding better the nature of these equations would turn out to be very helpful
in several areas, as for example attempts to obtain a higher dimensional version of the
Teukolsky equation have failed up to date. We present a new approach to the Newman-Penrose
formalism that aims to simplify considerably the whole formalism, giving a better understanding
of the known features, and suggesting procedures to extend such features to more general
scenarios of interest.
Canonical Treatment of Noncanonical pN Potentials for Spinning Compact Binaries
Essentially there are two different ways to derive EOMs for spinning
compact binaries in post-Newtonian (pN) approximation. One method is
called the Effective Field Theory approach that aims to calculate an
effective potential for the interaction with the disadvantage to
depend on noncanonical coordinates in nonreduced phase space, i.e the
spin supplementary condition specifying the frame of reference is not
yet eliminated. A more elaborate method is to directly derive a
Hamiltonian within the ADM approach. Starting from a fourdimensional
covariant action functional the general procedure and formulae to
compare the corresponding potentials and Hamiltonians are derived,
clarifying the short notice on this procedure in arXiv:1002.2093.
Complete phenomenological waveforms from spinning coalescing binaries
An accurate knowledge of the coalescing binary gravitational waveform
is crucial for experimental searches as the ones performed by the LIGO-Virgo
collaboration. We present the construction
of analytical phenomenological waveforms describing the signal sourced
by generically spinning binary systems.
The gap between the initial inspiral part of the waveform, described by
spin-Taylor approximants, and its final ring-down part, described by damped
exponentials, is bridged by a phenomenological phase calibrated by
comparison with the dominant spherical harmonic mode of a set of waveforms
including both numerical and phenomenological waveforms of different type.
The Advanced LIGO noise-weighted overlap integral between the numerical and
phenomenological waveforms presented here ranges between 0.95 and 0.99
for a wide span of mass values.
The energy of a binary system at 3PN and beyond
I will show how the effective field theory methods for the gravitationally bound
two-body system proposed by Goldberger and Rothstein can be employed to efficiently
compute the conservative dynamics of a binary system.
In particular, I will show how this method successfully reproduce the
already known effective action at 3PN order, and I will sketch the steps to extend
the computation to the yet-unknown 4PN order.
||Chair: S. Foffa
Tidal interaction in compact binaries: a post-Newtonian affine framework
Semi-analytical approaches can be very useful in
describing compact star coalescing binaries.
In our approach, based on the post-Newtonian
expansion and on the affine approximation, we
model the tidal deformation of neutron stars
in the coalescence of compact binary systems.
We apply our approach to study black hole-neutron
star coalescences up to the onset of neutron star
tidal disruption, comparing our results with the
outcome of numerical relativity simulations.
The effective one body description of tidal effects in compact
binaries and its comparison with numerical relativity simulations
The late part of the gravitational wave signal of binary neutron star inspirals
can in principle yield crucial information on the nuclear equation of state via
its dependence on relativistic tidal parameters. In the hope of describing
analytically the late part of the gravitational wave signal, I will briefly introduce
an extension of the effective-one-body formalism that includes the tidal interaction.
The analytical predictions are then compared/constrasted with two numerical
relativity simulations of inspiralling and coalescing neutron star binaries.
By calibrating one single flexibility parameter accounting for higher-order
tidal effects, one finds that the EOB model can reproduce, within the
numerical error, the two waveforms essentially up to merger.
The PN Approximation Beyond Point-Masses
Compact objects like black holes or neutron stars can
approximately be described by point masses very well. However, very
interesting astronomical information might be contained in effects to
gravitational waves arising from the object's higher multipoles (or
their finite size). Some of these effects can be modeled by an
extension of the point mass action. Based on such an action,
contributions of dipole (i.e., spin) and quadrupole to the
post-Newtonian (PN) approximation can be obtained. The potential
relevance of recent results (such as arXiv:1104.3079 and
arXiv:1002.2093) for gravitational wave astronomy is briefly discussed.
||Chair: A. Nagar
Self-force calculations for black hole inspirals
Advances in numerical relativity (NR) since 2005 have led to rapid
progress in the modelling of black hole inspirals. Yet an important
frontier awaits: the large mass-ratio regime. For example, in the
final year before merger, an Extreme Mass-Ratio Inspiral (EMRI) will
undergo $~ 10^5$ orbits in the strong-field regime. EMRIs may be
analysed via black hole perturbation theory, by assuming the small
body follows a trajectory on the background spacetime of the large
black hole, and that the trajectory is perturbed away from a geodesic
of the background by a `self-force'. Practical methods for computing
self-force effects at first order in the mass ratio are now
In this short review, I will focus on four emerging themes in the
self-force programme: (i) comparison of gauge-invariant results from
gravitational self-force (GSF) calculations with other methodologies
(e.g. Post-Newtonian, EOB and NR in arXiv:1106.3278); (ii) ongoing
development of numerical schemes for highly accurate calculations of
GSF on Kerr spacetime; (iii) aspirations to achieve accurate,
self-consistent long-term orbital evolutions of EMRIs using GSF
calculations; (iv) understanding of new qualitatively new phenomena,
such as resonances [arXiv:1009.4923], which have practical
implications for data analysis strategies.
A quasi-radial stability criterion for rotating relativistic stars
The stability properties of relativistic stars against gravitational
collapse to black holes is a classical problem in general relativity.
In 1988, a sufficient criterion for secular instability was
established by Friedman, Ipser \& Sorkin, who proved that a sequence of
uniformly rotating barotropic stars are secularly unstable on one side
of a turning point and then argued that a stronger result should hold:
that the sequence should be stable on the opposite side, with the
turning point marking the onset of secular instability. We show here
that this expectation is not met. By computing in full general
relativity the F-mode frequency for a large number of rotating stars,
we show that the neutral-stability point, that is, where the frequency
becomes zero, differs from the turning point for rotating stars. Using
numerical simulations, we validate that the new criterion can be used
to assess the dynamical stability of relativistic rotating stars.
(This work is appeared in MNRAL(2011).)
Properties of stationary differentially rotating relativistic cold stars
Stationary configurations of differentially rotating relativistic
polytrops are studied using a multidomain pseudo-spectral code based
on the method developed in Jena (Ansorg, Kleinwächter, Meinel,
2003). Results concerning the solution space, the maximal masses, and
the maximal values of rotation parameters such as the ratio between
kinetic and gravitational energies will be presented and analyzed for
several cold equations of states. Implications for the emission of
gravitational waves from binary neutron star mergers will be
At the "Trattoria ai Corriere" with a menu of the tipical
A vegeterian option will available on advanced request.