SFB Transregio 7 - Gravitational Wave Astronomy

List of Abstracts

Name Title/Abstract of contribution
Andersson, Nils Asteroseismology
[176 KByte]
I will review the basics of neutron star pulsation theory.
Particular focus will be on the modes that are potentially relevant
for gravitational-wave observations. I will discuss the
character of these modes and scenarios in which they may be excited to
relevant amplitudes. The idea of "gravitational-wave asterosesimology",
wherein observed modes lead to inferences concerning the
stars physics, is the central theme of the lecture.

The r-mode instability
[146 KByte]
In this talk I will summarise the current status of
the gravitational-wave driven r-mode instability.
Of particular importance are dissipation mechanisms that tend to
counteract the instability, and I will discuss the
effects of i) the core-crust interface, ii) the presence of
exotic particles like hyperons in the stars core, iii)
superfluidity and the associated mutual friction.
The possible role of the magnetic field will also be described.
Cutler, Curt Neutron Stars and Gravitational Waves

An overview of neutron stars as gravitational-wave sources.

Introduction to the Post-Newtonian Approximation I & II

A pedagogical introduction to the post-Newtonian approximation, emphasizing the basic ideas.
Dain, Sergio
Elliptic Problems in Relativistic Astrophysics

[various formats available]
In these lectures I will review some basic results on elliptic
boundary value problems with applications to General Relativity
Font, J. Antonio
Numerical relativistic hydrodynamics.
[6667 KByte]
These two lectures are devoted to present the existing formulations
of the general relativistic hydrodynamics equations (restricted to
perfect fluids) which are most widely employed in numerical
investigations in relativistic astrophysics. The lectures are divided
into six main sections, with a first half devoted to mathematical
issues such as the derivation of the equations and a second half
devoted to numerical aspects. The first section deals with a basic
introduction to the defining properties of fluids and to the equations
of classical (Newtonian) fluid dynamics. Next, from the conservation
laws of density current and stress-energy we show how the equations of
general relativistic hydrodynamics are obtained. These can be
formulated in various ways, which in turn has important implications
on the numerical procedure to solve them, depending on the choice of
the state-vector of the hyperbolic system they form or on the slicing
chosen to foliate the spacetime. The most frequently used formulations
of those equations are described to some length, paying particular
attention to the issue of nonconservative versus conservative
approaches. The second part of the lectures focuses on presenting a
broad review of current approaches to numerically solve nonlinear
hyperbolic systems of conservation laws. Here, much of the emphasis is
on Riemann solvers and high-resolution shock-capturing (Godunov-type)
schemes. The lectures end with test demonstrations showing the
accuracy of the numerical schemes discussed. A number of applications
in relativistic astrophysics in scenarios involving compact objects is
presented last.

Friedman, John
Instabilities of Rotating Relativistic Stars
[1714 KByte]
Dynamical nonaxisymmetric instabilities may precede the formation of
neutron stars. Related instabilities driven by gravitational waves make
all perfect-fluid stars formally unstable and may limit the spin of
rapidly rotating, nascent neutron stars and of old, accreting neutron
stars as well. In particular the instability of the l=m=2 r-mode (a
mode with axial parity) is a leading candidate for the rough clustering
observed in the spins of low-mass x-ray binaries; and gravitational
waves emitted by these stars may be observable by detectors with the
expected sensitivity of advanced LIGO. As discussed in this talk and
in a related talk by Nils Andersson, to radiate detectable power, the
instability would have to overcome a number of obstacles; in
particular, recent studies of rapid cooling and high viscosity
associated with hyperons in neutron-star cores, of quark cores, and of
amplitude saturation by nonlinear coupling, have sharply reduced the
likelihood of observing waves from nascent neutron stars.
Surprisingly, however, the recent studies may have increased the chance
of detecting gravitational waves from old accreting stars.

Binary neutron stars in general relativity
I. Formalism and analytic results
[8059 KByte]
The first of two talks is primarily concerned with the formalism
used to construct initial data sets for models of binary neutron stars.
The data sets can be used to compute quasistationary sequences and
to find the approximate location of an innermost stable circular orbit
using a turning-point method. The initial data are commonly found by solving
a truncated set of Einstein equations that include the initial value
equations and the equation of hydrostatic equilibrium. Several related
approaches (using spatial conformal flatness, helical symmetry, or a
waveless approximation) are currently in use. Asymptotic identity of
the Komar and ADM masses and a related virial theorem can be used to
improve the accuracy of the relation between the angular velocity and
radius of the initial orbit.
Meinel, Reinhard
Rotating fluids and black holes
gzipped PostScript
[523 KByte]
In this talk I shall give an overview of equilibrium configurations of
homogeneous fluids in general relativity. The classical Maclaurin sequence of
rotating spheroids serves as a point of departure for describing the
corresponding relativistic picture, which leads continuously up to extreme
Kerr black holes. It can be shown that extreme, i.e. maximally rotating,
black holes are indeed the only candidates for black hole limits of rotating
fluid bodies in equilibrium.

[1] M. Ansorg, T. Fischer, A. Kleinwächter, R. Meinel, D. Petroff and K.
Schöbel, Equilibrium configurations of homogeneous fluids in general
relativity, MNRAS, in press [gr-qc/0402102]

[2] R. Meinel, Quasistationary collapse to the extreme Kerr black hole, Ann.
Phys. (Leipzig) 13 (2004) 600 [gr-qc/0405074]

Müther, Herbert
Equations of State I & II
[987 KByte]

Peitz, Jochen
Dissipative Relativistic Flow

I will review the relativistic Navier-Stokes/Fourier equations,
discuss issues related to their numerical solution and comment
on recent results for neutron stars.

Pollney, Denis
Numerical evolutions of Einstein's equations
[140 KByte]
This lecture will cover various issues in obtaining numerical
solutions of Einstein's equations. Formulated as an initial boundary
value problem, the field equations become a coupled elliptic-hyperbolic
system. Special care needs to be taken in the choice of variables, and
form of the evolution system, choice of gauge, and boundary conditions.
The lecture will provide an introduction to these points and discuss
current techniques being applied in simulations of black hole
[2254 KByte]
Binary black hole simulations in general relativity

Massive binary systems (neutron stars or black holes) in the
nearby universe are one of the more likely events to be observed by
the first generation of gravitational wave detectors. This talk
outlines recent progress in the numerical simulation of black
hole spacetimes, in particular focussing on evolutions of binaries
in close quasi-circular orbit, and the extraction of physical
information from horizon dynamics and far-zone wave indicators.

Pons, Jose
The role of neutrinos in the formation and
evolution of neutron stars and strange stars.
[8555 KByte]
[94 KByte]
This talk is a general overview of the astrophysical
situations involving neutron stars (or strange stars) in which
neutrinos play a relevant role in the dynamics or thermal
gzipped PostScript
[93 KByte]
Neutrino transport: from diffusion to Boltzmann solvers.

I review the basis and fundamental equations of neutrino transport,
describing all the different levels of approximation that are
normally used to simplify the problem and build numerical codes.
It is discussed under which circumstances some simplifications fail
to give a satisfactory result and some attention is paid at the
way the microphysics (neutrino opacities) is implemented.
Rezzolla, Luciano Magnetic fields in neutron stars: I, II

gzipped PostScript
[900 KByte]
[937 KByte]
These lectures are aimed at introducing the properties of magnetized neutron stars (NSs) and the impact that magnetic fields have on the structure, stability, and electromagnetic observability of neutron stars. I will start by discussing the observational evidence of magnetic fields in neutron stars and the basic principles behind the pulsed emission in radio pulsars. I will then pass on to introducing the magnetohydrodynamics (MHD) equations and the form they assume in the case of interest of neutron stars and when they are at the origin of a dynamo action in proto-neutron stars (PNSs). After providing a possible explanation for the origin of intense magnetic fields in neutron stars, I will discuss the impact these have on the structure and shape of stars in magnetohydrostatic equilibrium, as well the stability criteria for magnetic fields of different intensity and topology. Finally, I will briefly discuss the electrodynamics of neutron stars in general relativity, the corrections introduced with respect to the picture in Newtonian physics and the decay of magnetic fields in a neutron star that is undergoing thermal and rotational evolution. A brief summary of the main topics covered is listed below.
- Observational evidence of intense magnetic fields
* The inclined rotator model in pulsars

- Introduction to the MHD equations
* The ideal MHD limit
* The Alfven theorem
* Dissipative effects

- Generation of magnetic fields in PNSs and NSs
* dynamo action in turbulent PNSs
* magnetic fields produced by stellar instabilities

- Structure and stability of magnetized neutron stars
* relativistic models of highly magnetized NSs
* stability of magnetic fields in NSs

- General relativistic electrodynamics of NSs
* the vacuum electromagnetic fields of a rotating relativistic NS
* electromagnetic radiation from a rotating relativistic NS
* magnetic field evolution in rotating and cooling NSs

Schäfer, Gerhard
Post-Newtonian results in the analytical treatment of compact binaries
scanned slides
The talk gives an overview of what has been achieved in the
post-Newtonian treatment of the analytical dynamics of compact binaries.
The topics discussed are: canonical approach by Arnowitt, Deser, and
Misner; use of Dirac delta functions in general relativity; initial
data; binary Hamiltonian to 3PN conservative order; approximate
innermost stable circular orbit; explicit solution for the motion of the
3PN conservative dynamics; dissipative dynamics to 3.5PN order; spatial
conformal flatness; skeleton model and identity of Komar and ADM masses;
comparison with the puncture method of numerical relativity.
Stergioulas, Nikolaos Equilibrium models of relativistic stars
[48 KByte]
The equations of structure for compact objects in
equilibrium are reviewed. Apart from perfect fluid
rotating stars, models with magnetic field and
non-zero temperature will also be covered. A summary
of the main properties of such models will be given.

Nonlinear dynamics of relativistic stars
[161 KByte]
A review of various astrophysical situations in which
nonlinear dynamics in relativistic stars becomes
important will be given. Such cases include the nonlinear
development of dynamical and secular instabilities and
the collapse of unstable relativistic stars.
Uryu, Koji
Binary neutron stars in GR II: Numerical method
[805 KByte]
The second part begins with a brief review of earlier computations of
binary neutron stars, including both semi-analytic methods and numerical
methods. A particular numerical implementation is then introduced,
involving a concrete form of the field equations and the hydrostatic
equations, together with the boundary conditions and a choice of parameter
sets that are found empirically to yield a convergent iteration. The
numerical solution of each elliptic equation by means of a Green's
function in spherical coordinates is explained as an example for design of
a numerical code. Recent work on binary inspiral involves initial data
sets obtained in a waveless approximation, and the latest of these results
are presented. Also, as important applications, a determination of the
ISCO from the equilibrium sequence, a construction of gravitational
waveform, and results of binary neutron star merger simulations are