Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.Comment: 17 pages, 15 figures. Small changes in the text, and a change in the list of authors. One new reference adde

Nonlinear r-modes in rapidly rotating relativistic stars

SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Axisymmetric modes of rotating relativistic stars in the cowling approximation

Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, nonlinear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l=0, 1, 2 and 3, for a sequence of rotating stars from the non-rotating limit to the mass-shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50% of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions. (orig.)SIGLEAvailable from Internet: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman