5,230 research outputs found

### Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution
central (HRC) scheme is robust enough to yield accurate hydrodynamical
simulations of special relativistic flows in the presence of ultrarelativistic
speeds and strong shock waves. In this paper we apply this scheme in full
general relativity (involving {\it dynamical} spacetimes), and assess its
suitability by performing test simulations for oscillations of rapidly rotating
neutron stars and merger of binary neutron stars. It is demonstrated that this
HRC scheme can yield results as accurate as those by the so-called
high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers.
Furthermore, the adopted HRC scheme has increased computational efficiency as
it avoids the costly solution of Riemann problems and has practical advantages
in the modeling of neutron star spacetimes. Namely, it allows simulations with
stiff equations of state by successfully dealing with very low-density
unphysical atmospheres. These facts not only suggest that such a HRC scheme may
be a desirable tool for hydrodynamical simulations in general relativity, but
also open the possibility to perform accurate magnetohydrodynamical simulations
in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

### Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

We show that the so-called flat-space rotational Killing vector method for
measuring the Cartesian components of a black hole spin can be derived from the
surface integral of Weinberg's pseudotensor over the apparent horizon surface
when using Gaussian normal coordinates in the integration. Moreover, the
integration of the pseudotensor in this gauge yields the Komar angular momentum
integral in a foliation adapted to the axisymmetry of the spacetime. As a
result, the method does not explicitly depend on the evolved lapse $\alpha$ and
shift $\beta^i$ on the respective timeslice, as they are fixed to Gaussian
normal coordinates, while leaving the coordinate labels of the spatial metric
$\gamma_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing
endows the method with coordinate invariance, which is not present in integral
expressions using Weinberg's pseudotensor, as they normally rely on the
explicit use of Cartesian coordinates

### Dynamics of thick discs around Schwarzschild-de Sitter black holes

We consider the effects of a cosmological constant on the dynamics of
constant angular momentum discs orbiting Schwarzschild-de Sitter black holes.
The motivation behind this study is to investigate whether the presence of a
radial force contrasting the black hole's gravitational attraction can
influence the occurrence of the runaway instability, a robust feature of the
dynamics of constant angular momentum tori in Schwarzschild and Kerr
spacetimes. In addition to the inner cusp near the black hole horizon through
which matter can accrete onto the black hole, in fact, a positive cosmological
constant introduces also an outer cusp through which matter can leave the torus
without accreting onto the black hole. To assess the impact of this outflow on
the development of the instability we have performed time-dependent and
axisymmetric hydrodynamical simulations of equilibrium initial configurations
in a sequence of background spacetimes of Schwarzschild-de Sitter black holes
with increasing masses. The simulations have been performed with an unrealistic
value for the cosmological constant which, however, yields sufficiently small
discs to be resolved accurately on numerical grids and thus provides a first
qualitative picture of the dynamics. The calculations, carried out for a wide
range of initial conditions, show that the mass-loss from the outer cusp can
have a considerable impact on the instability, with the latter being rapidly
suppressed if the outflow is large enough.Comment: 12 pages; A&A, in pres

### Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars
using a general relativistic hydrodynamics code under the assumption of a
conformal flatness. We compare our results to previous simulations where the
spacetime dynamics was neglected. The pulsations are studied along various
sequences of both uniformly and differentially rotating relativistic polytropes
with index N = 1. We identify several modes, including the lowest-order l = 0,
2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes.
Differential rotation significantly lowers mode frequencies, increasing
prospects for detection by current gravitational wave interferometers. We
observe an extended avoided crossing between the l = 0 and l = 4 first
overtones, which is important for correctly identifying mode frequencies in
case of detection. For uniformly rotating stars near the mass-shedding limit,
we confirm the existence of the mass-shedding-induced damping of pulsations,
though the effect is not as strong as in the Cowling approximation. We also
investigate non-linear harmonics of the linear modes and notice that rotation
changes the pulsation frequencies in a way that would allow for various
parametric instabilities between two or three modes to take place. We assess
the detectability of each obtained mode by current gravitational wave detectors
and outline how the empirical relations that have been constructed for
gravitational wave asteroseismology could be extended to include the effects of
rotation.Comment: 24 pages, 20 figures; minor corrections, added extended discussion
and one figure in one subsectio

### Numerical evolution of matter in dynamical axisymmetric black hole spacetimes. I. Methods and tests

We have developed a numerical code to study the evolution of self-gravitating
matter in dynamic black hole axisymmetric spacetimes in general relativity. The
matter fields are evolved with a high-resolution shock-capturing scheme that
uses the characteristic information of the general relativistic hydrodynamic
equations to build up a linearized Riemann solver. The spacetime is evolved
with an axisymmetric ADM code designed to evolve a wormhole in full general
relativity. We discuss the numerical and algorithmic issues related to the
effective coupling of the hydrodynamical and spacetime pieces of the code, as
well as the numerical methods and gauge conditions we use to evolve such
spacetimes. The code has been put through a series of tests that verify that it
functions correctly. Particularly, we develop and describe a new set of testbed
calculations and techniques designed to handle dynamically sliced,
self-gravitating matter flows on black holes, and subject the code to these
tests. We make some studies of the spherical and axisymmetric accretion onto a
dynamic black hole, the fully dynamical evolution of imploding shells of dust
with a black hole, the evolution of matter in rotating spacetimes, the
gravitational radiation induced by the presence of the matter fields and the
behavior of apparent horizons through the evolution.Comment: 42 pages, 20 figures, submitted to Phys Rev

### Nonlinear r-modes in Rapidly Rotating Relativistic Stars

The r-mode instability in rotating relativistic stars has been shown recently
to have important astrophysical implications (including the emission of
detectable gravitational radiation, the explanation of the initial spins of
young neutron stars and the spin-distribution of millisecond pulsars and the
explanation of one type of gamma-ray bursts), provided that r-modes are not
saturated at low amplitudes by nonlinear effects or by dissipative mechanisms.
Here, we present the first study of nonlinear r-modes in isentropic, rapidly
rotating relativistic stars, via 3-D general-relativistic hydrodynamical
evolutions. Our numerical simulations show that (1) on dynamical timescales,
there is no strong nonlinear coupling of r-modes to other modes at amplitudes
of order one -- unless nonlinear saturation occurs on longer timescales, the
maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is
of the same order as the rotational velocity at the equator). An absolute upper
limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars)
is set by causality. (2) r-modes and inertial modes in isentropic stars are
predominantly discrete modes and possible associated continuous parts were not
identified in our simulations. (3) In addition, the kinematical drift
associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000),
appears to be present in our simulations, but an unambiguous confirmation
requires more precise initial data. We discuss the implications of our findings
for the detectability of gravitational waves from the r-mode instability.Comment: 4 pages, 4 eps figures, accepted in Physical Review Letter

- â€¦