6,796 research outputs found
Isometries on spaces of absolutely continuous functions in a noncompact framework
In this paper we deal with surjective linear isometries between spaces of scalar-valued absolutely continuous functions on arbitrary (not necessarily closed or bounded) subsets of the real line (with at least two points). As a corollary, it is shown that when the underlying spaces are connected, each surjective linear isometry of these function spaces is a weighted composition operator, a result which generalizes all the previous known results concerning such isometries
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
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
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 and
shift on the respective timeslice, as they are fixed to Gaussian
normal coordinates, while leaving the coordinate labels of the spatial metric
and the extrinsic curvature 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
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
- …