1,218 research outputs found
Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes
We have developed the formalism necessary to employ the
discontinuous-Galerkin approach in general-relativistic hydrodynamics. The
formalism is firstly presented in a general 4-dimensional setting and then
specialized to the case of spherical symmetry within a 3+1 splitting of
spacetime. As a direct application, we have constructed a one-dimensional code,
EDGES, which has been used to asses the viability of these methods via a series
of tests involving highly relativistic flows in strong gravity. Our results
show that discontinuous Galerkin methods are able not only to handle strong
relativistic shock waves but, at the same time, to attain very high orders of
accuracy and exponential convergence rates in smooth regions of the flow. Given
these promising prospects and their affinity with a pseudospectral solution of
the Einstein equations, discontinuous Galerkin methods could represent a new
paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR
Twisted-torus configurations with large toroidal magnetic fields in relativistic stars
Understanding the properties of the internal magnetic field of neutron stars
remains a theoretical challenge. Over the last years, twisted-torus geometries
have been considered both in Newtonian and general-relativistic equilibrium
models, as they represent a potentially good description of neutron star
interiors. All of these works have found an apparent intrinsic limitation to
geometries that are poloidal-field-dominated, with a toroidal-to-poloidal
energy ratio inside the star that are <10%, unless surface currents are
included and magnetic fields are allowed to be discontinuous. This limitation
is in stark contrast with the general expectation that much higher toroidal
fields should be present in the stellar interior and casts doubt about the
stability and hence realism of these configurations. We here discuss how to
overcome this limitation by adopting a new prescription for the azimuthal
currents that leads to magnetized equilibria where the toroidal-to-total
magnetic-field energy ratio can be as high as 90%, thus including geometries
that are toroidal-field-dominated. Moreover, our results show that for a fixed
exterior magnetic-field strength, a higher toroidal-field energy implies a much
higher total magnetic energy stored in the star, with a potentially strong
impact on the expected electromagnetic and gravitational-wave emission from
highly magnetized neutron stars.Comment: 5 pages, 3 figures, 1 tabl
Invited papers from the international meeting on 'New Frontiers in Numerical Relativity' (Albert Einstein Institute, Potsdam, Germany, 17-21 July 2006)
Traditionally, frontiers represent a treacherous terrain to venture into, where hidden obstacles are present and uncharted territories lie ahead. At the same time, frontiers are also a place where new perspectives can be appreciated and have often been the cradle of new and thriving developments. With this in mind and inspired by this spirit, the Numerical Relativity Group at the Albert Einstein Institute (AEI) organized a `New Frontiers in Numerical Relativity' meeting on 17–21 July 2006 at the AEI campus in Potsdam, Germany
Distortion of neutron stars with a toroidal magnetic field
Models of rotating relativistic stars with a toroidal magnetic field have
been computed for a sample of eight equations of state of cold dense matter.
Non-rotating models admit important levels of magnetization and quadrupole
distortion accompanied by a seemingly unlimited growth in size. Rotating models
reach the mass-shedding limit at smaller angular velocities than in the
non-magnetized case according to the larger circumferential equatorial radius
induced by the magnetic field. Moreover, they can be classified as
prolate-prolate, oblate-prolate, or oblate-oblate with respect to surface
deformation and quadrupole distortion. Simple expressions for surface and
quadrupole deformation are provided that are valid up to magnetar field
strengths and rapid rotation.Comment: 3 pages, 2 figures, to appear in the Proceedings of the 13th Marcel
Grossmann Meeting held in Stockholm 1-7 July, 2012, based on arXiv:1207.4035.
Updated to final published versio
Equilibrium models of relativistic stars with a toroidal magnetic field
We have computed models of rotating relativistic stars with a toroidal
magnetic field and investigated the combined effects of magnetic field and
rotation on the apparent shape (i.e. the surface deformation), which could be
relevant for the electromagnetic emission, and on the internal matter
distribution (i.e. the quadrupole distortion), which could be relevant for the
emission of gravitational waves. Using a sample of eight different cold nuclear
physics equations of state, we have computed models of maximum field strength,
as well as the distortion coefficients for the surface and the quadrupolar
deformations. Surprisingly, we find that non-rotating models admit arbitrary
levels of magnetization, accompanied by a growth of size and quadrupole
distortion to which we could not find a limit. Rotating models, on the other
hand, are subject to a mass-shedding limit at frequencies well below the
corresponding ones for unmagnetized stars. Overall, the space of solutions can
be split into three distinct classes for which the surface deformation and the
quadrupole distortion are either prolate and prolate, oblate and prolate, or
oblate and oblate, respectively. We also derive a simple formula expressing the
relativistic distortion coefficients, which allows one to compute the surface
deformation and the quadrupole distortion up to significant levels of rotation
and magnetization, essentially covering all known magnetars. Such a formula
replaces Newtonian equivalent expressions that overestimate the magnetic
quadrupole distortion by about a factor of 6 and are inadequate for strongly
relativistic objects like neutron stars.Comment: Published version with additional correction of remaining typo
The Exact Solution of the Riemann Problem in Relativistic MHD
We discuss the procedure for the exact solution of the Riemann problem in
special relativistic magnetohydrodynamics (MHD). We consider both initial
states leading to a set of only three waves analogous to the ones in
relativistic hydrodynamics, as well as generic initial states leading to the
full set of seven MHD waves. Because of its generality, the solution presented
here could serve as an important test for those numerical codes solving the MHD
equations in relativistic regimes.Comment: 36 pages, 13 figures. Minor changes to match published versio
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