529 research outputs found
A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars I. Construction
R-modes of a rotating neutron star are unstable because of the emission of
gravitational radiation. We explore the saturation amplitudes of these modes
determined by nonlinear mode-mode coupling. Modelling the star as
incompressible allows the analytic computation of the coupling coefficients.
All couplings up to n=30 are obtained, and analytic values for the shear
damping and mode normalization are presented. In a subsequent paper we perform
numerical simulations of a large set of coupled modes.Comment: 15 pages 3 figure
The Kerr metric
This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the 'miraculous' nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity
The Federal Administrative Court Proposal: An Examination of General Principals
Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features—a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not—with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method
Numerical relativity: maximizing the scientific payoff from gravitational wave detection
For many of the proposed LIGO sources, we are currently unable to produce reliable theoretical waveforms or event rates. Usually the difficulty is in performing numerical simulations. These problems seriously undermine our ability to extract science from LIGO, or in some cases even to detect sources at all. We describe two sources where these problems are present: the merger of a binary black hole system, and a newborn neutron star unstable to r-modes. We explain the origin of the difficulties, and how they might be overcome
Nonlinear Couplings of R-modes: Energy Transfer and Saturation Amplitudes at Realistic Timescales
Non-linear interactions among the inertial modes of a rotating fluid can be
described by a network of coupled oscillators. We use such a description for an
incompressible fluid to study the development of the r-mode instability of
rotating neutron stars. A previous hydrodynamical simulation of the r-mode
reported the catastrophic decay of large amplitude r-modes. We explain the
dynamics and timescale of this decay analytically by means of a single three
mode coupling. We argue that at realistic driving and damping rates such large
amplitudes will never actually be reached. By numerically integrating a network
of nearly 5000 coupled modes, we find that the linear growth of the r-mode
ceases before it reaches an amplitude of around 10^(-4). The lowest parametric
instability thresholds for the r-mode are calculated and it is found that the
r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included.
Using the network of coupled oscillators, integration times of 10^6 rotational
periods are attainable for realistic values of driving and damping rates.
Complicated dynamics of the modal amplitudes are observed. The initial
development is governed by the three mode coupling with the lowest parametric
instability. Subsequently a large number of modes are excited, which greatly
decreases the linear growth rate of the r-mode.Comment: 3 figures 4 pages Submitted to PR
Evolving relativistic fluid spacetimes using pseudospectral methods and finite differencing
We present a new code for solving the coupled Einstein-hydrodynamics
equations to evolve relativistic, self-gravitating fluids. The Einstein field
equations are solved on one grid using pseudospectral methods, while the fluids
are evolved on another grid by finite differencing. We discuss implementation
details, such as the communication between the grids and the treatment of
stellar surfaces, and present code tests.Comment: To appear in the Proceedings of the Eleventh Marcel Grossmann Meetin
Short note on the mass matrix for Gauss-Lobatto grid points
The mass matrix for Gauss-Lobatto grid points is usually approximated by
Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy
to invert. The exact mass matrix and its inverse are full. We show that the
exact mass matrix \emph{and} its inverse differ from the approximate diagonal
ones by a simple rank-1 update (outer product). They can thus be applied to an
arbitrary vector in operations instead of
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