21,944 research outputs found
General Relativistic Models of Binary Neutron Stars in Quasiequilibrium
We perform fully relativistic calculations of binary neutron stars in
corotating, circular orbit. While Newtonian gravity allows for a strict
equilibrium, a relativistic binary system emits gravitational radiation,
causing the system to lose energy and slowly spiral inwards. However, since
inspiral occurs on a time scale much longer than the orbital period, we can
treat the binary to be in quasiequilibrium. In this approximation, we integrate
a subset of the Einstein equations coupled to the relativistic equation of
hydrostatic equilibrium to solve the initial value problem for binaries of
arbitrary separation. We adopt a polytropic equation of state to determine the
structure and maximum mass of neutron stars in close binaries for polytropic
indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate
turning points along energy equilibrium curves to identify the onset of orbital
instability. In particular, we locate the innermost stable circular orbit
(ISCO) and its angular velocity. We construct the first contact binary systems
in full general relativity. These arise whenever the equation of state is
sufficiently soft >= 1.5. A radial stability analysis reveals no tendency for
neutron stars in close binaries to collapse to black holes prior to merger.Comment: 14 pages, 8 figures, RevTe
Symbolic Maximum Likelihood Estimation with Mathematica
Mathematica is a symbolic programming language that empowers the user to undertake complicated algebraic tasks. One such task is the derivation of maximum likelihood estimators, demonstrably an important topic in statistics at both the research and expository level. In this paper, a Mathematica package is provided that contains a function entitled SuperLog. This function utilises pattern-matching code that enhances Mathematica's ability to simplify expressions involving the natural logarithm of a product of algebraic terms. This enhancement to Mathematica's functionality can be of particular benefit for maximum likelihood estimation
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Numerical Relativity As A Tool For Computational Astrophysics
The astrophysics of compact objects, which requires Einstein's theory of
general relativity for understanding phenomena such as black holes and neutron
stars, is attracting increasing attention. In general relativity, gravity is
governed by an extremely complex set of coupled, nonlinear, hyperbolic-elliptic
partial differential equations. The largest parallel supercomputers are finally
approaching the speed and memory required to solve the complete set of
Einstein's equations for the first time since they were written over 80 years
ago, allowing one to attempt full 3D simulations of such exciting events as
colliding black holes and neutron stars. In this paper we review the
computational effort in this direction, and discuss a new 3D multi-purpose
parallel code called ``Cactus'' for general relativistic astrophysics.
Directions for further work are indicated where appropriate.Comment: Review for JCA
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