72 research outputs found
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
Path integration in relativistic quantum mechanics
The simple physics of a free particle reveals important features of the
path-integral formulation of relativistic quantum theories. The exact
quantum-mechanical propagator is calculated here for a particle described by
the simple relativistic action proportional to its proper time. This propagator
is nonvanishing outside the light cone, implying that spacelike trajectories
must be included in the path integral. The propagator matches the WKB
approximation to the corresponding configuration-space path integral far from
the light cone; outside the light cone that approximation consists of the
contribution from a single spacelike geodesic. This propagator also has the
unusual property that its short-time limit does not coincide with the WKB
approximation, making the construction of a concrete skeletonized version of
the path integral more complicated than in nonrelativistic theory.Comment: 14 page
Critical Phenomena in Head-on Collisions of Neutron Stars
We found type I critical collapses of compact objects modeled by a polytropic
equation of state (EOS) with polytropic index without the
ultra-relativistic assumption. The object is formed in head-on collisions of
neutron stars. Further we showed that the critical collapse can occur due to a
change of the EOS, without fine tuning of initial data. This opens the
possibility that a neutron star like compact object, not just those formed in a
collision, may undergo a critical collapse in processes which slowly change the
EOS, such as cooling.Comment: 4 pages,6 figures, 15 reference
A Conformal Hyperbolic Formulation of the Einstein Equations
We propose a re-formulation of the Einstein evolution equations that cleanly
separates the conformal degrees of freedom and the non-conformal degrees of
freedom with the latter satisfying a first order strongly hyperbolic system.
The conformal degrees of freedom are taken to be determined by the choice of
slicing and the initial data, and are regarded as given functions (along with
the lapse and the shift) in the hyperbolic part of the evolution.
We find that there is a two parameter family of hyperbolic systems for the
non-conformal degrees of freedom for a given set of trace free variables. The
two parameters are uniquely fixed if we require the system to be ``consistently
trace-free'', i.e., the time derivatives of the trace free variables remains
trace-free to the principal part, even in the presence of constraint violations
due to numerical truncation error. We show that by forming linear combinations
of the trace free variables a conformal hyperbolic system with only physical
characteristic speeds can also be constructed.Comment: 4 page
- …