52,424 research outputs found
The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory
A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the
singularity in generic gravitational collapse is spacelike, local, and
oscillatory is explored analytically and numerically in spatially inhomogeneous
cosmological spacetimes. With a convenient choice of variables, it can be seen
analytically how nonlinear terms in Einstein's equations control the approach
to the singularity and cause oscillatory behavior. The analytic picture
requires the drastic assumption that each spatial point evolves toward the
singularity as an independent spatially homogeneous universe. In every case,
detailed numerical simulations of the full Einstein evolution equations support
this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received
"honorable mention" in 1998 Gravity Research Foundation essay contest.
Submitted to Mod. Phys. Lett.
Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies
Heuristic arguments and numerical simulations support the Belinskii et al
(BKL) claim that the approach to the singularity in generic gravitational
collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to
identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By
writing the metric of one spacetime in the standard variables of another,
signatures for LMD may be found. Such signatures for the dynamics of spatially
homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are
reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the
dynamics of generic -symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime
Safari: Essays in Honour of Vincent Moncrief
Why Solve the Hamiltonian Constraint in Numerical Relativity?
The indefinite sign of the Hamiltonian constraint means that solutions to
Einstein's equations must achieve a delicate balance--often among numerically
large terms that nearly cancel. If numerical errors cause a violation of the
Hamiltonian constraint, the failure of the delicate balance could lead to
qualitatively wrong behavior rather than just decreased accuracy. This issue is
different from instabilities caused by constraint-violating modes. Examples of
stable numerical simulations of collapsing cosmological spacetimes exhibiting
local mixmaster dynamics with and without Hamiltonian constraint enforcement
are presented.Comment: Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk
given at GR1
- …