46,179 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
Harmonic coordinate method for simulating generic singularities
This paper presents both a numerical method for general relativity and an
application of that method. The method involves the use of harmonic coordinates
in a 3+1 code to evolve the Einstein equations with scalar field matter. In
such coordinates, the terms in Einstein's equations with the highest number of
derivatives take a form similar to that of the wave equation. The application
is an exploration of the generic approach to the singularity for this type of
matter. The preliminary results indicate that the dynamics as one approaches
the singularity is locally the dynamics of the Kasner spacetimes.Comment: 5 pages, 4 figures, Revtex, discussion expanded, references adde
Top quark physics at muon and other future colliders
The top quark will be extensively studied at future muon colliders. The
threshold cross section can be measured precisely, and the small beam energy
spread is especially effective at making the measurement useful. We report on
all the activities of the top quark working group, including talks on top quark
physics at other future colliders.Comment: 16 pages, 9 figures, Summary report of the Top Quark Working Group at
the Workshop on Physics at the First Muon Collider and at the Front End of a
Muon Collider, November 6-9, 1997, Fermi National Accelerator Laborator
Oscillatory approach to the singularity in vacuum symmetric spacetimes
A combination of qualitative analysis and numerical study indicates that
vacuum symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all
known cases" changed to "various known cases" in the first paragrap
Timelike Compton scattering: exclusive photoproduction of lepton pairs
We investigate the exclusive photoproduction of a heavy timelike photon which
decays into a lepton pair, gamma p -> l+ l- p. This can be seen as the analog
of deeply virtual Compton scattering, and we argue that the two processes are
complementary for studying generalized parton distributions in the nucleon. In
an unpolarized experiment the angular distribution of the leptons readily
provides access to the real part of the Compton amplitude. We estimate the
possible size of this effect in kinematics where the Compton process should be
dominated by quark exchange.Comment: 31 pages, 17 figure
On the area of the symmetry orbits in symmetric spacetimes
We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the group orbits takes on all positive values. This
result shows that the areal time coordinate which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the
inequality appearing as the first stage of (52) is not necessarily true), and
since the appendix is unnecessary for the proof of our results, we leave it
out. version 2 -- clarifications added, version 3 -- reference correcte
Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on
A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the
singularity in generic gravitational collapse is locally oscillatory is tested
numerically in vacuum, U(1) symmetric cosmological spacetimes on . If the velocity term dominated (VTD) solution to Einstein's equations is
substituted into the Hamiltonian for the full Einstein evolution equations, one
term is found to grow exponentially. This generates a prediction that
oscillatory behavior involving this term and another (which the VTD solution
causes to decay exponentially) should be observed in the approach to the
singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution
versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to
ftp://vela.acs.oakland.edu/pub/berger/u1genfig
Shintani functions, real spherical manifolds, and symmetry breaking operators
For a pair of reductive groups , we prove a geometric criterion
for the space of Shintani functions to be finite-dimensional
in the Archimedean case.
This criterion leads us to a complete classification of the symmetric pairs
having finite-dimensional Shintani spaces.
A geometric criterion for uniform boundedness of is
also obtained.
Furthermore, we prove that symmetry breaking operators of the restriction of
smooth admissible representations yield Shintani functions of moderate growth,
of which the dimension is determined for .Comment: to appear in Progress in Mathematics, Birkhause
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