497 research outputs found
Asymptotic Behavior of the Gowdy Spacetimes
We present new evidence in support of the Penrose's strong cosmic censorship
conjecture in the class of Gowdy spacetimes with spatial topology.
Solving Einstein's equations perturbatively to all orders we show that
asymptotically close to the boundary of the maximal Cauchy development the
dominant term in the expansion gives rise to curvature singularity for almost
all initial data. The dominant term, which we call the ``geodesic loop
solution'', is a solution of the Einstein's equations with all space
derivatives dropped. We also describe the extent to which our perturbative
results can be rigorously justified.Comment: 30 page
Blow-Up of Test Fields Near Cauchy Horizons
The behaviour of test fields near a compact Cauchy horizon is investigated.
It is shown that solutions of nonlinear wave equations on Taub spacetime with
generic initial data cannot be continued smoothly to both extensions of the
spacetime through the Cauchy horizon. This is proved using an energy method.
Similar results are obtained for the spacetimes of Moncrief containing a
compact Cauchy horizon and for more general matter models.Comment: 10 pages, Plain TeX, MPA-AR-92-
Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity
Constants of motion are calculated for 2+1 dimensional gravity with topology
R x T^2 and negative cosmological constant. Certain linear combinations of them
satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy
variables. Quantisation is straightforward in terms of the holonomy parameters.
On inclusion of the Hamiltonian three new global constants are derived and the
quantum algebra extends to that of the conformal algebra so(2,3). The modular
group appears as a discrete subgroup of the conformal group. Its quantum action
is generated by these conserved quantities.Comment: 22 pages, Plain Tex, No Figure
Global constants in (2+1)--dimensional gravity
The extended conformal algebra (so)(2,3) of global, quantum, constants of
motion in 2+1 dimensional gravity with topology R x T^2 and negative
cosmological constant is reviewed. It is shown that the 10 global constants
form a complete set by expressing them in terms of two commuting spinors and
the Dirac gamma matrices. The spinor components are the globally constant
holonomy parameters, and their respective spinor norms are their quantum
commutators.Comment: 14 pages, to appear in Classical and Quantum Gravity, Spacetime
Safari: Essays in Honor of Vincent Moncrief on the Classical Physics of
Strong Gravitational Field
Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity
Neutron stars in binary orbit emit gravitational waves and spiral slowly
together. During this inspiral, they are expected to have very little
vorticity. It is in fact a good approximation to treat the system as having
zero vorticity, i.e., as irrotational. Because the orbital period is much
shorter than the radiation reaction time scale, it is also an excellent
approximation to treat the system as evolving through a sequence of equilibrium
states, in each of which the gravitational radiation is neglected. In Newtonian
gravity, one can simplify the hydrodynamic equations considerably for an
equilibrium irrotational binary by introducing a velocity potential. The
equations reduce to a Poisson-like equation for the potential, and a
Bernoulli-type integral for the density. We show that a similar simplification
can be carried out in general relativity. The resulting equations are much
easier to solve than other formulations of the problem.Comment: 14 pages, AASTeX, accepted in ApJ. Simplified final form of equation
(eq. 52). Added Shibata re
Perturbations of Spatially Closed Bianchi III Spacetimes
Motivated by the recent interest in dynamical properties of topologically
nontrivial spacetimes, we study linear perturbations of spatially closed
Bianchi III vacuum spacetimes, whose spatial topology is the direct product of
a higher genus surface and the circle. We first develop necessary mode
functions, vectors, and tensors, and then perform separations of (perturbation)
variables. The perturbation equations decouple in a way that is similar to but
a generalization of those of the Regge--Wheeler spherically symmetric case. We
further achieve a decoupling of each set of perturbation equations into
gauge-dependent and independent parts, by which we obtain wave equations for
the gauge-invariant variables. We then discuss choices of gauge and stability
properties. Details of the compactification of Bianchi III manifolds and
spacetimes are presented in an appendix. In the other appendices we study
scalar field and electromagnetic equations on the same background to compare
asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear
in Class. Quant. Gravi
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