Mathematics – Logic
Scientific paper
Apr 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997aps..apr.k1113b&link_type=abstract
American Physical Society, APS/AAPT Joint Meeting, April 18-21, 1997, abstract #K11.13
Mathematics
Logic
Scientific paper
The T^2 symmetric vacuum Gowdy cosmology on T^3 × R can be interpreted as two nonlinearly interacting polarizations of gravitational waves propagating in one direction in a homogeneous background universe. The decoupling of the dynamical wave equations from the constraints used to construct the background makes this model a useful test case for the numerical study of generic cosmological singularities. Velocity dominance arises when terms containing spatial derivatives no longer influence the evolution so that each spatial point evolves toward the singularity as a separate universe. With a certain choice of variables, the amplitude of the + polarization, P, grows linearly while that of the × polarization remains constant. However, velocity dominance requires the time derivative P, v, to be between zero and one. If v > 1, one of the (nonlinear) spatial derivative terms in the wave equation for P grows exponentially as the singularity is approached. This term then acts as a potential with v → 2-v after scattering. If v < 0, another nonlinear term acts as a potential with v → -v. The interaction between P and these potentials drives the system to velocity dominance.
Berger Beverly K.
Garfinkle David
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