Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-08-06
Class.Quant.Grav.26:025012,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
version 3: 20 pages iopart style, 19 eps figure files for 8 latex figures; added example of a transient true spike to contrast
Scientific paper
10.1088/0264-9381/26/2/025012
The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index $\mathcal{S}$, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except for the time used to parametrize it. Its graph versus time characterized by correlated isolated pulses in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such pulse pair arising from a single circuit or ``complex pulse'' around the origin in the complex plane. These pulses in the speciality index and their limiting points on the real axis seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role as a gauge invariant lens through which to view current investigations of inhomogeneous Mixmaster dynamics.
Bini Donato
Cherubini Christian
Geralico Andrea
Jantzen Robert T.
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