Physics
Scientific paper
May 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007jphcs..68a2039c&link_type=abstract
Journal of Physics: Conference Series, Volume 68, Issue 1, pp. 012039 (2007).
Physics
Scientific paper
The theory of symmetries of systems of coupled, ordinary differential equations (ODE's) is used to develop a concise algorithm for cartographing the space of solutions to vacuum Bianchi Einstein's Field Equations (EFE). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time reparameterization symmetry. Application of the method to Type III results in: a) the recovery of all known solutions without prior assumption of any extra symmetry, b) the enclosure of the entire unknown part of the solution space into a single, second order ODE in terms of one dependent variable and c) a partial solution to this ODE. It is also worth-mentioning the fact that the solution space is seen to be naturally partitioned into three distinct, disconnected pieces: one consisting of the known Siklos (pp-wave) solution, another occupied by the Type III member of the known Ellis-MacCallum family and the third described by the aforementioned ODE. Lastly, preliminary results reported show that the unknown part of the solution space for other Bianchi Types is described by a strikingly similar ODE, pointing to a natural operational unification as far as the problem of solving the cosmological EFE's is concerned.
Christodoulakis Th.
Terzis Petros A.
No associations
LandOfFree
The General Solution of Bianchi Type III Vacuum Cosmology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The General Solution of Bianchi Type III Vacuum Cosmology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The General Solution of Bianchi Type III Vacuum Cosmology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-771016