ES1 - Exact Solutions in Four and Higher Dimensions: Mathematical Aspects |
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Speaker |
Briscese, Fabio |
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Coauthors |
Francesco Calogero |
| Talk Title |
Isochronous Spacetimes |
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Abstract |
It has been shown that, given any (translation-invariant, classical) nonrelativistic many-body problem characterized by a Hamiltonian H, it is possible to manufacture another (translation-invariant) many-body problem characterized by a suitably modified Hamiltonian $\tilde{H}$ which features an isochronous time evolution with an arbitrarily assigned period $\tilde{T}$--so that all its solutions are periodic with period $\tilde{T}$--yet mimics exactly the dynamics of the Hamiltonian H over times T; with both $\tilde{T}$ and T arbitrarily assigned, except for the restriction $T < \tilde{T}$. We show how this result is extended to a general relativistic context by enlarging the class of admissible solutions of Einstein’s equations to degenerate metrics. We show how these degenerate isochronous metrics are obtained from a generic spacetime, and we discuss their properties. This talk is based on the following papers: Fabio Briscese and Francesco Calogero, "Isochronous solutions of Einstein.s equations and their Newtonian limit", Int. J. Geom. Meth. Mod. Phys. 15 (2018) 185010; "Isochronous Spacetimes", Acta Appl.Math. 137 (2015) 3-16; "Isochronous Cosmologies", Int. J. Geom. Meth. Mod. Phys. 11 (2014) 1450054. |
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