Regular Article – Theoretical Physics
On perturbation theory and critical exponents for self-similar systems
Center for Theoretical Physics and College of Physics, Jilin University, 130012, Changchun, China
2 Scuola Normale Superiore and I.N.F.N, Piazza dei Cavalieri 7, 56126, Pisa, Italy
Accepted: 20 December 2020
Published online: 12 January 2021
Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent . We complete the existing literature on the subject by computing the linear perturbation equations in the case where the axion-dilaton system assumes a parabolic form. Next, we solve the perturbation equations in a newly discovered self-similar solution in the hyperbolic case, which allows us to extract the Choptuik exponent. Our main result is that this exponent depends not only on the dimensions of spacetime but also the particular ansatz and the critical solutions that one started with.
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