European Physical Journal C: Particles and Fields (Jan 2021)

On perturbation theory and critical exponents for self-similar systems

  • Ehsan Hatefi,
  • Adrien Kuntz

DOI
https://doi.org/10.1140/epjc/s10052-020-08788-w
Journal volume & issue
Vol. 81, no. 1
pp. 1 – 9

Abstract

Read online

Abstract Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $$\gamma $$ γ . 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.