Upper bound on the black-hole critical exponents
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2 The Hadassah Institute, 91010, Jerusalem, Israel
Accepted: 6 June 2022
Published online: 20 June 2022
We derive the model-independent upper bound on the Choptuik critical exponents that characterize the scaling relation at the threshold of black-hole formation in type-II nearly self-similar gravitational collapse scenarios [here and are, respectively, the initial phase space deviation of a near-critical initial data from the exact self-similar critical solution and the horizon radius of the corresponding super-critical dynamically formed black hole]. Our compact proof is based on the non-decreasing nature of the coarse-grained phase space volume of the dynamical system. The analytically derived upper bound is confirmed by the numerical results that have been published in the physics literature about the Choptuik black-hole critical phenomena during the last three decades. The present work may shed new light on the relation between the critical phenomena in gravitational collapse and statistical physics.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022