https://doi.org/10.1140/epjc/s10052-019-7340-0
Regular Article - Theoretical Physics
Critical phenomena in gravitational collapse of Husain–Martinez–Nunez scalar field
1
Department of Physics, Beijing Normal University, Beijing, 100875, China
2
College of Science, Beijing Information Science and Technology University, Beijing, 100192, China
3
Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, P.O. Box 2734, Beijing, 100080, China
* e-mail: sijie@bnu.edu.cn
Received:
21
August
2019
Accepted:
21
September
2019
Published online:
8
October
2019
We construct analytical models to study the critical phenomena in gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We first use the cut-and-paste technique to match the conformally flat solution (
) onto an outgoing Vaidya solution. To guarantee the continuity of the metric and the extrinsic curvature, we prove that the two solutions must be joined at a null hypersurface and the metric function in Vaidya spacetime must satisfy certain constraints. We find that the mass of the black hole in the resulting spacetime takes the form 
, where the critical exponent 
is equal to 0.5. For the case 
, we show that the scalar field must be joined onto two pieces of Vaidya spacetimes to avoid a naked singularity. We also derive the power-law mass formula with 
. Compared with previous analytical models which were constructed from a different scalar field with continuous self-similarity, we obtain the same value of . However, we show that the solution with is not self-similar. Therefore, we provide a rare example that a scalar field without self-similarity also possesses the features of critical collapse.
© The Author(s), 2019
