Symmetry inheritance and no-hair theorems

Details

Written by Ivica Smolić

We say that a matter or a gauge field inherits a spacetime symmetry, generated by a Killing vector field, if it is necessarily invariant under the action of that Killing vector field. Symmetry inheritance is not only used as a convenient assumption in a choice of the ansatz, but is also an important ingredient of the various gravitational uniqueness theorems. Its breaking may point to some novel, potentially interesting physical phenomena, such as the recently discovered rotating black hole solutions with the complex scalar hair.

In this talk I shall present an overview of the recent novel results about the symmetry inheritance of the real and the complex scalar fields [1,3], as well as the symmetry inheritance of the electromagnetic field in (1+2)-dimensional spacetimes [2]. Also, I will discuss the ramifications of these theorems on the classification of the black hole hair, and present a survey of various open problems.

[1] I. Smolić: Symmetry Inheritance of Scalar Fields, Class. Quantum Grav. 32 (2015) 145010 [arXiv: 1501.04967]

[2] M. Cvitan, P. Dominis Prester and I. Smolić: Does three dimensional electromagnetic field inherit the spacetime symmetries?, Class. Quantum Grav. 33 (2016) 077001 [arXiv: 1508.03343]

[3] I. Smolić: Constraints on the symmetry noninheriting scalar black hole hair, Phys. Rev. D 95 (2017) 024016 [arXiv: 1609.04013]