Nonexistence of black holes with noncanonical scalar fields

Abstract

We study the existence of black holes with a noncanonical scalar field as a matter source. We prove a simple no-hair theorem which rules out the existence of stationary, asymptotically flat black holes possessing scalar hair for a wide class of noncanonical scalar field theories. This applies to scalar field theories which are of the form of K-essence theories. In particular, we rule out the existence of such black holes in the ghost condensate model, and in large sectors of the dilatonic ghost condensate and Dirac-Born-Infeld models.

Stationary black holes with time-dependent scalar fields

“…After all, the original no-hair theorem of Bekenstein generalises fairly straightforwardly to a complex scalar field (this is also the case for the results involving a non-canonical scalar field presented in Ref. [13]). We will therefore consider this case briefly.…”

“…The best known results rule out the existence of stationary black holes with scalar hair for a real scalar field with self-interaction potential V (φ) obeying V ,φφ > 0 or φV ,φ ≥ 0, and static, spherically symmetric black holes with scalar hair assuming only that the potential is bounded from below. These proofs can even be extended to non-canonical scalar fields [11,13] and to Galileons to some extent [14,15].…”

Asymptotically flat black holes with scalar hair: A review

“…Thus, the action depends only on first derivates of the scalar field and not higher order ones, but it can have a non-canonical kinetic term. In particular, as an earlier theorem by the same authors, 63 it applies to the scalar fields used in K−essence models. The key point in the argument, based on an earlier observation, 64 is that, assuming a stationary geometry -which is thus also axi-symmetric by the rigidity theorem, assuming the scalar field to obey the null energy condition -and writing it in the form…”

Instability of hairy black holes in shift-symmetric Horndeski theories

“…In many scalar-tensor theories, it has been shown that black holes cannot support nontrivial scalar hair. This was first pointed out in the context of the Brans-Dicke theory [10], and later the theorem was extended to more general scalar-tensor theories [11] including k−essence [12,13]. It was also proven that a Galileon cannot develop a nontrivial configuration around a static and spherically symmetric black hole [14].…”