Towards a novel no-hair theorem for black holes

Abstract

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalarhair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

Holographic entanglement entropy in imbalanced superconductors

“…On the other hand, if one finds a non-zero scalar field it is understood that a condensate has been formed in the dual field theory. Of course this situation has a serious contradiction with the black hole no-hair theorem that supports the vanishing scalar field, but the fact of getting non-zero scalar field in the context of holographic superconductors hints that one needs to re-examine the no-hair theorem itself [31,32]. The above statement is true for any holographic superconductor.…”

Scaling symmetry and scalar hairy rotatingAdS3black holes

“…(31). It seems very plausible that the integral is negative for the scalar potential consistent with the positive energy theorem since the no-hair theorem is argued to hold in such a case [30].…”

Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

“…In this case, positive-energy theorems allow for a stable ground state solitonic solution, but standard no-hair theorems forbid the existence of BB solutions with a regular horizon [29,30]. For this reason, models whose potential V has a minimum have not been taken into consideration in this context.…”

“…The falloff behavior of the scalar field is therefore given by $ r 6 . The above-mentioned stability theorem allows in principle for the existence of a stable ground state hairy solitonic solution, but standard no-hair theorems forbid the existence of BB solutions with AdS asymptotics when m 2 is positive [29,30]. Even if a solitonic solution exists, it cannot be obtained as the extremal limit of an asymptotically AdS solution.…”