Abstract
Kerr black holes with synchronised scalar hair and azimuthal harmonic index m>1 are constructed and studied. The corresponding domain of existence has a broader frequency range than the fundamental m=1 family; moreover, larger ADM masses, M and angular momenta J are allowed. Amongst other salient features, non-uniqueness of solutions for fixed global quantities is observed: solutions with the same M and J co-exist, for consecutive values of m, and the ones with larger m are always entropically favoured. Our analysis demonstrates, moreover, the qualitative universality of various features observed for m=1 solutions, such as the shape of the domain of existence, the typology of ergo-regions, and the horizon geometry, which is studied through its isometric embedding in Euclidean 3-space.
Highlights
Kerr black holes (BHs) with synchronised scalar hair [1] are a counterexample to the no-hair conjecture [2] – see [3,4,5] for reviews – occurring in a simple and physically sound model: Einstein-(complex and massive-)KleinGordon theory
An incomplete list of references, including various studies of physical properties, is [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66]. These hairy BH solutions have a relation with the physical phenomenon of superradiance [67], from which they can form dynamically from the Kerr solution [45,46,47] - see [54,57] for a discussion on the metastability of these solutions against superradiance
The existence of the hairy BH solutions does not rely on particular choices of scalar field potentials that violate energy conditions, unlike other examples of asymptotically flat BHs with scalar hair, see e.g. [72, 73]
Summary
Kerr black holes (BHs) with synchronised scalar hair [1] are a counterexample to the no-hair conjecture [2] – see [3,4,5] for reviews – occurring in a simple and physically sound model: Einstein-(complex and massive-)KleinGordon theory. As we shall see this is always the case: comparing solutions with consecutive values of m with the same global quantities, the higher m solution has a larger horizon area Another motivation for studying this higher m solutions is to assess the universality of some physical properties. It was observed in [11] that, when scanning the domain of existence, these BHs exhibit a more diverse structure of ergo-regions than the standard one of the Kerr BH.
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