Abstract
We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the Reissner-Nordström black hole with the same quasilocal mass and charge. So hairy black holes are natural candidates for the endpoint of the superradiant/near-horizon instabilities of the black hole bomb system. We also relate hairy black holes to the boson stars of the theory. When it has a zero horizon radius limit, the hairy black hole family terminates on the boson star family. Finally, we find the Israel surface tensor of the box required to confine the scalar condensate and that it can obey suitable energy conditions.
Highlights
Find all possible stationary solutions of the theory with boundary conditions that confine the scalar field inside the box
We find the phase diagram of solutions of the charged black hole bomb system
We find that the spectrum of hairy black holes and boson stars of the theory is qualitatively distinct depending on whether e is smaller or bigger than four pivotal critical scalar field charges — eNH, eγ, ec and eS — which obey the relations 0 < eNH < eγ < ec < eS
Summary
The Einstein-Maxwell-Klein-Gordon theory, whereby the scalar field is confined inside a box of radius L in an asymptotically flat background, is fully specified once we fix the mass and charge q of the scalar field. The AdS boundary conditions act as a natural gravitational box with radius inversely proportional to the cosmological length that provides bound states In this sense, our work complements and completes previous AdS studies since the existence range of the secondary/non-perturbative boson star family, its merger with the main/perturbative soliton at e = ec, and the fact that hairy BHs can terminate on this soliton family for eγ ≤ e < ec was not established in detail in [25, 37,38,39,40]
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