Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner-Nordstr\"om black-hole spacetime

It is worth mentioning the physically interesting fact that, as explicitly shown in [ 4 , 5 ] , non-spherically symmetric rotating black holes in asymptotically flat spacetimes can support external stationary matter configurations which are made of (neutral or charged) massive scalar fields

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In particular, as shown in [ 6 ] , the lifetimes of the external quasi-bound matter configurations can be very large on the scale M M set by the black-hole mass

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It is worth noting that the familiar quasinormal resonances (free oscillations) of the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system studied in [ 9 , 10 , 11 , 12 ] are characterized by the boundary condition of free outgoing waves at spatial infinity. On the other hand, as emphasized above, the quasi-bound state black-hole-field resonances that we shall study in the present paper are characterized by exponentially decaying (bounded) radial eigenfunctions at spatial infinity [see Eqs. ( 10

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We shall use natural units in which G = c = ℏ = 1 G=c=\hbar=1

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Here M M and Q Q are respectively the mass and electric charge of the central Reissner-Nordström black hole

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Note that μ \mu and q q stand for μ / ℏ \mu/\hbar and q / ℏ q/\hbar , respectively. Hence, these physical parameters of the charged massive scalar fields have the dimensions of ( ( length OPEN ) − 1 )^{-1}

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