Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell

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It is worth mentioning that it has recently been proved Hodrc ; HerR that non-spherically symmetric rotating black holes can support stationary (rather than static) regular massive scalar field configurations in their exterior regions

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Here the term ‘regular spacetimes’ refers to curved spacetimes which possess no event horizons

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A reflecting star is defined as a compact regular object for which the external scalar field vanishes on its surface [see Eq. ( 6

Cited in the paper.

Here l l is the spherical harmonic index of the charged massive scalar field [see Eq. ( 2

Cited in the paper.

We shall use natural units in which G = c = ℏ = k B = 1 G=c=\hbar=k_{\text{B}}=1

Cited in the paper.

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

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