Abstract
Horizonless spacetimes describing highly compact exotic objects with reflecting (instead of absorbing) surfaces have recently attracted much attention from physicists and mathematicians as possible quantum-gravity alternatives to canonical classical black-hole spacetimes. Interestingly, it has recently been proved that spinning compact objects with angular momenta in the sub-critical regime a¯≡J/M2≤1 are characterized by an infinite countable set of surface radii, {rc(a¯;n)}n=1n=∞, that can support asymptotically flat static configurations made of massless scalar fields. In the present paper we study analytically the physical properties of ultra-spinning exotic compact objects with dimensionless angular momenta in the complementary regime a¯>1. It is proved that ultra-spinning reflecting compact objects with dimensionless angular momenta in the super-critical regime 1−[m/(l+2)]2≤|a¯|−1<1 are characterized by a finite discrete family of surface radii, {rc(a¯;n)}n=1n=Nr, distributed symmetrically around r=M, that can support spatially regular static configurations of massless scalar fields (here the integers {l,m} are the harmonic indices of the supported static scalar field modes). Interestingly, the largest supporting surface radius rcmax(a¯)≡maxn{rc(a¯;n)} marks the onset of superradiant instabilities in the composed ultra-spinning-exotic-compact-object-massless-scalar-field system.
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