Self-gravitating razor-thin disks around black holes via multi-hole seeds

Abstract

We construct self-gravitating razor-thin disks of counterrotating dust around Schwarzschild black holes (BHs) by applying the "displace, cut, and reflect" method to known seed solutions representing multi-holes. All but one of the sources of the seed solution generate the surrounding annular disk, whereas the remaining BH is kept unaltered and lies at the disk center after the transformation. The disks are infinite in extent, have annular character, and are linearly stable up to the innermost stable circular orbit of the system. Moreover, all energy conditions are satisfied along the disk and the spacetime is asymptotically flat, having finite ADM mass. We also comment on charged disks around extremal Reissner-Nordstr\"om BHs constructed from a Majumdar-Papapetrou $N$-BH seed solution. These simple examples can be extended to more general "BH + disk" solutions, obtained by the same method from seeds of the type "BH + arbitrary axisymmetric source". A natural follow-up of this work would be to construct disks around Reissner-Nordstr\"om BHs with arbitrary charge-to-mass ratio and around Kerr BHs.