Equilibrium non-selfgravitating tori around black holes in parameterised spherically symmetric spacetimes

Non-selfgravitating equilibrium tori orbiting around black holes have a long history and have been employed in numerous simulations of accretion flows onto black holes and other compact objects. We have revisited the problem of constructing such equilibria starting from spherically symmetric black-hole spacetimes expressed in terms of a fully generic and rapidly converging parameterisation: the RZ metric. Within this framework, we have extended the definitions of all of the quantities characterising these equilibria, starting from the concept of the von Zeipel cylinders and up to the possible ranges of the specific angular momenta that are employed to construct families of tori. Within the allowed space of parameters we have then encountered both standard ``single-torus'' solutions, but also non-standard ``double-tori'' solutions. While the properties of the first ones in terms of the presence of a single cusp, of a local pressure maximum and of a varying outer radius, are very similar to those encountered in general relativity, the properties of double-tori solutions are far richer and naturally allow for configurations having the same constant specific angular momentum and hence are potentially easier to produce in nature. The existence of these objects is at present very hypothetical, but these equilibrium tori were to be observed, they would provide very valuable information on the properties of the spacetime and on its deviation from general relativity.