Black saturn

Abstract

Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing "black saturn": a spherical black hole surrounded by a black ring. Angular momentum keeps the configuration in equilibrium. Black saturn reveals a number of interesting gravitational phenomena: (1) The balanced solution exhibits 2-fold continuous non-uniqueness for fixed mass and angular momentum;(2) Remarkably, the 4+1d Schwarzschild black hole is not unique, since the black ring and black hole of black saturn can counter-rotate to give zero total angular momentum at infinity, while maintaining balance; (3) The system cleanly demonstrates rotational framedragging when a black hole with vanishing Komar angular momentum is rotating as the black ring drags the surrounding spacetime. Possible generalizations include multiple rings of saturn as well as doubly spinning black saturn configurations.

Black rings in (Anti)-de Sitter space

“…For example, with a proper choice of the function V (ρ) this allows to describe the bending of a black string in the background of static black holes and thus construct thin black Saturns, in the sense that the black ring surrounding the black hole is thin. Exact solutions for black Saturns in five-dimensional vacuum gravity were obtained in [31]. Our approach here allows to extend them and could be used to refine the arguments in [32].…”

Rotating black rings on Taub-NUT

“…In fact, it has been used with much success to generate new black-hole solutions in five dimensions, such as the doubly rotating black ring [5,7], multiple-horizon solutions like the black Saturn [25] and bi-ring [26], as well as black holes on non-trivial gravitational instanton backgrounds [8]. A recent review of some of this progress can be found in [17].…”

Black Holes in Higher-Dimensional Gravity

“…In particular, a multi-black hole configuration with k black holes has k independent parameters. This implies a continuous non-uniqueness in the (µ, n) phase diagram (or for a given mass), much like the one observed for bubble-black hole sequences [49] and for other classes of black hole solutions [99,17,19,18] (see also Sec. 6).…”

“…The qualitative behavior of the non-uniform string branch depends on the sign of γ. If γ is positive, then the branch emerges at the mass µ = µ GL with increasing µ and decreasing n. If instead γ is negative the branch emerges at µ = µ GL with decreasing µ and decreasing n. To see what this means for the entropy we note that from (17) and the first law of thermodynamics one finds…”

“…For rotating black holes most progress in recent years has been in five dimensions. Here, it has been found that in addition to the Myers-Perry (MP) black holes [15], there exist rotating black rings [16,2] and multi-black hole solutions like black-Saturns and multi-black rings [17,18,19,20] including those with two independent angular momenta [21,22,23]. All of these are exact solutions which have been obtained with the aid of special ansätze [24,25] based on symmetries and inverse-scattering techniques [26,27,28,29].…”