We study solutions in the Plebański–Demiański family which describe an accelerating, rotating, and dyonically charged black hole in ${\mathrm{AdS}}_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is nonvanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein seven-manifold, $S{E}_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $S{E}_7$ fibration over a two-dimensional weighted projective space, $\mathbb{W}\mathbb{C}{\mathbb{P}}_{[n_{-},n_{+}]}^1$, also known as a spindle, which is labeled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric ${\mathrm{AdS}}_2\times Y_9$ solutions of $D=11$ supergravity, which generalize a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain $\mathcal{N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with the appropriate magnetic flux.

We construct supersymmetric ${\text{AdS}}_3\times \mathrm{\Sigma }$ solutions of minimal gauged supergravity in $D=5$, where $\mathrm{\Sigma }$ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on $S^5$, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on $\mathrm{\Sigma }$.

We study the thermodynamics of ${\mathrm{AdS}}_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and nonextremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.

We construct supersymmetric "Image missing"<!-- image only, no MathML or LaTex -->solutions of D = 6 gauged supergravity, where "Image missing"<!-- image only, no MathML or LaTex --> is a two-dimensional orbifold known as a spindle. These uplift to solutions of massive type IIA supergravity using a general prescription, that we describe. We argue that these solutions correspond to the near-horizon limit of a system of N_f D8-branes, together with N D4-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. The dual field theories are d = 3, $$ \mathcal{N} $$N = 2 SCFTs that arise from a twisted compactification of the d = 5, $$ \mathcal{N} $$N = 1 USp(2N) gauge theory. We show that the holographic free energy associated to these solutions is reproduced by extremizing an off- shell free energy, that we conjecture to arise in the large N limit of the localized partition function of the d = 5 theories on "Image missing"<!-- image only, no MathML or LaTex -->. We formulate a universal proposal for a class of off-shell free energies, whose extremization reproduces all previous results for branes wrapped on spindles, as well as on genus g Riemann surfaces Σ_g. We further illustrate this proposal discussing D4-branes wrapped on "Image missing"<!-- image only, no MathML or LaTex -->, for which we present a supersymmetric "Image missing"<!-- image only, no MathML or LaTex --> solution of D = 6 gauged supergravity along with the associated entropy function.

We construct a family of multidyonically charged and rotating supersymmetric ${\mathrm{AdS}}_2\times \mathrm{\Sigma }$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $\mathrm{\Sigma }$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in ${\mathrm{AdS}}_4$ that we conjecture to exist. We demonstrate this in the nonrotating limit, constructing the accelerating black hole solutions and showing that the nonspinning spindle solutions arise as the near horizon limit of the supersymmetric and extremal subclass of these black holes. From the near horizon solutions we compute the Bekenstein-Hawking entropy of the black holes as a function of the conserved charges, and show that this may equivalently be obtained by extremizing a simple entropy function. For appropriately quantized magnetic fluxes, the solutions uplift on $S^7$, or its $\mathcal{N}=4$ orbifolds $S^7/\mathrm{\Gamma }$, to smooth supersymmetric solutions to $D=11$ supergravity, where the entropy is expected to count microstates of the theory on $N$ M2-branes wrapped on a spinning spindle, in the large $N$ limit.

We construct supersymmetric AdS₅ × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S⁴ to solutions of D = 11 supergravity which have orbifold singularites. We argue that the solutions are dual to d = 4, $$ \mathcal{N} $$N = 1 SCFTs that arise from N M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge.