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A bstract We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS 3 × S 3 × T 4 in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other $$ {\textrm{AdS}}_D\times \mathcal{C} $$ AdS D × C settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitly derive solutions by applying the charged Weyl formalism that we have previously developed. These are sourced internally by a chain of bolts that correspond to regions where the orbits of the commuting Killing vectors collapse smoothly. We show that these geometries can be interpreted as non-BPS T 4 and S 3 deformations on global AdS 3 × S 3 × T 4 that are located at the center of AdS 3 . These non-BPS deformations can be made arbitrarily small and should therefore correspond to non-supersymmetric operators in the D1-D5 CFT. Finally, we also construct interesting bound states of non-extremal BTZ black holes connected by regular bolts. 

A bstract We derive a non-BPS linear ansatz using the charged Weyl formalism in string and M-theory backgrounds. Generic solutions are static and axially-symmetric with an arbitrary number of non-BPS sources corresponding to various brane, momentum and KKm charges. Regular sources are either four-charge non-extremal black holes or smooth non-BPS bubbles. We construct several families such as chains of non-extremal black holes or smooth non-BPS bubbling geometries and study their physics. The smooth horizonless geometries can have the same mass and charges as non-extremal black holes. Furthermore, we find examples that scale towards the four-charge BPS black hole when the non-BPS parameters are taken to be small, but the horizon is smoothly resolved by adding a small amount of non-extremality. 

A bstract We study the existence of smooth topological solitons and black strings as locally-stable saddles of the Euclidean gravitational action of five dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein background of four dimensional Minkowski with an S 1 . We compute the off-shell gravitational action in the canonical ensemble with fixed boundary data corresponding to the asymptotic radius of S 1 , and to the electric and magnetic charges that label the solitons and black strings. We show that these objects are locally-stable in large sectors of the phase space with varying lifetime. Furthermore, we determine the globally-stable phases for different regimes of the boundary data, and show that there can be Hawking-Page transitions between the locally-stable phases of the topological solitons and black strings. This analysis demonstrates the existence of a large family of globally-stable smooth solitonic objects in gravity beyond supersymmetry, and presents a mechanism through which they can arise from the black strings. 

A bstract We construct a family of smooth charged bubbling solitons in $$ \mathbbm{M} $$ M 4 ×T 2 , four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in $$ \mathbbm{M} $$ M 4 defining a chain of topological cycles. They live in the same parameter regime as non-BPS non-extremal four-dimensional black holes, and are ultracompact with sizes ranging from miscroscopic to macroscopic scales. The six-dimensional framework can be embedded in type IIB supergravity where the solitons are identified with geometric transitions of non-BPS D1-D5-KKm bound states. Interestingly, the geometries admit a minimal surface that smoothly opens up to a bubbly end of space. Away from the solitons, the solutions are indistinguishable from a new class of singular geometries. By taking a limit of large number of bubbles, the soliton geometries can be matched arbitrarily close to the singular spacetimes. This provides the first classical resolution of a curvature singularity beyond the framework of supersymmetry and supergravity by blowing up topological cycles wrapped by fluxes at the vicinity of the singularity. 

A bstract We construct smooth static bubble solutions, denoted as topological stars, in five-dimensional Einstein-Maxwell theories which are asymptotic to ℝ 1 , 3 ×S 1 . The bubbles are supported by allowing electromagnetic fluxes to wrap smooth topological cycles. The solutions live in the same regime as non-extremal static charged black strings, that reduce to black holes in four dimensions. We generalize to multi-body configurations on a line by constructing closed-form generalized charged Weyl solutions in the same theory. Generic solutions consist of topological stars and black strings stacked on a line, that are wrapped by electromagnetic fluxes. We embed the solutions in type IIB String Theory on S 1 ×T 4 . In this framework, the charged Weyl solutions provide a novel class in String Theory of multiple charged objects in the non-supersymmetric and non-extremal black hole regime. 

A bstract We construct the first smooth bubbling geometries using the Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. We classify the charged Weyl solutions in this framework. Smooth solutions consist of a chain of Kaluza-Klein bubbles that can be neutral or wrapped by electromagnetic fluxes, and are free of curvature and conical singularities. We discuss how such topological structures are prevented from gravitational collapse without struts. When embedded in type IIB, the class of solutions describes D1-D5-KKm solutions in the non-BPS regime, and the smooth bubbling solutions have the same conserved charges as a static four-dimensional non-extremal Cvetic-Youm black hole. 

A bstract We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the black hole differ significantly from Kerr as they depend non-trivially on the charge-to-mass ratio. The horizonless microstate geometries (that are comparable in size to a black hole) have a similar multipole structure as their corresponding black hole, with deviations to the black hole multipole values set by the scale of their microstructure.