Bubble bag end: a bubbly resolution of curvature singularity

We construct a family of smooth charged bubbling solitons in $$ \mathbbm{M} $$ M 4×T2, 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.

Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

The island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

A substrate for brane shells from $$ T\overline{T} $$

A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace $$ T\overline{T} $$ T T ¯ . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

The Rayleigh–Taylor instability in a porous medium

The classical Rayleigh–Taylor instability occurs when a heavy fluid overlies a lighter one, and the two fluids are separated by a horizontal interface. The configuration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar flow, but in a porous medium governed by Darcy’s law. First, the fully saturated situation is considered, where the two horizontal fluids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely diffuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding flow for two free fluids.

Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

Antipodal Identification in the Schwarzschild Spacetime

"Through a Möbius transformation, we study aspects like topology, ligth cones, horizons, curvature singularity, lines of constant Schwarzschild coordinates r and t, null geodesics, and transformed metric, of the spacetime (SKS/2)^' that results from: i) the antipode identification in the Schwarzschild-Kruskal-Szekeres (SKS) spacetime, and ii) the suppression of the consequent conical singularity. In particular, one obtains a non simply-connected topology: (SKS/2)^' = R^2* ×S^2 and, as expected, bending light cones."

$$ T\overline{T} $$ , black holes and negative strings

String theory on AdS3 has a solvable single-trace irrelevant deformation that is closely related to $$ T\overline{T} $$ T T ¯ . For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum. For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states. Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity. We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture. The singularity does not give rise to a hard ultraviolet wall for excitations -one must include the region beyond it to understand the theory. The size of black holes diverges as their energy approaches the upper bound, as does the location of the singularity. Fundamental strings pass smoothly through the singularity, but if their energy is above the upper bound, their trajectories are singular. From the point of view of the boundary at infinity, this background can be thought of as a vacuum of Little String Theory which contains a large number of negative strings.