AdS3 from M-branes at conical singularities

M-theory is known to possess supersymmetric solutions where the geometry is AdS3 × S3 × S3 warped over a Riemann surface Σ2. The simplest examples in this class can be engineered by placing M2 and M5 branes as defects inside of a stack of background M5 branes. In this paper we show that a generalization of this construction yields more general solutions in the aforementioned class. The background branes are now M5’s carrying M2 brane charge, while the defect branes are now placed at the origin of a flat hyperplane with a conical defect. The equations of motion imply a relation between the deficit angle produced by the conical defect and the M2 charge carried by the background branes.

On the spectrum of pure higher spin gravity

We study the spectrum of pure massless higher spin theories in AdS3. The light spectrum is given by a tower of massless particles of spin s = 2, ⋯ , N and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the $$ {\mathcal{W}}_N $$ W N algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle 2π(1 − 1/M). Unitarity allows the inclusion of such defects into the path integral provided M ≥ N.

The Extension of the Massless Fermion Behaviour in the Cosmic String Spacetime

In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy-dependent potentials, and position-dependent mass models are investigated for the Dirac Hamiltonians, and an extension of these three potential models and their solutions is also obtained. The energy spectrum and potential graphs for each case are discussed for the α deficit angle.

Isometric bending requires local constraints on free edges

While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive. Intuitively, unstretchability is captured by a constraint on the metric within the bulk. Naïvely one would then guess that this constraint is enough to ensure that the deformations determining the boundary conditions on these edges respect the isometry constraint. If matters were this simple, unfortunately, it would imply unbalanced torques (as well as forces) along the edge unless manifestly unphysical constraints are met by the boundary geometry. In this article, we identify the source of the problem: not only the local arc-length but also the geodesic curvature need to be constrained explicitly on all free edges. We derive the boundary conditions which follow. In contrast to conventional wisdom, there is no need to introduce boundary layers. This framework is applied to isolated conical defects, both with deficit as well, but more briefly, as surplus angles. Using these boundary conditions, we show that the lateral tension within a circular cone of fixed radius is equal but opposite to the radial compression, and independent of the deficit angle itself. We proceed to examine the effect of an oblique outer edge on this cone perturbatively demonstrating that both the correction to the geometry as well as the stress distribution in the cone kicks in at second order in the eccentricity of the edge.

Universes Inside a Black Hole with the de Sitter Interior

We outline the basic ideas and analyze the possibilities of the quantum birth of universes inside regular black holes with the de Sitter interior replacing a singularity. We compare different cases and show that the most plausible case is the birth of a flat universe from an initial quantum fluctuation with a small admixture of radiation and strings with the negative deficit angle, which provides the existence of a potential barrier needed for quantum tunneling.

The Letelier spacetime with quintessence: Solution, thermodynamics and Hawking radiation

We obtain the solution corresponding to a static and spherically symmetric black hole with a cloud of strings (Letelier spacetime) immersed in a quintessential fluid. We discuss some aspects of its thermodynamics and complete proceeding studies in the spacetime of Schwarzschild with quintessence and a solid deficit angle, which is mathematically analogous to the solution we obtained. We also present a discussion about Hawking radiation of particles, in the background under consideration and compare with related studies in the literature.

Magnetic brane of cubic quasi-topological gravity in the presence of Maxwell and Born–Infeld electromagnetic field

The main purpose of the present paper is analyzing magnetic brane solutions of cubic quasi-topological gravity in the presence of a linear electromagnetic Maxwell field and a nonlinear electromagnetic Born–Infeld field. We show that the mentioned magnetic solutions have no curvature singularity and also no horizons, but we observe that there is a conic geometry with a related deficit angle. We obtain the metric function and deficit angle and consider their behavior. We show that the attributes of our solution are dependent on cubic quasi-topological coefficient and the Gauss–Bonnet parameter.

Possible imprints of cosmic strings in the shadows of galactic black holes

We examine the shadow cast by a Kerr black hole pierced by a cosmic string. The observable images depend not only on the black hole spin parameter and the angle of inclination, but also on the deficit angle yielded by the cosmic string. The dependence of the observable characteristics of the shadow on the deficit angle is explored. The imprints in the black hole shadow left by the presence of a cosmic string can serve in principle as a method for observational detection of such strings.

Asymptotically anti-de Sitter magnetic branes in (n + 1)-dimensional dilaton gravity

We present a new class of asymptotically anti-de Sitter (AdS) magnetic solutions in (n + 1)-dimensional dilaton gravity in the presence of an appropriate combination of three Liouville-type potentials. This class of solutions is asymptotically AdS in six and higher dimensions and yields a space–time with a longitudinal magnetic field generated by a static brane. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle. We find that the brane tension depends on the dilaton field and approaches a constant as the coupling constant of the dilaton field goes to infinity. We generalized this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge that is proportional to the magnitude of the rotation parameters. Finally, we used the counterterm method inspired by AdS – conformal field theory correspondence and computed the conserved quantities of these space–times. We found that the conserved quantities do not depend on the dilaton field, which is evident from the fact that the dilaton field vanishes on the boundary at infinity.

SHAPE TRANSFORMATIONS OF A MODEL OF SELF-AVOIDING TRIANGULATED SURFACES OF SPHERE TOPOLOGY

We study a surface model with a self-avoiding (SA) interaction using the canonical Monte Carlo simulation technique on fixed-connectivity (FC) triangulated lattices of sphere topology. The model is defined by an area energy, a deficit angle energy, and the SA potential. A pressure term is also included in the Hamiltonian. The volume enclosed by the surface is well defined because of the self-avoidance. We focus on whether or not the interaction influences the phase structure of the FC model under two different conditions of pressure Δp; zero and small negative. The results are compared with the previous results of the self-intersecting model, which has a rich variety of phases; the smooth spherical phase, the tubular phase, the linear phase, and the collapsed phase. We find that the influence of the SA interaction on the multitude of phases is almost negligible except for the evidence that no crumpled surface appears under Δp = 0 at least even in the limit of zero bending rigidity α → 0. The Hausdorff dimension is obtained in the limit of α → 0 and compared with previous results of SA models, which are different from the one in this paper.