Point-like Singularities Research Articles

Magnetoelectric effects in magnetic films with alternating magnetic anisotropy: the emergence and stability of Bloch points.

Magnetic topological states are a subject of intense investigation due to their potential for advancing scalable logic and information storage technologies. In this article, we investigate topological defects in magnetic films, focusing on Bloch point-like singularities in magnetization distribution with significant implications for magnetoelectric and ferroelectric properties. We explore exchange-coupled ferromagnetic films composed of alternating magnetic layers with distinct in-plane and out-of-plane magnetic anisotropy. Through micromagnetic simulations, we analyze the magnetization reversal processes and the emergence of Bloch point-like configurations induced by external magnetic fields. We identify the conditions necessary for stabilizing these states and elucidate their ferroelectric properties. Our study reveals that Bloch points act as sources of electrical charge due to the inhomogeneous distribution of magnetization, offering opportunities for implementing their electric properties in future devices.

On the intermediate Jacobian of M5-branes

We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal ℤ2 singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.

Quantum corrections on geodesic structure and shadow behavior of the Schwarzschild black hole

Point-like singularities of black hole space–times in general theory of relativity (GR) and alternative theories of gravity are one of the controversial issues for decades. One way to remove the central singularity of the Schwarzschild black hole is the Kazakov–Solodukhin (KS) proposal, which takes into account the effects of quantum field theory within the GR framework leading to the KS black hole. On the other hand, the Event Horizon Telescope (EHT) becomes a noteworthy tool for constraining the black hole parameters in gravitational theories. Hence, in this work, we plan to study the null geodesic structure, shadow behavior, energy emission rate, and deflection angle of the KS black hole. Then, we constrain the quantum correction parameter of the KS black hole via EHT data of the M87* supermassive black hole. We observe that increasing the quantum effects in the KS black hole leads to amplification of the shadow size of the KS black hole.

Accelerating Airy beams with particle-like polarization topologies and free-space bimeronic lattices.

Phase and polarization singularities in electromagnetic waves are usually attributed to one-dimensional topologies-lines, knots, and braids. Recently, particle-like structures have been predicted and observed: optical Skyrmions, vortices with spherical polarization, etc. In this article, we devise vector Airy beams with point-like singularity in the focal plane, thus leading to the presence of a particle-like topology. We present an extensive analytical analysis of the spatial spectra and focal structure of such beams. We report on the presence of a free-space lattice of bimerons in such vector Airy beams.

Group structure of Wilson loops in 2D tight-binding models with 2-band and 4-band energy spectra

Tight-binding models represent one of the basic approaches for studying the topological states of a matter. In the given account, we consider a tight-binding model set by a matrix Hamiltonian over 2D Brillouin zone. The corresponding multiband energy spectrum gives rise to non-Abelian gauge construction formed by the non-Abelian Berry connection [Formula: see text]. The main gauge invariant quantities in such cases are the eigenvalues of Wilson loops. The purpose followed is the search for any special (on top of general) properties of Wilson loops for 2D tight-binding models which impose certain restrictions on the structure of its eigenvalues. The non-Abelian Berry connection is shown to be pure gauge with point-like singularities. The corresponding curvature tensor [Formula: see text] vanishes throughout the Brillouin zone except the isolated points where [Formula: see text] is singular. Combining such behavior of [Formula: see text] with non-Abelian Stokes theorem allows to avoid the path-ordering procedure in calculating the Wilson loops. In this approach, we show that Wilson loops are endowed by the group structure isomorphic to the fundamental group of the Brillouin zone. The latter is the Abelian group [Formula: see text] forcing the set of eigenvalues of Wilson loops to comprise of two fixed phases associated with the two primitive elements (generators) of [Formula: see text].

Point-like mechanical singularity in the method of boundary states

This paper presents an effective technique for solving some spatial problems in the theory of elasticity, particularly for a bounded set of point-like physical singularities. This technique development involves the advanced energy method of boundary states (MBS) for a class of solutions with singularities. A test problem for a single singularity such as the center of expansion complying with the proposed technique calculations reliability has been solved and analyzed. The use of the method of boundary states demonstrates the efficiency of the technique in solving problems with many centers of expansion and concentrated forces in an unbounded medium. The results of problem solving are displayed in a convenient graphical form.

New massless and massive infinite derivative gravity in three dimensions

In this paper we will consider the most general quadratic curvature action with infinitely many covariant derivatives of massless gravity in three spacetime dimensions. The action is parity invariant and torsion-free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened to a Gaussian distribution, while in the infrared the theory reduces to general relativity. We will also show how to embed new massive gravity in ghost-free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the tree-level unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter spacetimes in three dimensions by perturbing the geometries.

Nonlocal gravity with worldline inversion symmetry

We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-2 graviton of Einstein’s general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein’s theory are smeared out.

Plethora of relativistic charged spheres: The full spectrum of Guifoyle’s static, electrically charged spherical solutions

We show that Guilfoyle's exact solutions of the Einstein-Maxwell equations for spherical symmetric static electrically charged matter with a Reissner-Nordstr\"om exterior possess a bewildering plethora of different types of solutions. For the parameter space of the solutions we use two normalized variables, $q^2/R^2$ and $r_0/R$, where $q$ is the total electric charge, $r_0$ is the radius of the object, and $R$ is a length representing the square root of the inverse energy density of the matter. The two other parameters, the mass $m$ and the Guilfoyle parameter $a$, both dependent on $q$, $r_0$ and $R$, are analyzed in detail. The full parameter space of solutions $q^2/R^2\times r_0/R$ is explored with the corresponding types of solutions being identified and analyzed. The different types of solutions are regular charged stars, including charged dust stars and stars saturating the Buchdahl-Andr\'easson bound, quasiblack holes, regular charged black holes with a de Sitter core, regular black holes with a core of phantom charged matter, other exotic regular black holes, Schwarzschild stars, Schwarzschild black holes, Kasner spacetimes, pointlike and planar naked singularities, and the Minkowski spacetime. Allowing for $q^2<0$, in which case it is not possible to interpret $q$ as electric charge, also yields new solutions, some of which are interesting and regular, others are singular. Some of these types of solutions as well as the matter properties have been previously found and studied, here the full spectrum being presented in a unified manner.

α′ Inflation: moduli stabilisation and observable tensors from higher derivatives

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $\alpha'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative $\alpha'$ corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its potential is generated by both higher derivative $\alpha'$ and winding loop corrections. Natural values of the underlying parameters give a spectral index in agreement with observational data and a tensor-to-scalar ratio of order $r=0.01$ which could be observed by forthcoming CMB experiments. Dangerous corrections from higher dimensional operators are suppressed due to the presence of an approximate non-compact shift symmetry.

Black hole solutions in functional extensions of Born-Infeld gravity

We consider electrovacuum black hole spacetimes in classical extensions of Eddington-inspired Born-Infeld gravity. By rewriting Born-Infeld action as the square root of the determinant of a matrix $\hat{\Omega}$, we consider the family of models $f (|\hat{\Omega}|)$, and study black hole solutions for a power-law family of models labelled by a simple parameter. We show how the innermost structure of the corresponding black holes is modified as compared to their General Relativity counterparts, discussing in which cases a wormhole structure replaces the point-like singularity. We go forward to argue that in such cases a geodesically complete and thus non-singular spacetime is present, despite the existence of curvature divergences at the wormhole throat.

Time-reversal constraint limits unidirectional photon emission in slow-light photonic crystals.

Photonic crystal waveguides are known to support C-points-point-like polarization singularities with local chirality. Such points can couple with dipole-like emitters to produce highly directional emission, from which spin-photon entanglers can be built. Much is made of the promise of using slow-light modes to enhance this light-matter coupling. Here we explore the transition from travelling to standing waves for two different photonic crystal waveguide designs. We find that time-reversal symmetry and the reciprocal nature of light places constraints on using C-points in the slow-light regime. We observe two distinctly different mechanisms through which this condition is satisfied in the two waveguides. In the waveguide designs, we consider a modest group velocity of vg≈c/10 is found to be the optimum for slow-light coupling to the C-points.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

Wormholes and nonsingular spacetimes in Palatinif(R)gravity

We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric space-time, we find solutions which reduce to their Reissner-Nordstr\"om counterparts at large distances but undergo important non-perturbative modifications close to the center. Our new analysis reveals that the point-like singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular space-time, despite the existence of curvature divergences at the wormhole throat. Implications of these results, in particular for the cosmic censorship conjecture, are discussed.

Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon

In this paper, we use our recently generalized black hole entropy formula to propose a quantum version of the Friedmann equations. In particular, starting from the differential version of the first law of thermodynamics, we are able to find Planckian (noncommutative) corrections to the Friedmann flat equations. The so modified equations are formally similar to the ones present in Gauss–Bonnet gravity, but in the ordinary 3+1 dimensions. As a consequence of these corrections, by considering negative fluctuations in the internal energy that are allowed by quantum field theory, our equations imply a maximum value both for the energy density [Formula: see text] and for the Hubble flow H, i.e. the big bang is ruled out. Conversely, by considering positive quantum fluctuations, we found no maximum for [Formula: see text] and H. Nevertheless, by starting with an early time energy density [Formula: see text], we obtain a value for the scale factor [Formula: see text], implying a finite Planckian universe at t = 0, i.e. the point-like big bang singularity is substituted by a universe of Planckian size at t = 0. Finally, we found possible higher order Planckian terms to our equations together with the related corrections of our generalized Bekenstein–Hawking entropy.

Complete classification of four-dimensional black hole and membrane solutions in IR-modified Hořava gravity

Ho\v{r}ava gravity has been proposed as a renormalizable, higher-derivative gravity without ghost problems, by considering different scaling dimensions for space and time. In the non-relativistic higher-derivative generalization of Einstein gravity, the meaning and physical properties of black hole and membrane space-times are quite different from the conventional ones. Here, we study the singularity and horizon structures of such geometries in IR-modified Ho\v{r}ava gravity, where the so-called "detailed balance" condition is softly broken in IR. We classify all the viable static solutions without naked singularities and study its close connection to non-singular cosmology solutions. We find that, in addition to the usual point-like singularity at $r=0$, there exists a "surface-like" curvature singularity at finite $r=r_S$ which is the cutting edge of the real-valued space-time. The degree of divergence of such singularities is milder than those of general relativity, and the Hawking temperature of the horizons diverges when they coincide with the singularities. As a byproduct we find that, in addition to the usual "asymptotic limit," a consistent flow of coupling constants, that we called "GR flow limit," is needed in order to recover general relativity in the IR.

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann–Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realization of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

Dipoles in thin sheets

A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar multipole construction in electrostatics. However, here the underlying field theory is non-linear, and superposition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three dimensions. We consider a "charge-neutral" dipole composed of two conical singularities of opposite sign. Unlike the relatively simple electrostatic case, here there are two distinct stable minima and an infinity of unstable equilibria. We determine the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates over stretching. Our predictions are in surprisingly good agreement with experiments on paper sheets.

A Little Quantum Help for Cosmic Censorship and a Step Beyond All That

The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the classical (e.g., nonquantum) level. More than 40 years after it was proposed, the validity of the hypothesis remains an open question. We reconsider CCH in both its weak and strong versions, concerning point-like singularities, with respect to the provisions of Heisenberg’s uncertainty principle. We argue that the shielding of the singularities from observers at infinity by an event horizon is also quantum mechanically favored, but ultimately it seems more appropriate to accept that singularities never actually form in the usual sense; thus no naked singularity danger exists in the first place.

Analysis of a New Variational Model to Restore Point-Like and Curve-Like Singularities in Imaging

The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme.

Effective dynamics in Bianchi type II loop quantum cosmology

We numerically investigate the solutions to the effective equations of the Bianchi II model within the ``improved'' loop quantum cosmology dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big bang singularity is replaced by a bounce and the pointlike singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the ``vacuum limit,'' solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the Belinskii, Khalatnikov, Lifshitz conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general spacelike singularities, when loop-geometric corrections are present.