Null Direction Research Articles

A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces

A well-known application of the Raychaudhuri equation shows that, under geodesic completeness, totally geodesic null hypersurfaces are unique which satisfy that the Ricci curvature is nonnegative in the null direction. The proof of this fact is based on a direct analysis of a differential inequality. In this paper, we show, without assuming the geodesic completeness, that an inequality involving the squared null mean curvature and the Ricci curvature in a compact three-dimensional null hypersurface also implies that it is totally geodesic. The proof is completely different from the above, since Riemannanian tools are used in the null hypersurface thanks to the rigging technique.

Petrov type I spacetime curvature: Principal null vector spanning dimension

The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension 4 (maximally spanning type I) or dimension 3 (nonmaximally spanning type I). Explicit examples are provided for both vacuum and nonvacuum spacetimes.

Fast Multinull Steering of Antenna Array

In this letter, a fast multinull steering technique is demonstrated by a linearly polarized linear antenna array. The new technique is based on the electric fields generated by each antenna element on a far-field arc of the antenna array, which are extracted in advance by simulation or measurement. The power transmission efficiency is used as the performance index to control the pattern nulls. By solving a matrix eigenvalue equation, in which the matrix is made up by selecting the corresponding electric fields on different positions on the arc standing for the null directions, the eigenvector corresponding to the zero eigenvalue is identified and used as the optimized distribution of excitations (ODEs) for the antenna array. Single-null and multinull patterns are tested from the ODEs and the results indicate that the number and directions of the multiple nulls can be controlled in the elevation space. The simulated and measured 2-D null patterns are shown in good agreement.

Dual diffeomorphisms and finite distance asymptotic symmetries in 3D gravity

We study the finite distance boundary symmetry current algebra of the most general first order theory of 3d gravity. We show that the space of quadratic generators contains diffeomorphisms but also a notion of dual diffeomorphisms, which together form either a double Witt or centreless BMS$_3$ algebra. The relationship with the usual asymptotic symmetry algebra relies on a duality between the null and angular directions, which is possible thanks to the existence of the dual diffeomorphisms.

Scattering Amplitudes: Celestial and Carrollian.

Recent attempts at the construction of holography for asymptotically flat spacetime have taken two different routes. Celestial holography, involving a two dimensional (2D) conformal field theory (CFT) dual to 4D Minkowski spacetime, has generated novel results in asymptotic symmetry and scattering amplitudes. A different formulation, using Carrollian CFTs, has been principally used to provide some evidence for flat holography in lower dimensions. Understanding of flat space scattering has been lacking in the Carroll framework. In this Letter, using ideas from Celestial holography, we show that 3D Carrollian CFTs living on the null boundary of 4D flat space can potentially compute bulk scattering amplitudes. Three-dimensional Carrollian conformal correlators have two different branches, one depending on the null time direction and one independent of it. We propose that it is the time-dependent branch that is related to bulk scattering. We construct an explicit field theoretic example of a free massless Carrollian scalar that realizes some desired properties.

An examination of Intolerance of Uncertainty and contingency instruction on multiple indices during threat acquisition and extinction training

Individuals who score high in self-reported Intolerance of Uncertainty (IU) tend to find uncertainty aversive. Prior research has demonstrated that under uncertainty individuals with high IU display difficulties in updating learned threat associations to safety associations. Importantly, recent research has shown that providing contingency instructions about threat and safety contingencies (i.e. reducing uncertainty) to individuals with high IU promotes the updating of learned threat associations to safety associations. Here we aimed to conceptually replicate IU and contingency instruction-based effects by conducting a secondary analysis of self-reported IU, ratings, skin conductance, and functional magnetic resonance imaging (fMRI) data recorded during uninstructed/instructed blocks of threat acquisition and threat extinction training (n = 48). Generally, no significant associations were observed between self-reported IU and differential responding to learned threat and safety cues for any measure during uninstructed/instructed blocks of threat acquisition and threat extinction training. There was some tentative evidence that higher IU was associated with greater ratings of unpleasantness and arousal to the safety cue after the experiment and greater skin conductance response to the safety cue during extinction generally. Potential explanations for these null effects and directions for future research are discussed.

Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, is necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentums that are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the nonsaturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length l always thermalizes in time l/2 with an exponent 3/2. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any l, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

Null cosmic strings: Scattering by black holes, optics, and spacetime content

Equations of motion of null cosmic strings near black holes, or other massive sources, are solved exactly in the weak field approximation. The stress-energy tensor of a null string in a curved spacetime is introduced and used to show how scattering by black holes transforms linear and angular momenta of the string. The corresponding recoil effect of a black hole and change of its angular momentum caused by a null cosmic string are calculated. For a null string, its energy $\mu$ per unit length evolves along the null direction of the string trajectory. The evolution of $\mu$ is connected with a string optical scalar $Z$. Optical properties of null strings are that their energy is concentrated on caustics, where $Z$ has poles. String parameters $\mu$ and $Z$ capture important features of the spacetime where strings move. Explicit dependence of $\mu$ and $Z$ on the strain and Bondi news tensors of gravitational wave background, mass and angular momentum aspects are established, near the future null infinity, up to the 4-th order in expansion in an inverse null parameter in asymptotically flat spacetimes.

Plebański-Demiański solutions with dynamical torsion and nonmetricity fields

We construct Plebański-Demiański stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolský and Vrátný, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characterised by the mass, orbital angular momentum, acceleration, NUT parameter, cosmological constant and electromagnetic charges of the Riemannian sector of the theory, as well as by the spin and dilation charges of the torsion and nonmetricity fields. The former is subject to a constraint representing a decoupling limit with the parameters responsible of axial symmetry, beyond which the geometry of the space-time is expected to be corrected.

Semi-local Bounds on Null Energy in QFT

We investigate whether the null energy, averaged over some region of spacetime, is bounded below in QFT. First, we use light-sheet quantization to prove a version of the ``Smeared Null Energy Condition" (SNEC) proposed in [1], applicable for free and super-renormalizable QFT's equipped with a UV cutoff. Through an explicit construction of squeezed states, we show that the SNEC bound cannot be improved by smearing on a light-sheet alone. We propose that smearing the null energy over two null directions defines an operator that is bounded below and independent of the UV cutoff, in what we call the ``Double-Smeared Null Energy Condition," or DSNEC. We indicate schematically how this bound behaves with respect to the smearing lengths and argue that the DSNEC displays a transition when the smearing lengths are comparable to the correlation length.

A Combined Inverse Source and Scattering Technique for Dielectric Profile Design to Tailor Electromagnetic Fields

This article augments existing gradient-based inverse scattering algorithms to enable the design of reflectionless lossless permittivity profiles within a given design domain that can transform an input incident field into an output field of desired characteristics. These desired characteristics are often some user-defined far-field performance criteria, such as main beam directions, null directions, and half-power beamwidth (HPBW). To this end, two extra steps will be performed prior to the inverse scattering step. First, an inverse source algorithm inverts the desired far-field performance criteria to infer a set of equivalent surface currents on a boundary close to the design domain. These equivalent currents are then converted to a set of field values that constitute the required aperture fields. Second, these aperture fields are scaled such that the input incident power to the design domain is approximately equal to the output power leaving the design domain. Finally, the desired scattered fields are formed and then inverted by an inverse scattering algorithm to reconstruct a lossless reflectionless dielectric profile within the design domain. We also show that the inverse scattering algorithm can employ appropriate regularization methods, in particular a binary regularization term, to facilitate the physical implementation of reconstructed dielectric profiles.

Dimensional reduction of M5 branes

We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along the circle. When the gauge group is Abelian and the fields appear quadratically in the Lagrangian, we can always obtain a supersymmetric five-dimensional theory by keeping fermionic nonzero modes that match with the corresponding nonzero modes of the supersymmetry parameter, and by keeping the zero modes for the bosonic fields as usual. But a supersymmetric non-Abelian generalization can be found only under special circumstances. One instance where we find a non-Abelian supersymmetric generalization is when we perform dimensional reduction along a null direction.

Five-dimensional path integrals for six-dimensional conformal field theories

In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an SU(1, 3) spacetime symmetry in the presence of instantons. We explicitly show how SU(1, 3) is enhanced to SU(1, 3) × U(1) where the additional U(1) acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters.

Conformal rigidity from focusing

The null curvature condition (NCC) is the requirement that the Ricci curvature of a Lorentzian manifold be nonnegative along null directions, which ensures the focusing of null geodesic congruences. In this paper, we show that the NCC together with the causal structure significantly constrain the metric. In particular, we prove that any conformal rescaling of a vacuum spacetime introduces either geodesic incompleteness or negative null curvature, provided the conformal factor is non-constant on at least one complete null geodesic. In the context of bulk reconstruction in anti-de Sitter/CFT, our results combined with the technique of light-cone cuts can be used in vacuum spacetimes to reconstruct the full metric in regions probed by complete null geodesics reaching the boundary. For non-vacuum spacetimes, our results constrain the conformal factor, giving an approximate reconstruction of the metric.

Bootstrapping octagons in reduced kinematics from A2 cluster algebras

Multi-loop scattering amplitudes/null polygonal Wilson loops in mathcal{N} = 4 super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an 1 + 1 dimensional subspace of Minkowski spacetime (or boundary of the AdS3 subspace). Since the edges of a 2n-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of G(2, n)/T ∼ An−3. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping A2 functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters v, 1 + v, w, 1 + w of A1 × A1, there are two letters v − w, 1 − vw mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping A2 functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to 2n-gons in terms of A2 functions and beyond.

Mechanism of Motion Direction Detection Based on Barlow’s Retina Inhibitory Scheme in Direction-Selective Ganglion Cells

Previous studies have reported that directionally selective ganglion cells respond strongly in their preferred direction, but are only weakly excited by stimuli moving in the opposite null direction. Various studies have attempted to elucidate the mechanisms underlying direction selectivity with cellular basis. However, these studies have not elucidated the mechanism underlying motion direction detection. In this study, we propose the mechanism based on Barlow’s inhibitory scheme for motion direction detection. We described the local motion-sensing direction-selective neurons. Next, this model was used to construct the two-dimensional multi-directional detection neurons which detect the local motion directions. The information of local motion directions was finally used to infer the global motion direction. To verify the validity of the proposed mechanism, we conducted a series of experiments involving a dataset with a number of images. The proposed mechanism exhibited good performance in all experiments with high detection accuracy. Furthermore, we compare the performance of our proposed system and traditional Convolution Neural Network (CNN) on motion direction prediction. It is found that the performance of our system is much better than that of CNN in terms of accuracy, calculation speed and cost.

Petrov type, principal null directions, and Killing tensors of slowly rotating black holes in quadratic gravity

The ability to test general relativity in extreme gravity regimes using gravitational wave observations from current ground-based or future space-based detectors motivates the mathematical study of the symmetries of black holes in modified theories of gravity. In this paper we focus on spinning black hole solutions in two quadratic gravity theories: dynamical Chern-Simons and scalar Gauss-Bonnet gravity. We compute the principal null directions, Weyl scalars, and complex null tetrad in the small-coupling, slow rotation approximation for both theories, confirming that both spacetimes are Petrov type I. Additionally, we solve the Killing equation through rank 6 in dynamical Chern-Simons gravity and rank 2 in scalar Gauss-Bonnet gravity, showing that there is no nontrivial Killing tensor through those ranks for each theory. We therefore conjecture that the still-unknown, exact, quadratic-gravity, black-hole solutions do not possess a fourth constant of motion.

Linear Pattern Correction Technique for Compensating the Effects of Mutual Coupling and Deformation in Wedge-Shaped Conformal Antenna Arrays

In this paper, the effects of mutual coupling and antenna surface deformity in a conformal wedge-shaped antenna array are compensated using a linear pattern correction technique. The problem is formulated to reduce the absolute distance between the actual (simulated) and the desired radiation patterns and to allow for null positioning control. The individual field patterns for the antenna elements are deformed due to changes in mutual coupling and the conformal surface. The deformed patterns of the individual antennas for specific bend angles are stored as lookup tables and interpolated to get the desired radiation pattern at any arbitrary bend-angle. The problem is linearly and quadratically constrained at the null points and performance compared with unconstrained optimization. The proposed solution for diminishing the effect of mutual coupling and surface deformity is independent of main lobe direction, type of individual antenna, array geometry, and spacing between antenna elements. The closed-form results are validated through Computer Simulation Technology (CST) for the wedge-shaped deformed dipole antenna array. The results for the proposed scheme are also assessed with the traditional Open Circuit Voltage Method (OCVM) and show superior compensation for deformity and the mutual coupling effects in conformal beam-forming arrays in terms of main beam direction, position and depth of nulls.

Causal description of marginally trapped surfaces in D dimensions

In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don't comply with the standard inner and outer horizon classification for degenerate horizons. we propose an alternate prescription for this classification of these degenerate horizons.

Deception Jamming Detection Based on Beam Scanning for Satellite Navigation Systems

A scheme for deception jamming detection based on beam scanning is proposed in this letter. This scheme detects the authenticity of the corresponding signal by forming a null in the direction of each visible satellite in turn. At the same time, the null direction is adjusted based on the attitude angle measured by the inertial unit to support the applicability of the scheme in scenarios where the attitude of the array changes continuously. Then, from an engineering point of view, an equalization scheme for arrays and radio frequency (RF) channels is proposed to improve the accuracy of the null direction. Finally, the effectiveness of the proposed scheme is verified by simulation.