Abstract We investigate the quasinormal modes (QNMs) of static and spherically symmetric black holes (BHs) in vacuum within the framework of f ( ℚ ) = ℚ + α ℚ 2 gravity, and compare them with those in f ( T ) = T + α T 2 gravity. Based on the symmetric teleparallel equivalent of general relativity, we notice that the gravitational effects arise from non-metricity (the covariant derivative of metrics) in f ( ℚ ) gravity rather than curvature in f ( R ) or torsion in f ( T ) . Using the finite difference method and the sixth-order Wentzel-Kramers-Brillouin (WKB) method, we compute the QNMs of massless scalar field and electromagnetic field perturbations. Tables of quasinormal frequencies for various parameter configurations are provided based on the sixth-order WKB method. Our findings reveal the differences in the QNMs of BHs in f ( ℚ ) gravity compared to those in f ( R ) and f ( T ) gravity. This variation demonstrates the impact of different parameter values, offering insights into the characteristics of f ( ℚ ) gravity. These results provide the theoretical groundwork for assessing alternative gravities’ viability through gravitational wave data, and aid probably in picking out the alternative gravity theory that best aligns with the empirical reality.

In this paper, we analyze from a geometric perspective the Hamiltonian formulation of a recent modification of the Husain–Kuchař model where, while preserving the connection as a dynamical variable, the other field is restricted to be the exterior covariant derivative of a Lie algebra-valued function. We prove that three-dimensional diffeomorphisms can be accommodated among the local gauge transformations of the model in addition to the internal gauge symmetries.

We discuss the propagation of gravitational waves over a non-Riemannian space-time, when a non-minimal coupling between the geometry and matter is considered in the form of contractions of the energy momentum tensor with the Ricci and co-Ricci curvature tensors. We focus our analysis on perturbations on a Minkowski background, elucidating how derivatives of the energy momentum tensor can sustain non-trivial torsion and non-metricity excitations, eventually resulting in additional source terms for the metric field. These can be reorganized in the form of d'Alembert operator acting on the energy momentum tensor and the equivalence principle can be reinforced at the linear level by a suitable choice of the parameters of the model. We show how tensor polarizations can exhibit a subluminal phase velocity in matter, evading the constraints found in General Relativity, and how this allows for the kinematic damping in specific configurations of the medium and of the geometry-matter coupling. These in turn define regions in the wavenumber space where propagation is forbidden, leading to the appearance of typical cut-off scale in the frequency spectrum.

We construct a version of geodesic normal coordinates adapted to a submanifold of a pseudo-Riemannian manifold and show that the Taylor coefficients of the metric in these coordinates can be expressed as universal polynomials in the components of the covariant derivatives of the background curvature tensor and the covariant derivatives of the second fundamental form. We formulate a definition of natural submanifold tensors and show that these are linear combinations of contractions of covariant derivatives of the background curvature tensor and covariant derivatives of the second fundamental form. We also describe how this result gives a similar characterization of natural submanifold differential operators.

We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a pseudodifferential operator calculus that allows one to build a linear operator map from the heat kernel of the minimal operator to the nonminimal one. This map is realized as a local expansion in powers of spacetime curvature, dimensional background fields, and their covariant derivatives with the coefficients—the functions of the Synge world function and its derivatives. Finiteness of these functions, determined by multiple proper time integrals, is achieved by a special subtraction procedure, which is an important part of the calculational scheme. We illustrate this technique on the examples of the vector Proca model and the vector field operator with a nondegenerate principal symbol. We also discuss smoothness properties of heat kernels of nonminimal operators in connection with the nondegenerate nature of their operator symbols.

Abstract A bundle geometric formulation of non‐relativistic many‐particles Quantum Mechanics is presented. A wave function is seen to be a ‐valued cocyclic tensorial 0‐form on configuration space‐time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a (flat) cocyclic connection 1‐form on the configuration bundle. In line with the historical motivations of Dirac and Feynman, ours is thus a Lagrangian geometric formulation of QM, in which the Dirac–Feynman path integral arises in a geometrically natural way. Applying the dressing field method , we obtain a relational reformulation of this geometric non‐relativistic QM: a relational wave function is realised as a basic cocyclic 0‐form on the configuration bundle. In this relational QM, any particle position can be used as a dressing field, i.e., as a “physical reference frame.” The dressing field method naturally accounts for the freedom in choosing the dressing field, which is readily understood as a covariance of the relational formulation under changes of physical reference frame.

Abstract Double Field Theory (DFT) has emerged as a comprehensive framework for gravity, presenting a testable and robust alternative to General Relativity (GR), rooted in the $$\textbf{O}(D,D)$$ O ( D , D ) symmetry principle of string theory. These lecture notes aim to provide an accessible introduction to DFT, structured in a manner similar to traditional GR courses. Key topics include doubled-yet-gauged coordinates, Riemannian versus non-Riemannian parametrisations of fundamental fields, covariant derivatives, curvatures, and the $$\textbf{O}(D,D)$$ O ( D , D ) -symmetric augmentation of the Einstein field equation, identified as the unified field equation for the closed string massless sector. By offering a novel perspective, DFT addresses unresolved questions in GR and enables the exploration of diverse physical phenomena, paving the way for significant future research.

In this paper, we investigate the structure of generalized Hh-recurrent Finsler spaces (G-Hh-R-Fn) and establish several recurrence relations for Cartan’s h-curvature tensor and its associated geometric invariants. In particular, Theorems 3.1, 3.2, and 4a.3 provide novel conditions characterizing the stability and recurrence of curvature under horizontal covariant differentiation. To demonstrate the practical significance of these results, we extend the theoretical framework to the domain of digital image processing. A Finslerian metric derived from image gradients is constructed to model anisotropic features, and the recurrence conditions are shown to enhance edge preservation during anisotropic diffusion filtering. Simulation steps are outlined, illustrating how the recurrence properties of curvature tensors improve noise suppression and directional stability compared to standard Euclidean methods. The proposed approach highlights the dual role of generalized Finsler recurrence: as a fundamental extension in differential geometry and as a powerful tool for advanced computer vision applications such as denoising, segmentation, and texture analysis.

This paper explores Cartan's second curvature tensor within the framework of generalized recurrent spaces. We derive and analyze the generalized recurrence conditions, and show that satisfies the recurrence relations of the first, second, and third orders. Specifically, we investigate the conditions that lead to the tensor’s behavior in generalized -recurrent spaces, denoted as -G-TR , and establish several theorems regarding the curvature tensor’s covariant derivatives and its relationship with other curvature tensors. Furthermore, we connect these recurrence conditions to the P-Ricci tensor and vector fields in higher-dimensional spaces. We demonstrate the interrelations between these tensors through a series of covariant derivative computations and conclude that the curvature tensor cannot vanish under specific geometric conditions. This study advances the field of differential geometry and its applications in physics by offering a thorough foundation for comprehending the characteristics of Cartan's curvature tensor in generalized recurrent spaces.

An automated protocolenabling the efficient computationof uniquepotential coupling constants is presented. Several modern densityfunctional (DFT) methods are tested against coupled cluster theory(CCSD­(T)) in order to evaluate their quality in producing reliablecompliance matrix off-diagonal elements. While force coupling constantscould serve as descriptors of electron delocalization in general,we tested the ability of coupling compliance constants as descriptorsof the Dewar–Chatt–Duncanson model in VCO–, CrCO, MnCO+, FeCO2+, NiCO, CuCO+, FeCO+ and the isoelectronic hexacarbonyls of the 3dand 5d series from Ti to Co, and Hf to Ir, respectively. A robustsemiautomated algorithm including the computation of all compliancecoupling constants as inverse covariant second derivatives is implementedin our open source version of the COMPLIANCE code.

Abstract Lepton-number-violating interactions occur in the Standard Model Effective Field Theory (SMEFT) at odd dimensions starting from the dimension-5 Weinberg operator. Although the operators at dimension-7 and higher are more suppressed by the heavy new scale, they can be crucial when traditional seesaw mechanisms leading to tree-level dimension-5 contributions are absent. We identify all minimal tree-level UV-completions for dimension-7 ∆L = 2 SMEFT operators without covariant derivatives and propose a new simplified approach for estimating the radiative neutrino masses arising from such operators. This dimensional-regularisation-based approach provides a more accurate estimate for the loop neutrino masses when the new physics fields are hierarchical in mass, as compared to the cut-off-regularisation-based approach often employed in the literature. This allows us to identify viable regions of parameter space in the full list of relevant simplified models close to the current limits set by neutrinoless double beta decay and the LHC that would previously have been thought to be excluded by neutrino-mass constraints.

Optimal off-line generated ϵ-stealthy attacks under the energy constraint in cyber-physical systems.

Rayleigh Quotient Iteration, cubic convergence, and second covariant derivative

In this paper, we investigate the properties of the Weyl conformal curvature tensor \(C_{jkh}^i\) in the context of n=4 Riemannian and Finslerian spaces, with a particular focus on generalized recurrent and birecurrent structures. We derive several equivalent forms of the conformal curvature tensor under various covariant derivatives, revealing deep interrelations between curvature tensors, Ricci tensors, scalar curvature, and their derivatives. By transvecting the conformal curvature expressions with vectors such as yi, yk, and tensors such as gij we deduce necessary and sufficient conditions for the conformal curvature tensor, torsion tensor, Ricci tensor, and projective deviation tensor to represent generalized recurrent and birecurrent Finsler spaces. The results culminate in a sequence of theorems (Theorems 3.1 to 3.8), offering a comprehensive characterization of G2nd C|h-RFn spaces and G2nd C|h-BRFn spaces. These findings contribute to the geometric understanding of recurrence structures in differential geometry and extend the theoretical framework of Finsler geometry.

In this paper, we introduce and investigate a new class of Finsler spaces, termed generalized \(R^h\)-recurrent Finsler spaces, denoted by \(F_n\) G \(R^h\) - R . These are defined via a generalized recurrence condition imposed on Cartan’s third curvature tensor, involving three non-null covariant vector fields. We derive the fundamental characterizations of such spaces and establish their equivalence through multiple tensorial identities. The behavior of related geometric objects such as the h(v)-torsion tensor, Ricci tensor, curvature vector, deviation tensor, and scalar curvature is analyzed. Furthermore, several non-trivial identities involving covariant derivatives and contractions are proven, demonstrating rich internal symmetries. The study concludes with a series of structural theorems that extend classical recurrence concepts in Finsler geometry.

Abstract We study off-shell n-particle form factors of half-BPS operators built from n complex scalar fields at the two-loop order in the planar maximally supersymmetric Yang-Mills theory (sYM). These are known as minimal form factors. We construct their representation as a sum of independent scalar Feynman integrals relying on two complementary techniques. First, by going to the Coulomb branch of the theory by employing the spontaneous symmetry breaking which induces masses, but only for external particles while retaining masslessness for virtual states propagating in quantum loops. For a low number of external legs, this entails an uplift of massless integrands to their massive counterparts. Second, utilizing the $$ \mathcal{N} $$ N = 1 superspace formulation of $$ \mathcal{N} $$ N = 4 sYM and performing algebra of covariant derivatives off-shell. Both techniques provide identical results. These form factors are then studied in the near-mass-shell limit with the off-shellness regularizing emerging infrared divergences. We observe their exponentiation and confirm the octagon anomalous dimension, not the cusp, as the coefficient of the Sudakov double logarithmic behavior. By subtracting these singularities and defining a finite remainder, we verified that its symbol is identical to the one found a decade ago in the conformal case. Beyond-the-symbol contributions are different in the two cases, however.

Papapetrou showed that the covariant derivative of a Killing vector field satisfies Maxwell’s equations in vacuum. Papapetrou’s result is extended, in this article, and it is shown that the covariant derivative of a Killing vector field satisfies Maxwell’s equations in non-vacuum backgrounds as well if one allows electromagnetic currents of purely geometric origin. It is then postulated that every Killing vector field gives rise to a physical electromagnetic field and, in a non-vacuum background, a physical electromagnetic current—hereafter called Killing electromagnetic field and Killing electromagnetic current, respectively. It is shown that the Killing electromagnetic field of the flat FLRW (Friedmann–Lemaître–Robertson–Walker) universe comprises a Killing magnetic field and a rotational Killing electric field; an upper bound on the Killing magnetic field is derived, and it is found that the upper bound is consistent with the current observational bounds on the cosmic magnetic field. Next, the time-like Killing vector of the Schwarzschild spacetime is shown to give rise to a radial Killing electric field. It is also shown that in the weak field regime—and far from the matter distribution—the back reaction of the radial Killing electric field changes the Schwarzschild metric to the Reissner–Nordström metric, establishing a partial converse of Wald’s result. Drawing upon Rainich’s work on Rainich–Riemann manifolds, the etiological question of how a physical electromagnetic field can arise out of geometry is discussed; it is also argued that detection of the Killing electric field of flat FLRW spacetime may be within the current experimental reach. Finally, this article discusses the relevance of Killing electromagnetic currents and the aforementioned transmutation of Schwarzschild spacetime to Reissner–Nordstrom spacetime, to Misner and Wheeler’s program of realizing “charge without charge”.

Vibrational sum frequency generation (SFG) spectroscopy is capable of probing the orientation of the interfacial molecules. A conventional approach assumes that hyperpolarizability tensors governing the SFG signal intensity can be determined based on the point group symmetry of individual functional groups. However, vibrational coupling among neighboring groups breaks the normal mode symmetry. This makes it difficult to accurately interpret SFG spectra, particularly for phenyl (C6H5-) groups. In this study, we employed density functional theory (DFT) calculations to predict the SFG spectral features of C6H5 groups at two-dimensional interfaces with C∞ symmetry. Using model compounds such as iodobenzene (C6H5-I) and various substituted phenyl derivatives, we systematically investigated the effect of vibrational coupling with neighboring atoms on the aromatic C-H stretching modes presented in the 3000-3100 cm-1 region. If the substituent group lacks C-H bonds capable of coupling with the phenyl ring vibrations, the computed polarizability and dipole derivative tensors align well with the A1 and B1 symmetries expected from the C2v point group. However, when the substituent contains C-H groups in the nearest or next-nearest positions to the phenyl ring, significant deviations from C2v symmetry arise, leading to shifts in peak positions and intensity variations in SFG spectra. These findings underscore the limitations of conventional C2v-based SFG analyses in determining the tilt angle of phenyl groups at polymer interfaces and emphasize the necessity of incorporating vibrational coupling effects for accurate SFG spectral interpretation. The approach presented in this work provides a more rigorous framework for accurately predicting and characterizing interfacial molecular orientations and can be extended to other complex systems, where vibrational interactions play a crucial role.

In this paper, we derive five-dimensional non-Abelian N=1 Chern-Simons action from its proposed definition of variation with respect to an infinitesimal deformation of the vector prepotential in a projective superspace setting. It has been a long-standing open problem how to integrate this variation. Now, thanks to the simplicity of a projective superspace technique, we are finally able to obtain this term. Our final result is expressed in terms of the real prepotential multiplets and projective covariant derivatives. The action reduces to the correct formula in the Abelian limit. As a bonus, we also give the supersymmetric Yang-Mills action with a half measure. Published by the American Physical Society 2025

Abstract The present work introduces a numerical method for mathematical modelling of the hydraulic fracture propagation process within a naturally fractured reservoir. We consider a poroelastoplasticity model with rock failure described by an advanced constitutive material model representing the tensile, shear, and compressional failure of the formation. We propose a discretization method for the elastoplastic model coupled to the equations for two-phase fluid flow in porous media. The discretization is based on a collocated cell-centered finite volume method that uses an advanced approximation of the traction vector for mechanics and the conventional single-point upstream-weighted two-point approximation of the Darcy flux. The Biot term coupling of the mechanical and flow models is approximated assuming piecewise constant pore pressure, leading to an inf-sup stable method. To solve the plasticity problem, we use the cutting plane algorithm. The plastic strain tensor derivatives are obtained in the solution process, thus bypassing the necessity of the consistent tangent elastoplastic stiffness tensor. We study the grid convergence for the discrete solution of poroelasticity equations on a set of problems with analytical solutions and demonstrate the application of proposed methods for poroplasticity to tensile fractures near a borehole and hydraulic fracturing experiments.