Narrow Results

Unifying the massive spin-1 field with gravity requires the implementation of a regular vector field that satisfies the spin-1 Proca equation and is a fundamental part of the space–time metric. That vector field is one of the pair of vectors in the line element field $(X,-X)$, which is paramount to the existence of all Lorentzian metrics and Modified General Relativity (MGR). Symmetrization of the spin-1 Klein–Gordon equation in a curved Lorentzian space–time introduces the Lie derivative of the metric along the flow of one of the regular vectors in the line element field. The Proca equation in curved space–time can then be described geometrically in terms of the line element vector, the Lie derivative of the Lorentzian metric and the Ricci tensor, which unifies gravity and the spin-1 field. Related issues concerning charge conservation and the Lorenz constraint, singularities in a spherically symmetric curved space–time and geometrical implications of MGR to quantum theory are discussed. A geometrical unification of gravity with quantum field theory is presented.

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB.

We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of $(p+1)$-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the $D$-dimensional Minkowski space.

In this study, the deformations and trajectories of elastic fresh tea leaf in a simple straight channel model are investigated using the combined immersed boundary–lattice Boltzmann method (IB–LBM). The objective is to qualitatively analyze the effects of gravity, diameter and the Reynolds number (Re) on the physical characteristics of flexible fresh tea leaf, which is driven by Poiseuille airflow in a channel model. The LBM is used to simulate the fluid domain with regular Eulerian grid, while the IB method is employed to model the fluid–membrane interaction, with a set of Lagrangian moving grids being adopted for the fresh tea leaf. Our results mainly reveal that a tea leaf undergoes deformation due to the shearing effect of the Poiseuille flow, resulting in lifting of the leaf toward the channel center. Under the influence of gravity, the leaf performs a tumbling motion with clockwise rotation and preserves an oscillating stable state. Furthermore, the diameter has a far greater influence on the dimensionless shape parameters than Re. For a leaf of a certain size and position, a series of relations between $L∕W$ and Re are established at various ratios of fresh leaves by least square method. Based on the above findings, such studies provide useful data and insights to obtain high-quality green tea by selecting mechanical-plucked fresh tea leaves according to shape consistency.

The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy–Wouthuysen transformations.

We clarify the status of 5D solitons by calculating their energies using a Hamiltonian approach. These objects in general possess gravitational, scalar and electromagnetic energy which complicates their space–time structure. However, the Schwarzschild case is unique in having an event horizon that gives back the usual 4D entropy. We outline applications to grand-unified theories and tests of the equivalence principle.

We discuss some issues arising in studying (linearized) gravity on non-BPS higher co-dimension branes in an infinite-volume bulk. In particular, such backgrounds are badly singular for codimension-3 and higher δ-function-like branes with nonzero tension. As we discuss in this note, nontrivial issues arise in smoothing out such singularities. Thus, adding higher curvature terms might be necessary in this context.

We propose a scenario for particle-mass generation, assuming the existence of a physical regime where, firstly, physical particles can be considered as point-like objects moving in a background space–time and, secondly, their mere presence spoils the invariance under the local diffeomorphism group, resulting in an anomalous realization of the latter. Under these hypotheses, we describe mass generation starting from the massless free theory. The mechanism is not sensitive to the detailed description of the underlying theory at higher energies, leaning only on general structural features of it, specifically diffeomorphism invariance.

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions.

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on the non-trivial part of the gravitational response, which is to the large momenta propagating around a closed loop. By taking a limiting case one can give a simple geometric description of this gravitational response. This is calculated in detail for the example of a closed Feynman loop in the form of a trefoil knot. The results show that when the magnitude of the momentum passes a certain threshold value, non-trivial gravitational configurations of the knot play an important role.

Using the canonical formalism, we study the asymptotic symmetries of the topological 3-dimensional gravity with torsion. In the anti-de Sitter sector, the symmetries are realized by two independent Virasoro algebras with classical central charges. In the simple case of the teleparallel vacuum geometry, the central charges are equal to each other and have the same value as in general relativity, while in the general Riemann-Cartan geometry, they become different.

As a simple example of the "blurring" influence of noncommutative geometry, a noncommutative version of a high-frequency perturbation of a background metric is calculated. The relation between the principal null vectors of the wave and those of the induced symplectic structure is in this case particularly clear.

A model for noncommutative scalar fields coupled to gravity based on the generalization of the Moyal product is proposed. Solutions compatible with homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial order in the perturbation of the star-product are presented. It is shown that in the context of a typical chaotic inflationary scenario, at least in the slow-roll regime, noncommutativity yields no observable effect.

The canonical structure of the Einstein–Hilbert Lagrange density is examined in two spacetime dimensions, using the metric density and symmetric affine connection as dynamical variables. The Hamiltonian reduces to a linear combination of three first-class constraints with a local SO(2, 1) algebra. The first-class constraints are used to find a generator of gauge transformations that has a closed off-shell algebra and which leaves the Lagrangian and det(h^μν) invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix ζ_μν.

The peculiarities of doing a canonical analysis of the first-order formulation of the Einstein–Hilbert action in terms of either the metric tensor g^αβ or the metric density along with the affine connection are discussed. It is shown that the difference between using g^αβ as opposed to h^αβ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off-shell generators of gauge transformations and off-shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first-class constraints, are different from a diffeomorphism transformation in both cases.

We study a gravity model where a tensionful codimension-one three-brane is embedded in a bulk with infinite transverse length. We find that 4D gravity is induced on the brane already at the classical level if we include higher-curvature (Gauss–Bonnet) terms in the bulk. Consistency conditions appear to require a negative brane tension as well as a negative coupling for the higher-curvature terms.

For the Poincaré gauge theory of gravity we consider the dynamical scalar torsion mode in a cosmological context. We explore in particular the possibility of using dynamical torsion to explain the current state of the accelerating Universe. With certain suitable sets of chosen parameters, this model can give a (qualitatively) proper description of the current universe without a cosmological constant, and the universe described is oscillating with a period of the Hubble time.

The personal view on some recent aspects of average spin and orbital momenta of partons in nucleon is discussed and compared with the previous understanding. The special attention is payed to the strangeness polarization mediated by gluon anomaly and treatment of the strange quarks in a heavy ones in a multiscale nucleon. The crucial role in the orbital structure of nucleon is played by relocalization (Belinfante) invariance and Equivalence Principle (EP). The new manifestation of EP for spin 1 particles is suggested and discussed.

We propose a new solution to problems of the hierarchy and smallness of the cosmological constant using the TeV scale of the Standard Model in a new framework of the higher-order gravity.