International Journal of Geometric Methods in Modern Physics

The purpose of this study is to examine the effect of topology change on anomaly in the initial universe. G-cobordism is introduced to argue about the topology change accompanied by gauge group. Our results revealed that change of anomalies results from topology change.

In this paper, we derive intrinsic equations for dual r-elastic line deformed on non-null surface by external field in dual Lorentzian space.

We present new formulae for the Cartan invariants of second- and third-order ODEs in terms of the Jacobi endomorphisms.

We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due to the partial isomorphism between CA(3, 1) and the centrally extended Sp( 8), we perform a nonlinear realization of the centrally extended (CE)Sp( 8) in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the nonlinear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constraints. Finally, we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.

We discuss in detail the weak field limit of f(R, 𝒢) gravity taking into account analytic functions of the Ricci scalar R and the Gauss–Bonnet invariant 𝒢. Specifically, we develop, in metric formalism, the Newtonian, Post-Newtonian (PN) and Parametrized Post-Newtonian (PPN) limits starting from general f(R, 𝒢) Lagrangian. The special cases of f(R) and f(𝒢) gravities are considered. In the case of the Newtonian limit of f(R, 𝒢) gravity, a general solution in terms of Green's functions is achieved.

In the study of the dynamics in a 5D bulk from brane world scenario, an extra force with abnormal properties was detected (cf. [D. Youm, Extra force in brane worlds, Phys. Rev. D62 (2000) 084002; D. Youm, Null geodesics in brane world universe, Mod. Phys. Lett. A16 (2001) 2371; L. F. Zhang and Y. Z. Zhang, Null geodesics in brane world scenarios, Commun. Theor. Phys. (Beijing)41 (2004) 48]). In this paper, by using the Riemannian horizontal connection introduced in [A. Bejancu, A new point of view on general Kaluza–Klein theories, Progr. Theor. Phys.128 (2012) 541], we give a new definition for the extra force in a 5D bulk, and show that it does not contradict the 4D physics. In particular, we show that this force appears very rarely along geodesics in a warped 5D bulk.

In this paper we study the stationary scattering problem of the Aharonov–Bohm (AB) effect. To achieve this goal we construct a Hamiltonian from the most general representations of the Heisenberg algebra. Such representations are defined on a non-simply-connected manifold which we set as the flat circular annulus. By means of the von Neumann's self-adjoint extensions formalism, the scattering data are then provided. No solenoid is considered in this paper. The corresponding Hamiltonian is based on a topological quantum degree of freedom inherent in such representations. This variable stands for the magnetic vector gauge potential at quantum level. Our outcomes confirm the topological nature of this effect.

In this paper we discuss a master equation applied to the two-level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three-level system. Our results may give a small hint to understand the huge transition from Quantum World to Classical World. To the best of our knowledge this is the finest method up to the present.

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

In this paper, we find a condition under which a Finsler space with Randers change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Randers transformed mth-root Finsler metric is locally dually flat. Moreover, if transformed Finsler metric is conformal to the mth-root Finsler metric, then we prove that both of them reduce to Riemannian metrics.

We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang–Mills–Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein–Yang–Mills–Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.

In this paper, we will investigate 2-symmetry type curvature conditions of a lightlike hypersurface of a semi-Riemannian space form. Then we find some results related with locally symmetric and 2-symmetric lightlike hypersurfaces. Finally the relation between semisymmetric and 2-symmetric lightlike hypersurfaces will be given.

Radial fall has historically played a momentous role. It is one of the most classical problems, the solutions of which represent the level of understanding of gravitation in a given epoch. A gedankenexperiment in a modern frame is given by a small body, like a compact star or a solar mass black hole, captured by a supermassive black hole. The mass of the small body itself and the emission of gravitational radiation cause the departure from the geodesic path due to the back-action, that is the self-force. For radial fall, as any other non-adiabatic motion, the instantaneous identity of the radiated energy and the loss of orbital energy cannot be imposed and provide the perturbed trajectory. In the first part of this paper, we present the effects due to the self-force computed on the geodesic trajectory in the background field. Compared to the latter trajectory, in the Regge–Wheeler, harmonic and all others smoothly related gauges, a far observer concludes that the self-force pushes inward (not outward) the falling body, with a strength proportional to the mass of the small body for a given large mass; further, the same observer notes a higher value of the maximal coordinate velocity, this value being reached earlier during infall. In the second part of this paper, we implement a self-consistent approach for which the trajectory is iteratively corrected by the self-force, this time computed on osculating geodesics. Finally, we compare the motion driven by the self-force without and with self-consistent orbital evolution. Subtle differences are noticeable, even if self-force effects have hardly the time to accumulate in such a short orbit.

A modified Mimetic gravity (MMG) is proposed as a generalization of general relativity. The model contains a physical metric which is the function of an auxiliary (unphysical) metric and a Lyra's metric. We construct different kinds of conformally invariant models in different levels of the expansion parameter λ. This model phenomenologically has been extended to higher-order forms. Cosmology of a certain class of such models has been investigated in detail. A cosmological solution has been proposed in inhomogeneous form of scalar field. For homogeneous case, energy conditions are widely investigated. We have shown that the system evaluated at intervals shorter than a certain time T_c meets all the energy conditions.

We give examples of Lie–Rinehart algebras whose universal enveloping algebra is not a Hopf algebroid either in the sense of Böhm and Szlachányi or in the sense of Lu. These examples are constructed as quotients of a canonical Lie–Rinehart algebra over a Jacobi algebra which does admit an antipode.