Search Results (14)

In this paper, we investigate the shadow properties of a rotating black hole with a weakly coupled global monopole charge using a modified Newman–Janis algorithm. This study explores how these charge and rotational effects shape the black hole’s shadow, causal structure, and ergoregions, with implications for distinguishing it from Kerr-like solutions. Analysis of null geodesics reveals observable features that may constrain the global monopole charge and weak coupling parameters within nonminimal gravity frameworks. Observational data from M87* and Sgr A* constrain the global monopole charge and coupling constant to $0\le \gamma \lesssim 0.036$ and $-0.2\lesssim \alpha \le 0$, respectively. Full article

This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex ($\alpha ,\beta$)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for both linear and nonlinear matrix equations. This paper extends the concept to partially ordered geodesic spaces and establishes new existence and convergence results. Illustrative examples are provided to demonstrate the practical relevance of the findings. Overall, this research contributes a novel approach to the field of matrix equations. Full article

In this study, the authors focus on quasi-hemi-slant submanifolds ($qhs$-submanifolds) of $(\alpha ,\beta )$-type almost contact manifolds, also known as trans-Sasakian manifolds. Essentially, we give sufficient and necessary conditions for the integrability of distributions using the concept of quasi-hemi-slant submanifolds of trans-Sasakian manifolds. We also consider the geometry of foliations dictated by the distribution and the requirements for submanifolds of trans-Sasakian manifolds with quasi-hemi-slant factors to be totally geodesic. Lastly, we give an illustration of a submanifold with a quasi-hemi-slant factor and discuss its application to number theory. Full article

In this paper, we focus on the research and analysis of the geometric properties and symmetry of slant curves and contact magnetic curves in Lorentzian $\alpha$-Sasakian 3-manifolds. To do this, we define the notion of Lorentzian cross product. From the perspectives of the Legendre and non-geodesic curves, we found the ratio relationship between the curvature and torsion of the slant curve and contact magnetic curve in the Lorentzian $\alpha$-Sasakian 3-manifolds. Moreover, we utilized the property of the contact magnetic curve to characterize the manifold as Lorentzian $\alpha$-Sasakian and to find the slant curve type of the Frenet contact magnetic curve. Furthermore, we found an example to verify the geometric properties of the slant curve and contact magnetic curve in the Lorentzian $\alpha$-Sasakian 3-manifolds. Full article

We have used publicly available kinematic data for the S2 star to constrain the parameter space of MOdified Gravity. Integrating geodesics and using a Markov Chain Monte Carlo algorithm, we have provided the first constraint on the scales of the Galactic Centre for the parameter $\alpha$ of the theory, which represents the fractional increment of the gravitational constant G with respect to its Newtonian value. Namely, $\alpha \lesssim 0.662$ at 99.7% confidence level (where $\alpha =0$ reduces the theory to General Relativity). Full article

In recent years, the modification of general relativity (GR) through $f\left(R\right)$ gravity is widely used to study gravity in a variety of scenarios. In this article, we study various physical properties of a black hole (BH) that emerged in the linear Maxwell $f\left(R\right)$ gravity to constrain the values of different BH parameters, i.e., c and $\alpha$. In particular, we study those values of the defining $\alpha$ and c for which the particles around the above-mentioned BH behave like other astrophysical BH in GR. The main motivation of the present research is to study the geodesics equations and discuss the possible orbits for $c=0.5$ in detail. Furthermore, the frequency shift of a photon emitted by a timelike particle orbiting around the BH is studied given different values of $\alpha$ and c. The stability of both timelike and null geodesics is discussed via Lyapunov’s exponent. Full article

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied. Full article

Polarimetric synthetic aperture radar (PolSAR) image classification plays a significant role in PolSAR image interpretation. This letter presents a novel unsupervised classification method for PolSAR images based on the geodesic distance and K-Wishart distribution. The geodesic distance is obtained between the Kennaugh matrices of the observed target and canonical targets, and it is further utilized to define scattering similarity. According to the maximum scattering similarity, initial segmentation is produced, and the image is divided into three main categories: surface scattering, double-bounce scattering, and random volume scattering. Then, using the shape parameter α of K-distribution, each scattering category is further divided into three sub-categories with different degrees of heterogeneity. Finally, the K-Wishart maximum likelihood classifier is applied iteratively to update the results and improve the classification accuracy. Experiments are carried out on three real PolSAR images, including L-band AIRSAR, L-band ESAR, and C-band GaoFen-3 datasets, containing different resolutions and various terrain types. Compared with four other classic and recently developed methods, the final classification results demonstrate the effectiveness and superiority of the proposed method. Full article

Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-existence of α-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati’s loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction. Full article

In this paper we consider the negative energy problem in generalized Vaidya spacetime. We consider several models where we have the naked singularity as a result of the gravitational collapse. In these models we investigate the geodesics for particles with negative energy when the II type of the matter field satisfies the equation of the state $P=\alpha \rho$ ($\alpha \in [0,1]$). Full article

The axiomatic geometric structure which lays at the basis of Covariant Classical and Quantum Gravity Theory is investigated. This refers specifically to fundamental aspects of the manifestly-covariant Hamiltonian representation of General Relativity which has recently been developed in the framework of a synchronous deDonder–Weyl variational formulation (2015–2019). In such a setting, the canonical variables defining the canonical state acquire different tensorial orders, with the momentum conjugate to the field variable $g_{\mu \nu }$ being realized by the third-order 4-tensor ${\mathrm{\Pi }}_{\mu \nu }^{\alpha }$ . It is shown that this generates a corresponding Hamilton–Jacobi theory in which the Hamilton principal function is a 4-tensor $S^{\alpha }$ . However, in order to express the Hamilton equations as evolution equations and apply standard quantization methods, the canonical variables must have the same tensorial dimension. This can be achieved by projection of the canonical momentum field along prescribed tensorial directions associated with geodesic trajectories defined with respect to the background space-time for either classical test particles or raylights. It is proved that this permits to recover a Hamilton principal function in the appropriate form of 4-scalar type. The corresponding Hamilton–Jacobi wave theory is studied and implications for the manifestly-covariant quantum gravity theory are discussed. This concerns in particular the possibility of achieving at quantum level physical solutions describing massive or massless quanta of the gravitational field. Full article

One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence). For an exponential family endowed with the Fisher metric and $\alpha$ -connections, the two loss functions are uniformly described as the energy difference along an $\alpha$ -geodesic path, for some $\alpha \in \{-1,0,1\}$ . Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle. Full article

We revisit the role of the cosmological constant Λ in the deflection of light by means of the Schwarzschild–de Sitter/Kottler metric. In order to obtain the total deflection angle α, the time transfer function approach is adopted, instead of the commonly used approach of solving the geodesic equation of photon. We show that the cosmological constant does appear in expression of the deflection angle, and it diminishes light bending due to the mass of the central body M. However, in contrast to previous results, for instance, that by Rindler and Ishak (Phys. Rev. D. 2007), the leading order effect due to the cosmological constant does not couple with the mass of the central body M. Full article

A divergence function on a manifold M defines a Riemannian metric g and dually coupled affine connections ∇ and ∇ * on M. When M is dually flat, that is flat with respect to ∇ and ∇ * , a canonical divergence is known, which is uniquely determined from ( M , g , ∇ , ∇ * ) . We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic integration of the inverse exponential map. The new definition of a canonical divergence reduces to the known canonical divergence in the case of dual flatness. Finally, we show that the integrability of the inverse exponential map implies the geodesic projection property. Full article