International Journal of Modern Physics D

In this paper, we focus on the secular changes of the orbital elements of a planet in the solar system, determined by the magnetic-like part of a gravitational wave field. Using Fermi coordinates, we show that the total force acting on a test particle is made of two contributions: a gravito-electric one and a gravito-magnetic one. While the electric-like force has been thoroughly discussed in the past, the effect of the gravito-magnetic force, which depends on the velocity of the test particle, has not been considered yet. We obtain approximated results to some orders in the orbital eccentricity and show that these effects are much smaller than the corresponding gravito-electric ones.

In this work, the spacetime geometry of the halo region in spiral galaxies is obtained considering the observed flat galactic rotation curve feature, invoking the Tully–Fisher relation and assuming the presence of cold dark matter in the galaxy. The gravitational lensing analysis is performed treating the so-obtained spacetime as a gravitational lens. It is found that the aforementioned spacetime as the gravitational lens can consistently explain the galaxy–galaxy weak gravitational lensing observations and the lensing observations of the well-known Abell 370 and Abell 2390 galaxy clusters.

We show the appearance of geometric phase in a Dirac particle traversing in nonrelativistic limit in a time-independent gravitational field. This turns out to be similar to the one originally described as a geometric phase in magnetic fields. We explore the geometric phase in the Kerr and Schwarzschild geometries, which have significant astrophysical implications. Nevertheless, the work can be extended to any spacetime background including that of time-dependent. In the Kerr background, i.e. around a rotating black hole, geometric phase reveals both the Aharonov–Bohm effect and Pancharatnam–Berry phase. However, in a Schwarzschild geometry, i.e. around a nonrotating black hole, only the latter emerges. We expect that our assertions can be validated in both the strong gravity scenarios, like the spacetime around black holes, and weak gravity environment around Earth.

A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for realistic anisotropic neutron stars was obtained using the general theory of relativity. Assuming a physically acceptable nonsingular form of one metric potential and radial pressure containing the curvature parameter $R$, the constant $k$ and the radius $r$, analytical solutions to Einstein’s field equations for anisotropic matter distribution were obtained. Taking the value of $k$ as −0.44, it was found that the proposed model obeys all necessary physical conditions, and it is potentially stable and realistic. The model also exhibits a linear equation of state, which can be applied to describe compact stars.

In this work, we have attempted to generalize the Raychaudhuri equation by using the concept of foliation of spacetime. Some studies are performed with a few special cases and their physical implication are discussed.

In this paper, we study anisotropic universes with Modified Chaplygin gas (MCG) in the context of Randall Sundrum-2 (RS2) braneworld model. The cosmological solutions for Kantowski–Sachs (KS) and Bianchi-I universes with MCG are obtained on the RS2 braneworld. The solutions are found to be dependent on MCG parameters but are modified from the GR solutions due to the braneworld correction term arising from high-energy effects. The anisotropy and deceleration parameters are obtained for each solution and the possibility of occurrence of future singularities is considered. Interestingly, we find that one drawback of the relativistic picture can be overcome in this model giving a universe close to the presently observed state.

Recently (Int. J. Mod. Phys. D 27 (2018) 1847025) an interesting property of closed light rings in Kerr black holes has been noticed. We explain its origin and derive a slightly more general result.

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere $(r_{\mathrm{\text{ps}}})$ and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow $R_s$. Also, we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency, whereas the imaginary part determines the instability timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike geodesics, we compute the innermost stable circular orbit (ISCO) and marginally bound circular orbit (MBCO) of the regular BHs which are closely related to the BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.