We investigate the deflection of light by a rotating global monopole spacetime and a rotating Letelier spacetime in the weak deflection approximation. To this end, we apply the Gauss-Bonnet theorem to the corresponding osculating optical geometries and show that the deflection of light increases in each spacetime due to the presence of the global monopole parameter and the string cloud parameter, respectively. The results obtained for the deflection angle in the equatorial plane generalize known results for the corresponding nonrotating global monopole and Letelier spacetimes as well as the Kerr solution.

In this article we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized metric potential, namely, Buchdahl ansatz [Phys. Rev. D 116, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar and Finch-Skea. We developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that has a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$ and analyzed them in a uniform manner. As a result it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the frame work of anisotropic hypothesis, we consider analogue objects with similar mass and radii, such as LMC X-4, SMC X-1, EXO 1785-248 etc. to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P=P(\rho )$, we demonstrate that equation of state (EoS) can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [ Phys. Rev. D 67, 104015 (2003)]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

Recent times witnessed a significant interest in regularizing, a $$ D \rightarrow 4 $$D→4 limit, of EGB gravity initiated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by re-scaling GB coupling constant as $$\alpha /(D-4)$$α/(D-4) and taking limit $$D \rightarrow 4$$D→4 , and in turn these regularized 4D gravities have nontrivial gravitational dynamics. Interestingly, the maximally or spherically symmetric solution to all the regularized gravities coincides in the 4D case. In view of this, we obtain an exact spherically symmetric wormhole solution in the 4D EGB gravity for an isotropic and anisotropic matter sources. In this regard, we consider also a wormhole with a specific radial-dependent shape function, a power-law density profile as well as by imposing a particular equation of state. To this end, we analyze the flare-out conditions, embedding diagrams, energy conditions and the volume integral quantifier. In particular our −ve branch results, in the limit $$\alpha \rightarrow 0$$α→0 , reduced exactly to vis- $$\grave{a}$$a` -vis 4D Morris-Thorne of GR.

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is...

In this paper, we study the deflection of light by a class of charged wormholes within the context of the Einstein-Maxwell-dilaton theory. The primordial wormholes are predicted to exist in the early universe, where inflation is driven by the dilaton field. We perform our analysis through optical geometry using the Gibbons-Werner method (GW) by adopting the Gauss-Bonnet theorem and the standard geodesics approach. We report an interesting result for the deflection angle in leading-order terms—namely, the deflection angle increases due to the electric charge $Q$ and the magnetic charge $P$, whereas it decreases due to the dilaton charge $\mathrm{\Sigma }$. Finally, we confirm our findings by means of geodesics equations. Our computations show that the GW method gives an exact result in leading-order terms.