This paper is devoted to discussing compact stars in $f(\mathcal{R},\mathcal{G})$ gravity, where $\mathcal{R}$ and $\mathcal{G}$ denote the Ricci scalar and Gauss-Bonnet invariant, respectively. To meet this aim, we consider spherically symmetric space-time with an anisotropic fluid distribution. In particular, the Karmarkar condition is used to explore the compact star solutions. Furthermore, we choose two specific models of compact stars, namely LMC X-4 ($\mathrm{mass}=1.29M/M_{\odot }$ and $\mathrm{radii}=9.711\mathrm{km}$) and EXO 1785-248 ($\mathrm{mass}=1.30M/M_{\odot }$ and $\mathrm{radii}=8.849\mathrm{km}$). We develop the field equations for $f(\mathcal{R},\mathcal{G})$ gravity by employing the Karmarkar condition with a specific model already reported in literature by Lake [ Phys. Rev. D 67, 104015 (2003)]. We further consider the Schwarzschild geometry for the matching conditions at the boundary. It is important to mention here that we calculate the values of all the involved parameters by imposing the matching condition. We have provided a detailed graphical analysis to discuss the physical acceptability of parameters, i.e., energy density, pressure, anisotropy, and gradients. We have also examined the stability of compacts stars by exploring the energy conditions, equation of state, generalized Tolman-Oppenheimer-Volkoff equation, causality condition, and adiabatic index. For the present analysis, we predict some numerical values in tabular form for central gravitational metric functions, central density, and central pressures components. We have also calculated the ratio $p_{rc}/{\rho }_c$ to check the validity of Zeldovich’s condition. Conclusively, it is found that our obtained solutions are physically viable with a well-behaved nature in $f(\mathcal{R},\mathcal{G})$ modified gravity for the compact star models under discussion.

In this paper, we have studied the particle dynamics, gravitational lensing and energy processes around the black hole (BH) in Kalb–Ramond (KR) gravity. The motion of particles is considered with parameters in KR BH and investigated for massive and massless particles. From this work, we have got the horizon structure, photon orbit of photon and ISCO (inner stable circular orbit) of a mass particle with parameters in KR gravity. The effective potential is also studied for the massless and mass particles. Additionally, we tested energy extracted from BH using the BSW (Banados–Silk–West) method and derived the expression of center mass-energy in KR gravity. The impact of the model parameters $$\gamma $$γ and $$\lambda $$λ is checked to study the size of the BH shadow in the KR gravity. Gravitational weak lensing has been explored using the general method and the derived deflection angle of light rays around the BH for the plasma of various concentration distributions. The magnification of brightness is obtained using the angle of deflection of the light rays.

The present study explores the $$f(\mathcal {R},\mathcal {T})$$f(R,T) modified gravity on the basis of observational data for three different compact stars with matter profile as anisotropic fluid without electric charge. In this respect, we adopt the well-known Karmarker condition and assume a specific and interesting model for $$\mathrm {g}_{rr}$$grr metric potential component which is compatible with this condition. This choice further leads to a viable form of metric component $$\mathrm {g}_{tt}$$gtt by utilizing the Karmarkar condition. We also present the interior geometry in the reference of Schwarzschild interior and Kohler–Chao cosmological like solutions for $$f(\mathcal {R},\mathcal {T})$$f(R,T) theory. Moreover, we calculate the spacetime constants by using the masses and radii from the observational data of three different compact stars namely 4U 1538-52, LMC X-4 and PSR J1614-2230. In order to explore the viability and stability of the obtained solutions, some physical parameters and properties are presented graphically for all three different compact object models. It is noticed that the parameters c and $$\lambda $$λ have some important and considerable role for these solutions. It is concluded that our obtained solutions are physically acceptable, bearing a well-behave nature in $$f(\mathcal {R},\mathcal {T})$$f(R,T) modified gravity.

We investigate the null geodesics and the shadow cast by the Kerr–Newman–Kiselev–Letelier (KNKL) black hole for the equation of state parameter $$\omega _q=-2/3$$ω q = - 2 / 3 and for different values of the spacetime parameters, including the quintessence parameter $$\gamma $$γ , the cloud of string (CS) parameter b, the spin parameter a and the charge Q of the black hole. We notice that for the increasing values of the parameters $$\gamma $$γ and b the size of the shadow of the KNKL black hole increases and consequently the strength of the gravitational field of the black hole increases. On the other hand with increase in the charge Q of the black hole the size of the shadow of the black hole decreases. Further with the increase in the values of the spin parameter a of the KNKL black hole, we see that the distortion of the shadow of the black hole becomes more prominent. Moreover we use the data released by the Event Horizon Telescope (EHT) collaboration, to restrict the parameters b and $$\gamma $$γ for the KNKL black hole, using the shadow cast by the KNKL black hole. To this end, we also explore the relation between the typical shadow radius and the equatorial and polar quasinormal mods (QNMs) for the KNKL black hole and extend this correspondence to non-asymptotically flat spacetimes. We also study the emission energy rate from the KNKL black hole for the various spacetime parameters, and observe that it increases for the increasing values of both the parameters $$\gamma $$γ and b for fixed charge-to-mass and spin-to-mass ratios of the KNKL black hole. Finally, we investigate the effects of plasma on the photon motion, size and shape of the shadow cast by the KNKL black hole. While keeping the spacetime parameters fixed, we notice that with increase in the strength of the plasma medium the size of the shadow of the KNKL black hole decreases and therefore the intensity of the gravitational field of the KNKL black hole decreases in the presence of plasma.