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.

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.

This paper is based on the study of compact stars in the context of electric fields and the nonmetricity effects of gravity. Due to this, we are motivated to build stellar models based on spherically symmetric space-time in f(Q) gravity. The space-time solution is obtained by Durgapal and Bannerji (Phys Rev D 27:328–331,1983) potential along with modified Van der Waals equation of state (EoS) $$p_r=\eta \rho ^2+ \frac{\beta \rho }{\gamma \rho +1}$$p r = η ρ 2 + β ρ γ ρ + 1 by introducing a specific form of electric charge function $$q(r)=kr^3$$q ( r ) = k r 3 . In order to validate our charge model, we used observational data from the literature for celestial objects like Her X-1, 4U 1538-52, SAX J1808.4-3658, and SMC X-1. Furthermore, we have also retrieved the uncharged effects of gravity for the model SMC X-1 by taking $$k=0$$k = 0 . Our present physical analysis shows that all the obtained features for the present solution are in excellent agreement with the viable model as far as observational data is concerned.

We investigate the thermodynamic properties and Joule–Thomson expansion for conical or BTZ-like black holes. To analyze the thermal stability, we discuss the temperature and thermal stability relative to the horizon radius for different values of model parameters $$\beta _0$$β 0 and $$\alpha _2$$α 2 . Moreover, we analyze thermodynamical geometries like Ruppeiner, Weinhold and Hendi Panahiyah Eslam Momennia formulation and calculate respective scalar curvatures for BTZ-like black holes. Interestingly, the black holes have no singularity in some cases, i.e., completely regular. We obtain the inversion temperatures and inversion curves and investigate the similarities and differences between van der Waals and charged fluids. To discuss this expansion, we use a BTZ-like black hole. Further, we establish the position of the inversion point versus different values of mass $$\mu $$μ , and the parameters $$\beta _0$$β 0 and $$\alpha _2$$α 2 for such a BTZ-like black hole. The Joule–Thomson coefficient $$\mu $$μ at this point disappears. A crucial trait upon which we relied to inspect the sign of quantity $$\mu $$μ to get the cooling-heating areas. We also investigate the energy emission depending upon the frequency $$\omega $$ω .

In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution $\{q_1(x,t),q_2(x,t)\}$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter $\lambda$ .