This study is devoted to explore the physical aspects of wormhole geometry under embedded class-1 spacetime in $$f(T,\tau )$$f ( T , τ ) gravity, where $$\tau $$τ denotes the trace of the energy-momentum tensor and T is the torsion. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. To complete this study, we take diagonal and off-diagonal tetrad, and try to build a comparison by considering the validity region of energy conditions in embedded class-1 spacetime. The embedded surface diagram is given to understand the connection between the two different regions of spacetime. The validity regions of all the energy conditions are calculated. A detailed graphical analysis is provided for validity regions of all the energy conditions. The presence of exotic matter is confirmed in both the cases as the null energy condition is violated.

This work mainly focuses on unveiling the particle dynamics features of black holes. For this objective, we utilize the charged black hole geometry consisting of the cloud strings and quintessence under the ansatz of Rastall gravity. We have calculated and analyzed the effective potential, angular momentum, particle energy, horizon radius, inner stable circular orbit, photon sphere radius, quasi-periodic oscillations, and effective force to reveal the dynamical features. We in detail discussed the effects of charge in black hole, Rastall parameter, strings of cloud parameter, and quintessential parameter on the calculated results. To ensure the scenario of accelerated expansion, ω _q lies in the range −1 < ω _q < −1/3. From this specific range, we choose ω _q = −2/3.

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 .

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.