Constraining spacetime metrics within and outside general relativity through the Galactic Center black hole (SgrA*) shadow

The Galactic Center (GC) black hole (Sgr A*) shadow detected by the Event Horizon Telescope (EHT) is a new probe for testing spacetime metric in strong field regime. In this work, the Schwarzschild de-Sitter (SdS), Kerr (K), Kerr de-Sitter (KdS), Reissner Nordstrom with tidal charge (RN), scalaron and the PPN metric have been used to put bounds on their parameters. Based on EHT’s angular size of the Sgr A* black hole shadow, we obtain constraints for the cosmological constant, λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} from the SdS and KdS metrics and find that the bounds on the cosmological constant are well above the cosmological bound. For the RN metric, the bounds obtained on the tidal charge q are stringent as compared to those reported for M87* shadow. In case of scalaron metric of f(R) modified gravity we have been able to narrow down the range of scalaron mass as compared to previous reports coming from the study of the pericenter shift of the compact stellar orbits. We find no significant deviation of the gravitational constant, G as expected from the modified gravity. For the PPN metric it has been found that it is not possible to constrain higher order correction in PPN metric for β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upbeta $$\end{document}, γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upgamma $$\end{document} given by present measurements of stellar orbits near Sgr A*. However, for solar system bounds (β-γ=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upbeta - \upgamma = 0$$\end{document}), there appears a wide range of the third order parameter ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upzeta $$\end{document}. Inferences for gravity on the basis of constrained parameters are presented.