As @UlrikeFischer has pointed out in a comment, lualatex-math is not suitable for loading fonts. In fact, if your TeX distribution is reasonably up to date, there's no reason for loading lualatex-math at all.
You mention that you want to use Stix fonts for math. Stix is a clone of Times Roman, but it hasn't been updated for quite a while. Instead of Stix, I suggest you use XITS/XITS Math, Stix Two Text/Stix Two Math, or the newtxtext/newtxmath pair.
One of the following three sets of instructions should work for you:
\usepackage[no-math]{fontspec}
\usepackage{newtxtext,newtxmath}
or
\usepackage{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
or
\usepackage{unicode-math}
\setmainfont{Stix Two Text}
\setmathfont{Stix Two Math}
Aside: I can't help but make some comments about your code: You seem to be unusually eager to use curly braces in math mode. That said, I cannot see a good reason for writing
${{{M}_{pl}}{\left({≡{\mathrm{ℏ}c/G}}\right)}}$
when
$M_{pl}$ ($≡ℏc/G$)
produces the same output and does so without any code clutter.
Similarly, do consider replacing
{\frac{G\mathrm{μ}}{{{c}^{{2}}}}}=\mathcal{O}{\left({{\frac{{{E}^{{2}}}}{{{M}_{pl}^{{2}}}}}}\right)}
with
\frac{G\symup{μ}}{c^2} = \mathcal{O}\left(\frac{E^2}{M_{pl}^2}\right)
Addendum to address the OP's follow-up posting: Since your document loads the hyperref package, I would replace
[\href{cqgab7bbabib1}{\textcolor{blue}{1}}]
with
\cite{cqgab7bbabib1}
In addition, I'd replace
\begin{thebibliography}{000}
\bibitem{cqgab7bbabib1}{Aasi Jet alLIGO Scientific and VIRGO Collaborations (2014) Constraints on cosmic strings from the LIGO-Virgo gravitational-wave detectors\textit{Phys. Rev. Lett.} \textcolor{blue}{\textbf{112}} }
\bibitem{cqgab7bbabib2}{Abbott B Pet alLIGO and Virgo Collaborations (2016) Astrophysical implications of the binary black hole merger GW150914\textit{Astrophys. J. Lett.} \textcolor{blue}{\textbf{818}} }
\end{thebibliography}
with
\begin{thebibliography}{9}
\bibitem{cqgab7bbabib1}%{
Aasi J et al, LIGO Scientific and VIRGO Collaborations (2014) Constraints on cosmic strings from the LIGO-Virgo gravitational-wave detectors. \textit{Phys. Rev. Lett.}
%\textcolor{blue}{\textbf{112}}}
\bibitem{cqgab7bbabib2}%{
Abbott B P et al, LIGO and Virgo Collaborations (2016) Astrophysical implications of the binary black hole merger GW150914. \textit{Astrophys. J. Lett.}
%\textcolor{blue}{\textbf{818}}}
\end{thebibliography}
Observe, in particular, that I replaced Aasi Jet alLIGO with Aasi J et al, LIGO and Abbott B Pet alLIGO with Abbott B P et al, LIGO. These changes should make it a lot easier to actually comprehend what's written.
Summing up, here is how I would rewrite your example to make it more efficient.
\documentclass{article}
\usepackage{amsmath,luacolor}
\usepackage{hyperref}
\hypersetup{colorlinks,citecolor=blue}
\usepackage{unicode-math}
\setmainfont{Stix Two Text}
\setmathfont{Stix Two Math}
\begin{document}
\title{Article Title Here}
\author{Author Here}
\maketitle
\section{Introduction}
The investigations of cylindrically symmetric spacetimes can be
traced back as far as to 1919 when Levi-Civita (LC) discovered
a class of solutions of Einstein's vacuum field equations,
corresponding to static cylindrical spacetimes
\cite{cqgab7bbabib1}.
\begin{equation}
\frac{G\symup{μ}}{c^2} =
\mathcal{O}\biggl(\frac{E^2}{M_{pl}^2}\biggr),,\tag{1.1}
\end{equation}
where $M_{pl}$ ($≡ℏc/G$) denotes the Planck mass.
\begin{thebibliography}{9}
\bibitem{cqgab7bbabib1}%{
Aasi J et al, LIGO Scientific and VIRGO Collaborations (2014)
Constraints on cosmic strings from the LIGO-Virgo
gravitational-wave detectors. \textit{Phys. Rev. Lett.}
%\textcolor{blue}{\textbf{112}}}
\bibitem{cqgab7bbabib2}%{
Abbott B P et al, LIGO and Virgo Collaborations (2016)
Astrophysical implications of the binary black hole merger
GW150914. \textit{Astrophys. J. Lett.}
%\textcolor{blue}{\textbf{818}}}
\end{thebibliography}
\end{document}
