Prospects for constraining the Yukawa gravity with pulsars around Sagittarius A*

The discovery of radio pulsars (PSRs) around the supermassive black hole (SMBH) in our Galactic Center (GC), Sagittarius A* (Sgr A*), will have significant implications for tests gravity. In this paper, we predict restrictions on parameters Yukawa gravity by timing a pulsar Sgr with variety orbital parameters. Based realistic accuracy times arrival (TOAs), $\sigma_{\rm TOA}=100\,\mu{\rm s}$, and using number 960 TOAs 20-yr observation, numerical simulations show that PSR-SMBH system improve current when range interaction varies between $10^{1}$-$10^{4}\,{\rm AU}$, it can limit graviton mass to be $m_g \lesssim 10^{-24}\,{\rm eV}/c^2$.