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