Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*

Motivated by the first image of a black hole captured by the Event Horizon Telescope (EHT), there has been a surge of research using observations of black hole shadows to test theories of gravity. In this paper, we carry out a study related to the shadow of Kerr black holes surrounded by a cloud of strings in Rastall gravity, which deviates from the Kerr black hole due to the presence of the string parameter $a_0$ and the parameter $\beta$. The horizons, ergospheres, and photon region of the black hole are shown. Moreover, we explore the shadow and observations of the black hole, which are closely linked to the parameters $a_0$ and $\beta$. By treating M87* as a Kerr black hole surrounded by a cloud of strings under Rastall gravity, we constrain the black hole parameters using the EHT observations. For a given $\beta$, the circularity deviation of the black hole obeys $\Delta C\lesssim 0.1$ in all regions. The angular diameter ${\theta }_d=42\pm 3\mu as$ provides the upper bound of parameters $a$ and $a_0$ for fixed $\beta$. The shadow axis ratio satisfies the observation data of EHT ($1<D_x\lesssim 4/3$) in the whole space for a given $\beta$. These results are consistent with the public information from EHT. In other words, candidates for real astrophysical black holes can be Kerr black holes surrounded by a cloud of strings in Rastall gravity.