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 less than or similar to 0.1 in all regions. The angular diameter theta(d)=42 +/- 3 mu as provides the upper bound of parameters a and a0 for fixed beta. The shadow axis ratio satisfies the observation data of EHT (1<D-x less than or similar to 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.