We study the black hole’s shadow for Schwarzschild–de Sitter and Kerr–de Sitter metrics with the contribution of the cosmological constant \(\varLambda \). Based on the reported parameters of the M87* black hole shadow, we obtain constraints for the \(\varLambda \) and show the agreement with the cosmological data. It is shown that the coupling of the \(\varLambda \)-term with the spin parameter reveals peculiarities for the photon spheres and hence for the shadows. Within the parametrized post-Newtonian formalism, the constraint for the corresponding \(\varLambda \)-determined parameter is obtained.

中文翻译：

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黑洞阴影可探测重力变化

我们利用宇宙学常数\（\ varLambda \）的贡献，研究Schwarzschild-de Sitter和Kerr-de Sitter度量的黑洞阴影。基于M87 *黑洞阴影的报告参数，我们获得了\（\ varLambda \）的约束条件，并显示出与宇宙学数据的一致性。结果表明，\（\ varLambda \）项与自旋参数的耦合揭示了光子球体以及阴影的特殊性。在参数化的后牛顿形式主义中，获得了对应的\（\ varLambda \）确定的参数的约束。