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Parameter constraints from shadows of Kerr–Newman-dS black holes with cloud strings and quintessence

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Abstract

Shadows of the Kerr–Newman-dS black hole surrounded by quintessence and a cloud of strings are investigated. For a spherically symmetric nonrotating black hole, its shadow is circular and its size is independent of an observation angle and a plane on which a circular photon orbit exists. The shadow sizes are significantly influenced by the parameters involving the cloud of strings, quintessence parameter, magnitude of quintessential state parameter, and cosmological constant. The black hole shadows increase with the cloud of strings and negative quintessential state parameter increasing or the quintessence parameter and cosmological constant decreasing. When the black hole is spinning and axially symmetric, the black hole shadow is dependent on the observation angle and the black hole spin. The effects of the parameters excluding the spin parameter and the observation angle on the sizes of black hole shadows in the rotating case are similar to those in the nonrotating case. The black hole shadows decrease as the black hole spins increase. When the observation angle in the range of 0 and \(\pi /2\) is large, the black hole shadow is deformed like the D shape for a high spin, but is close to a circle for a low spin. When the observation angle is small, the black hole shadow seems to be a circle regardless of the high or low spin case. Based on the Event Horizon Telescope observations of M87*, the constraint of the curvature radius is used to constrain these parameters. For slowly rotating black holes, the allowed regions of the parameters including the cosmological constant are given.

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Notes

  1. Strictly speaking, the generating function for the Hamiltonian (12) with \(E\rightarrow -p_t\) and \(L\rightarrow p_\phi \) should be \(S=-{\mathcal {H}}\lambda -Et+L\phi +S_{r}(r)+S_{\theta }(\theta )\), where \({\mathcal {H}}\) is the third constant of motion (12). The Hamilton–Jacobi equation is obtained by substituting \(p_t=\frac{\partial S}{\partial t}\), \(p_r=\frac{\partial S}{\partial r}\), \(p_\theta =\frac{\partial S}{\partial \theta }\) and \(p_\phi =\frac{\partial S}{\partial \phi }\) into the equation \(\frac{\partial S}{\partial \lambda }+\frac{1}{2}g^{\mu \nu }p_\mu p_\nu =0\), where \(g^{\mu \nu }\) denotes the contravariant tensor of the metric (1).

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Acknowledgements

The authors are very grateful to referees for useful suggestions. This research has been supported by the National Natural Science Foundation of China (Grant No. 11973020), and the Natural Science Foundation of Guangxi (Grant No. 2019GXNSFDA245019).

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  1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Wenfu Cao, Wenfang Liu & Xin Wu

  2. Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Wenfu Cao & Xin Wu

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Cao, W., Liu, W. & Wu, X. Parameter constraints from shadows of Kerr–Newman-dS black holes with cloud strings and quintessence. Gen Relativ Gravit 55, 120 (2023). https://doi.org/10.1007/s10714-023-03169-6

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