Abstract
The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable.
Highlights
Because of the black hole’s defining property at the event horizon and the surrounding photon region, it casts a dark region over the observer’s celestial sky, which is known as a shadow [1,2], which is an optical appearance cast by a black hole when it is in front of a distant luminous source
Considering the M87* as a new Kerr–de Sitter black hole, and using the mass M = 6.5 × 109 M and distance d = 16.8 Mpc as reported by the Event Horizon Telescope collaboration (EHT) [85,86,87], we estimate the value of the cosmological constant Λ = 1.046 × 10−52m−2, 1.368 × 10−52m−2 obtained, respectively, for (Rs, δs)= (4.985 × 1013m, 0.5) and (A, D)= (7.298 × 1027m2, 0.9812), which agree with the present estimated value of Λ = 1.11 × 10−52m−2 [88,89,90]
We explored the various spacetime properties in the strong-field regime of the new Kerr–de Sitter black holes and found the curvature’s warping effect
Summary
Because of the black hole’s defining property at the event horizon and the surrounding photon region, it casts a dark region over the observer’s celestial sky, which is known as a shadow [1,2], which is an optical appearance cast by a black hole when it is in front of a distant luminous source. Most investigations have been largely based on ray tracing in the respective spacetimes, rather than on analytical studies of the geodesic equation under the assumption that the observer is at infinity This prescription does not work when the black holes are no longer asymptotically flat but instead when it is asymptotically dS/AdS, and a cosmological horizon encompassing the event horizon is present [39,40,41,42,43,44,45]. To the Kerr black hole, the Kerr–de Sitter black holes have killing vectors δtμ and δφμ corresponding to cyclic coordinates t and φ
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