Estimating the Cosmological Constant from Shadows of Kerr–de Sitter Black Holes

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.

Testing Horndeski Gravity from EHT Observational Results for Rotating Black Holes

“…The black hole shadow is the projection of the photon sphere as observed at spatial infinity. The shadow shape depends on the black hole parameters, i.e., the spin and other hairs (Johannsen 2016;Afrin et al 2021;Afrin & Ghosh 2022), alongside the observation angle θ 0 relative to the spin axis, with the overall size scaled by the black hole mass M (Akiyama et al 2019a). Thus, at radial infinity and an inclination angle θ 0 , an observer can visualize the black hole shadow outlined by the celestial coordinates defined by Bardeen (1973), Frolov & Zelnikov (2011), and :…”

“…While the first-order correction to the circular shadow shape occurs due to the spin in Kerr spacetime, in MoGs the distortion for a given spin may arise due to other hairs (Cunha et al 2015(Cunha et al , 2019Afrin et al 2021;Ghosh et al 2021;Khodadi et al 2021)-this prompts the use of shadow observables for the determination of black hole parameters (Hioki & Maeda 2009;Afrin et al 2021;Afrin & Ghosh 2022). It has been shown in multiple studies that observables like the shadow radius R s and distortion δ s (Hioki & Maeda 2009) demand some specific symmetry in the shadow shape, and thus they may not be efficient in some MoGs (Tsukamoto et al 2014;Abdujabbarov et al 2015;).…”

Astrophysical consequences of dark matter for photon orbits and shadows of supermassive black holes

“…The separability constant K is related to a hidden symmetry of the Petrov type D metric (7), the Carter constant 3,9], where K determines the latitudinal motion of the photon. The geodesic worldline of the rotating PFDM BHs can be completely determined by the first integrals of motion, E, L and K. The only bound photon trajectories are those for which r = constant [3,9,28,52,53] and further, all photons, regardless of their energy, follow the same trajectories [9,10]. One can reduce the degrees of freedom by introducing two dimensionless parameters…”

Testing Rotating Regular Metrics with EHT Results of Sgr A*

“…Therefore, the photon ring structure is an essential tool to test the theories of gravity through the astrophysical black holesʼ observational predictions. Applications of shadow in understanding the nearhorizon geometry have aroused a flurry of activities analyzing, both analytically and numerically, shadows for black holes in GR (de Vries 2000; Falcke et al 2000;Shen et al 2005;Hioki & Maeda 2009;Yumoto et al 2012;Atamurotov et al 2013;Abdujabbarov et al 2015;Cunha & Herdeiro 2018;Afrin & Ghosh 2022a) and modified theories of gravity (MTGs; Amarilla et al 2010;Amarilla & Eiroa 2012Papnoi et al 2014;Amir et al 2018;Mizuno et al 2018;Vagnozzi & Visinelli 2019;Allahyari et al 2020;Afrin & Ghosh 2022b;Afrin et al 2021;Ghosh et al 2021;Vagnozzi et al 2022), and found the shadows of black holes in MTGs to be smaller and more distorted when compared with the Kerr black hole shadow. Also, the shadow of rotating regular spacetimes, which may be realized when GR is coupled to nonlinear electrodynamics, has been widely investigated to extract limits on the black hole magnetic charge Kumar et al 2019Allahyari et al 2020;, 2021.…”