Signatures of the accelerating black holes with a cosmological constant from the Sgr [formula omitted] and [formula omitted] shadow prospects

Abstract

Recently, the Event Horizon Telescope (EHT) achieved the realization of an image of the supermassive black hole Sgr A⋆ showing an angular shadow diameter D=48.7±7μas and the fractional deviation δ=−0.08−0.09+0.09(VLTI),−0.04−0.10+0.09(Keck), alongside the earlier image of M87⋆ with angular diameter D=42±3μas, deviation δ=−0.01−0.17+0.17 and deviations from circularity estimated to be ΔC≲10%. In addition, the shadow radii are assessed within the ranges 3.38≤rsM≤6.91 for M87⋆ and 3.85≤rsM≤5.72 as well as 3.95≤rsM≤5.92 for Sgr A⋆ using the Very Large Telescope Interferometer (VLTI) and Keck observatories, respectively. These values are provided with 1-σ and 2-σ measurements. Such realizations can unveil a better comprehension of gravitational physics at the horizon scale. In this paper, we use the EHT observational results for M87⋆ and Sgr A⋆ to elaborate the constraints on parameters of accelerating black holes with a cosmological constant. Concretely, we utilize the mass and distance of both black holes to derive the observables associated with the accelerating black hole shadow.First, we compare our findings with observed quantities such as angular diameter, circularity, shadow radius, and the fractional deviation from the M87⋆ data. This comparison reveals constraints within the acceleration parameter and the cosmological constant. In fact, the acceleration parameter A is found to be in the interval [0,0.475−0.0125+0.0125], the cosmological constant spans the range of Λ∈[−14.5801−1.1051×10−6+1.1051×10−6,(1.0086×10−6)−1.5396×10−4+9.2121×10−5]. Then by considering the Sgr A⋆ data, the acceleration scheme persists with the same interval range, while, the cosmological constant shifts very slightly to the following domain [−14.7266−1.1051×10−6+1.1051×10−6,(4.6200×10−5)−1.5888×10−4+6.7890×10−5] for the VLTI observatory. Moreover, within the Keck measurements, one can find Λ∈[−14.7266−1.1051×10−6+1.1051×10−6,(2.4149×10−5)−1.5094×10−4+7.2836×10−5]. Besides, for the others parameters, both black holes reveal the range of the spin parameter a in [0,1] and electrical/magnetic charges are {e,g}∈[0,0.09].Further, only the cosmological constant intervals are altered by rsM measurements, precisely within the M87⋆ data, the upper bound shifts to (Λ1-σ=1.1361×10−4,Λ2-σ=1.7822×10−4), the VLTI gives (Λ1-σ=1.5457×10−4,Λ2-σ=1.8208×10−4), while the Keck results uncover Λ2-σ=1.8015×10−4.Lastly, one cannot rule out the possibility of the negative values for the cosmological constant on the emergence of accelerated black hole solutions within the context of minimal gauged supergravity. This intriguing possibility raises the prospect of such solutions being plausible candidates for astrophysical black holes.