Signatures of the accelerating black holes with a cosmological constant from the $\textrm{Sgr~A}^\star$ and $\textrm{M87}^\star$ shadow prospects

Recently, the Event Horizon Telescope (EHT) achieved the realization of an image of the supermassive black hole $\textrm{Sgr~A}^\star$ showing an angular shadow diameter $\mathcal{D}= 48.7 \pm 7\mu as$ and the fractional deviation $\mathbf{\delta} = -0.08^{+0.09}_{-0.09}~\text{(VLTI)},-0.04^{+0.09}_{-0.10}~\text{(Keck)}$, alongside the earlier image of $\textrm{M87}^\star$ with angular diameter $ \mathcal{D}=42 \pm 3 \mu as$, deviation $\mathbf{\delta}=-0.01^{+0.17}_{-0.17}$ and deviations from circularity estimated to be $\Delta \mathcal{C}\lesssim 10\%$. In addition, the shadow radii are assessed within the ranges $3.38 \le \frac{r_{\text{s}}}{M} \le 6.91$ for $\textrm{M87}^\star$ and $3.85 \le \frac{r_{\text{s}}}{M} \le 5.72$ as well as $3.95 \le \frac{r_{\text{s}}}{M} \le 5.92$ for $\textrm{Sgr~A}^\star$ using the Very Large Telescope Interferometer (VLTI) and Keck observatories, respectively. These values are provided with $1$-$\sigma$ and $2$-$\sigma$ 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 $\textrm{M87}^\star$ and $\textrm{Sgr~A}^\star$ 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 $\textrm{M87}^\star$ data. This comparison reveals constraints within the acceleration parameter and the cosmological constant... 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...