Shadows of quintessence black holes: spherical accretion, photon trajectories, and geodesic observers

The presence of a quintessence-like field can influence the black hole shadow through three primary mechanisms: the dynamics of accretion flows, the trajectories of photons, and the motion of observers. Unlike standard shadow analyses that assume a static observer at spatial infinity, the non-asymptotically flat nature of quintessence-corrected spacetimes motivates the consideration of freely falling (geodesic) observers. Using a perturbative approach, we derive analytical expressions for the event-horizon location, photon-sphere radius, innermost stable circular orbit, and critical impact parameter. We compute the observed intensity profiles for both static and infalling spherical accretion flows. We find that, although the photon-sphere radius and the critical impact parameter are invariant properties of the spacetime, the apparent angular size of the shadow depends sensitively on the observer's motion and location. Freely infalling observers systematically measure smaller angular radii than static observers at the same radius, whereas freely outgoing observers measure larger ones, in agreement with relativistic aberration. In contrast to the Schwarzschild case, the impact parameter alone is insufficient to characterize the observed angular structure in non-asymptotically flat spacetimes. Applying our results to the Event Horizon Telescope observation of M87$^\ast$, we show that more negative equations of state lead to stronger constraints on the quintessence parameter, largely independent of the observer prescription. Our analysis highlights the importance of carefully specifying the observer in shadow studies of non-asymptotically flat black-hole spacetimes.