Gravitational lensing and accretion disk imaging of a Buchdahl dense core

Abstract

In this paper, we investigate the gravitational lensing and accretion disk imaging characteristics of a dense core modeled by the Buchdahl spacetime. By imposing the appropriate energy conditions and ensuring the absence of curvature singularities, we delineate the parameter space in which the dense core mimics key gravitational features of black holes while exhibiting unique deviations. We derive the photon orbital equation and calculate deflection angles, clearly distinguishing between weak- and strong-deflection regimes. Furthermore, we construct a mapping from the illuminated, geometrically thin accretion disk onto the observer's screen -- focusing on the isoradial curves corresponding to a representative source ring. For compactness values below a critical threshold, only a finite number of disk images are formed. In this range, their secondary and higher-order images typically display double-loop structures, with each loop individually capturing the entire source ring. Notably, the highest-order image sometimes appears as a single, crescent-shaped loop that does not enclose the screen's center, implying the existence of a cutoff angle that restricts the imaged portion of the source ring. In contrast, for compactness values above the critical threshold, an infinite sequence of double-loop structures appears -- a behavior closely linked to the presence of a photon sphere. These findings suggest that the lensing signatures of dense cores can distinguish them from black holes, offering new insights for high-resolution observations.

28 pages, 11 figures; v2: references added; v3: matches the published version

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