Shadows and optical appearance of quantum-corrected black holes illuminated by static thin accretions

Abstract Recently, two new quantum-corrected black hole models satisfying covariance have been proposed within the framework of effective quantum gravity. In this paper, we study how the quantum parameter $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> affects the optical properties of two quantum-corrected black hole models. We first analyze the photon sphere, critical impact parameter, and innermost stable circular orbit as $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> varies, and constrain $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> using Event Horizon Telescope data. Additionally, by employing the ray-tracing method to study photon trajectories near the two quantum-corrected black holes, we find that $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> can reduce the range of impact parameters corresponding to the photon ring and lensed ring. We then examine the optical appearance of these black holes with thin accretion disks, showing $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> significantly brightens the first model’s image but has little effect on the second. Meanwhile, we demonstrate the contributions of the transfer functions to the observed intensity of direct and lensed ring in the observer’s field of view, which has rarely been separately illustrated in previous studies. Finally, we study the optical appearance of both quantum-corrected black holes under a static spherical accretion model, with results consistent with the above. Therefore, we conclude that the second quantum-corrected black hole is almost indistinguishable from the Schwarzschild black hole, while the first quantum-corrected black hole can be distinguished from the Schwarzschild black hole through its optical appearance.