Shadows of rotating black holes in effective quantum gravity
Zhenglong Ban, J.K. Chen, Jinsong Yang
Abstract
Abstract Recently, two new spherically symmetric black hole models with covariance have been proposed in effective quantum gravity. Based on these models, we use the modified Newman–Janis algorithm to generate two rotating quantum-corrected black hole solutions, characterized by three parameters, the mass M , the spin a , and the quantum parameter $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> . To understand the effects of the quantum parameter $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> on these two rotating black holes, we investigate in detail the horizons and static limit surfaces. By constraining the possible range of the parameters, we study the shadows cast by these rotating black holes. The results indicate that for both rotating BHs, the parameter $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> mainly affects the shadow size in the non-extremal case, while it deforms the shadow shape by arising a cuspy edge in the near-extremal case. Through the presence of the cuspy edge in the shadow, we further discuss how to differentiate it from the shadows of other rotating quantum-corrected black holes. Utilizing the Event Horizon Telescope shadow observational results for M87* and Sgr A*, we set the black hole inclination angles to $$17^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>17</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> , $$50^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>50</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> , and $$90^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>90</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> and subsequently calculate the angular diameter of the black hole shadows. Our analysis indicates that in the constrained parameter space for M87* and Sgr A*, the common parameter constraints obtained from the RBH-I are $$0.569246M< \zeta < 0.924954M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.569246</mml:mn> <mml:mi>M</mml:mi> <mml:mo><</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.924954</mml:mn> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> . In contrast, the constraints from the RBH-II are $$0< \zeta < 3.018M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo><</mml:mo> <mml:mn>3.018</mml:mn> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> .