Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A*
Misba Afrin, Sunny Vagnozzi, Sushant G. Ghosh
Abstract
Abstract The Event Horizon Telescope (EHT) collaboration’s image of the compact object at the Galactic center is the first direct evidence of the supermassive black hole (BH) Sgr A*. The shadow of Sgr A* has an angular diameter d sh = 48.7 ± 7 μ as with fractional deviation from the Schwarzschild BH shadow diameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.08</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.04</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (for the VLTI and Keck mass-to-distance ratios). Sgr A*'s shadow size is within 10% of Kerr predictions, equipping us with yet another tool to analyze gravity in the strong-field regime, including testing loop quantum gravity (LQG). We use Sgr A*'s shadow to constrain the metrics of two well-motivated LQG-inspired rotating BH (LIRBH) models characterized by an additional deviation parameter L q , which recover the Kerr spacetime in the absence of quantum effects ( L q → 0). When increasing the quantum effects through L q , the shadow size increases monotonically, while the shape gets more distorted, allowing us to constrain the fundamental parameter L q . We use the astrophysical observables shadow area A and oblateness D to estimate the BH parameters. It may be useful in extracting additional information about LIRBHs. While the EHT observational results completely rule out the wormhole region in LIRBH-2, a substantial parameter region of the generic BHs in both models agrees with the EHT results. We find that the upper bounds on L q obtained from the shadow of Sgr A*— L q ≲ 0.0423 and L q ≲ 0.0821 for the two LIRBHs, respectively—are more stringent than those obtained from the EHT image of M87*.