Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A*

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*.

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