An Upper Limit on the Charge of the Black Hole Sgr A* from EHT Observations

Abstract The Event Horizon Telescope (EHT) recently released an image of the supermassive black hole Sgr A* showing an angular shadow diameter d sh = 48.7 ± 7 μ as and Schwarzschild shadow deviation <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:mspace width="0.25em"/> <mml:mo stretchy="false">(</mml:mo> <mml:mi>VLTI</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <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:mspace width="0.50em"/> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Keck</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> using a black hole mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>4.0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.1</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> . The EHT image of Sgr A* is consistent with a Kerr black hole’s expected appearance, and the results directly prove the existence of a supermassive black hole at the center of the Milky Way. Here, we use the EHT observational results for Sgr A* to investigate the constraints on its charge with the aid of Kerr-like black holes, paying attention to three leading rotating models, namely Kerr–Newman, Horndeski, and hairy black holes. Modeling the supermassive black hole Sgr A* as these Kerr-like black holes, we observe that the EHT results for Sgr A* place stricter upper limits on the parameter space of Kerr–Newman and Horndeski black holes than those placed by the EHT results for M87*. A systematic bias analysis reveals that observational results from future EHT experiments will place more precise limits on the charge of the black hole Sgr A*. Thus, the Kerr-like black holes and Kerr black holes are indiscernible in a substantial region of the EHT-constrained parameter space; the claim is substantiated by our bias analysis.

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