Constraints on charged symmergent black hole from shadow and lensing

Abstract In this paper, we report on exact charged black hole solutions in symmergent gravity with Maxwell field. Symmergent gravity induces the gravitational constant G , quadratic curvature coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> , and the vacuum energy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> can be expressed in terms of G and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> . We parametrize deviation from this limit by a parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>α</mml:mi> <mml:mo stretchy="false">ˆ</mml:mo> </mml:mover> </mml:mrow> </mml:math> such that the black hole spacetime is de Sitter (dS) for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>α</mml:mi> <mml:mo stretchy="false">ˆ</mml:mo> </mml:mover> </mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> and anti-de Sitter (AdS) for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>α</mml:mi> <mml:mo stretchy="false">ˆ</mml:mo> </mml:mover> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In our analysis, we study horizon formation, shadow cast and gravitational lensing as functions of the black hole charge, and find that there is an upper bound on the charge. At relatively low values of charge, applicable to astronomical black holes, we determine constraints on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>α</mml:mi> <mml:mo stretchy="false">ˆ</mml:mo> </mml:mover> </mml:mrow> </mml:math> using the Event Horizon Telescope (EHT) data from Sgr. A* and M87*. We apply these constraints to reveal how the shadow radius behaves as the observer distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> </mml:msub> </mml:math> varies. It is revealed that black hole charge directly influences the shadow silhouette, but the symmergent parameters have a tenuous effect. We also explored the weak field regime by using the Gauss–Bonnet theorem to study the weak deflection angle caused by the M87* black hole. We have found that impact parameters comparable to the actual distance D = 16.8 Mpc show the potential detectability of such an angle through advanced astronomical telescopes. Overall, our results provide new insights into the behavior of charged black holes in the context of symmergent gravity and offer a new way to test these theories against observational data.

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