Strong gravitational lensing, quasi-periodic oscillations and constraints from EHT observations for quantum-improved charged black hole
Abstract
Abstract We investigate strong gravitational lensing by quantum-improved charged black holes characterized by an additional parameter denoted as $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> , in addition to the mass M and charge Q . Our findings reveal that when both the parameters Q /2 M and $$\omega /4M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> increase simultaneously, various astrophysical consequences, such as the deflection angle $$\alpha _D(u)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and angular image separation increase. Concurrently, the angular position $$\theta _{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> , relative magnification $$r_{mag}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mi>mag</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and the time delay $$\Delta T_{2,1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> between the first and second relativistic images also decrease with the growing values of the parameters Q /2 M and $$\omega /4M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> . It is also observed that the Einstein ring $$\theta _1^E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mn>1</mml:mn> <mml:mi>E</mml:mi> </mml:msubsup> </mml:math> for the quantum-improved charged black hole is more significant than those for Schwarzschild, quantum-improved Schwarzschild, and Reisner–Nordström black holes. As with supermassive black holes such as $$M87^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:msup> <mml:mn>87</mml:mn> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> and $$SgrA^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>g</mml:mi> <mml:mi>r</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> , it is observed that to be a viable astrophysical black hole, the EHT results constrain the parameter space ( $$\omega /4M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , Q /2 M ). Remarkably, the EHT results for $$SgrA^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>g</mml:mi> <mml:mi>r</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> impose more stringent limits on the parameter space of quantum-improved charged black holes compared to those established by the EHT results for $$M87^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:msup> <mml:mn>87</mml:mn> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> . We investigate the radial profiles of orbital and radial harmonic oscillation frequencies as a function of the dimensionless coupling constants and black hole mass. The main characteristics of test particle quasi-periodic oscillations close to stable circular orbits in the black hole equatorial plane are also examined. We study the positioning of resonant radii in the background of quantum-improved charged black holes for high-frequency quasi-periodic oscillations models: warped disc (WD) models, relativistic precession (RP) and its types, and epicyclic resonance (ER) and its variants.