Shadow and strong gravitational lensing of new wormhole solutions supported by embedding Class-I condition

Abstract This study deals with the new class of embedded wormhole solutions in the background of general relativity. Two newly calculated wormhole solutions satisfy all the required properties. The embedded diagrams for both calculated wormhole solutions are provided. All the energy conditions are discussed through their validity regions for the different ranges of involved parameters. In maximum regions, all energy conditions are violated. We investigate the shadow and strong gravitational lensing by the wormhole throat for the two new wormhole models, namely Model-I and Model-II. The present paper considers the wormhole throat to act as a photon sphere. We first derive null geodesics using the Hamilton-Jacobi separation method to investigate the shadow and strong gravitational lensing caused by the wormhole throat. We then numerically obtain the radius of wormhole shadow, strong deflection angle, and various lensing observables by taking the example of supermassive black M87* and Sgr A* in the context of both Model-I and Model-II. Keeping all other parameters fixed, it is observed that the parameters $$\zeta _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $$\zeta _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> for Model-I; and $$\chi _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $$\chi _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> for Model-II have significant effects on the wormhole shadow and strong gravitational lensing phenomena. Our conclusion is that it is possible to detect relativistic images, such as Einstein rings, produced by wormholes with throat radii of $$r_{th}=3M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mi>th</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> . The stability analysis via Tolman–Oppenheimer–Volkov equation is included for both wormhole solutions. Additionally, current technology enables us to test hypotheses related to astrophysical wormholes.