A comprehensive study of Bardeen stars with conformal motion in $$f({\mathcal {G}})$$ gravity

Abstract In this manuscript, we use the conformal killing vectors to solve the Einstein–Maxwell field equations in the background of modified $$f({\mathcal {G}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. We consider the observational data for four different stars namely $$PSR~J1614-2230$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mspace/> <mml:mi>J</mml:mi> <mml:mn>1614</mml:mn> <mml:mo>-</mml:mo> <mml:mn>2230</mml:mn> </mml:mrow> </mml:math> , $$PSR ~J1930+327$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mspace/> <mml:mi>J</mml:mi> <mml:mn>1930</mml:mn> <mml:mo>+</mml:mo> <mml:mn>327</mml:mn> </mml:mrow> </mml:math> , $$Cen~X-3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>e</mml:mi> <mml:mi>n</mml:mi> <mml:mspace/> <mml:mi>X</mml:mi> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and $$Vela~X-1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mi>e</mml:mi> <mml:mi>l</mml:mi> <mml:mi>a</mml:mi> <mml:mspace/> <mml:mi>X</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> respectively. By using the data, we derive the physical parameters from the matching criteria using conformal killing vectors and the exterior Bardeen geometry. Furthermore, several physical properties of compact stellar structures are examined in order to achieve the physical validity and stability for considered models. The graphical analysis including energy density, pressure components, equation of state parameters, and energy conditions are examined. Moreover, the equilibrium conditions through Tolman–Oppenheimer–Volkoff equation and stability criteria through adiabatic index for the charged stellar structure study are investigated. It is worth noting that all of these compact objects are physically viable and stable under conformal motion in context of Bardeen geometry for two different models of $$f({\mathcal {G}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory of gravity. Conclusively, the results show that f ( G ) gravity with Bardeen model may provide more massive stellar objects as compared to general relativity.

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