Anisotropic stellar structure and maximum mass in curvature-matter coupled gravity using embedding class one approach

Abstract Inspired by the class one solution of Bhar et al. (Eur Phys J C 77:596, 2017) containing a hypergeometric function, we construct a new exact solution satisfying the Karmarkar condition in $$f({\mathcal {R}},{\mathcal {L}}_m,{\mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -gravity theory. The solution maintains finite metric potentials, density, and pressures, yielding a nonsingular and well-behaved stellar structure. Equilibrium and stability are verified using the Tolman–Oppenheimer–Volkoff equation, cracking approach, Harrison–Zeldovich condition, and the adiabatic index criterion $$\Omega _r &gt; 4/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . Central density and pressure values ( $$\sim 10^{15}\text {g/cm}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>15</mml:mn> </mml:msup> <mml:msup> <mml:mtext>g/cm</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> and $$\sim 10^{34}\text {dyne/cm}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>34</mml:mn> </mml:msup> <mml:msup> <mml:mtext>dyne/cm</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> ) confirm physical plausibility. Mass-radius analysis for high-mass pulsars including PSR J0740+6620, PSR J1810+1744, PSR J1748−2446ao, PSR J2215+5135, and GW190814 matches NICER and gravitational-wave constraints, establishing the anisotropic compact star model as stable, realistic, and observationally consistent whose radii lie within the range of 10.5 $$-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>-</mml:mo> </mml:math> 11.8 km.