Constraining <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi mathvariant="script">L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mi mathvariant="script">T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity with millisecond pulsar observations
Abstract
Pulsars, with their extreme densities and precise measurements, offer an exceptional probe of matter under intense gravity. We examined compact star structures within the extended f ( R , L m , T ) gravity framework, incorporating the Ricci scalar, matter Lagrangian, and energy-momentum trace. Introducing coupling constants λ 1 and λ 2 enabled a realistic description beyond general relativity. Using the Durgapal-Bannerji-type metric, we derived modified field and TOV equations, obtaining expressions for energy density and anisotropic pressures. With the transformation e B ( r ) = Φ 2 ( r ) and a chosen anisotropy function Δ( r ), regular stellar models were integrated and matched smoothly to the exterior Schwarzschild-de Sitter spacetime. All physical conditions are satisfied: density and pressures are positive and finite; Δ( r ) > 0 implies an outward-directed force; sound speeds remain subluminal; and the adiabatic index Γ > 4/3 ensures dynamical stability. The generalized TOV equation confirms equilibrium among gravitational, hydrostatic, anisotropic, and curvature-matter coupling forces. The M − R relations exhibit clear trends. For λ 1 = − 4 , λ 2 = 0.4 : PSR J2215+5135 (2.28, M ⊙ ) has R = 13 . 05 − 0.20 + 0.13 km (GR: 12.33 km); PSR J0740+6620 (2.08, M ⊙ ): 12.68 → 13.32 km; PSR J0348+0432 (2.01, M ⊙ ): 12.76 → 13.39 km; PSR J0030+0451 (1.44, M ⊙ ): 13.19 → 13.77 km. Positive λ 1 compresses stars ( R = 11 . 26 + 0.33 km for λ 1 = 5 ) , while λ 1 = − 5 expands to 13 . 07 − 0.20 + 0.14 km. At λ 1 = 3 , varying λ 2 shifts R from 12 . 32 − 0.29 + 0.18 km ( λ 2 = − 5 ) to 11 . 23 + 0.35 km ( λ 2 = 5 ) . Overall, including L m or T slightly enlarges radii, showing that tuning λ 1 , λ 2 precisely controls compactness and maximum mass—consistent with observations and testable by future data.