Constraining f(R) gravity by Pulsar SAX J1748.9-2021 observations

We discuss spherically symmetric dynamical systems in the framework of a general model of f ( R ) gravity, i.e. f ( R ) = R e ζ R , where ζ is a dimensional quantity in squared length units [L 2 ]. We initially assume that the internal structure of such systems is governed by the Krori–Barua ansatz, alongside the presence of fluid anisotropy. By employing astrophysical observations obtained from the pulsar S AX J1748.9-2021, derived from bursting X-ray binaries located within globular clusters, we determine that ζ is approximately equal to ± 5 km 2 . In particular, the model is capable of producing stable configurations for S AX J1748.9-2021, encompassing both its geometric and physical characteristics. We show that, within the framework of f ( R ) gravity, the Krori–Barua ansatz establishes semi-analytical connections between the radial ( p r ) and tangential ( p t ) pressures, and the density ( ρ ). These relations are described as p r ≈ v r 2 ( ρ - ρ I ) and p t ≈ v t 2 ( ρ - ρ II ) . In this context, v r and v t denote the sound speeds in the radial and tangential directions, respectively. Meanwhile, ρ I pertains to the surface density, and ρ II is derived from the model parameters. These connections are consistent with the equations of state derived from the best-fit solutions identified in the ongoing investigation. Notably, within the framework of f ( R ) gravity where ζ is negative, the maximum compactness, denoted as C , is inherently limited to values that do not exceed the Buchdahl limit. This contrasts with general relativity or f ( R ) gravity with ζ positive, where the compactness has the potential to asymptotically reach the black hole threshold ( C → 1 ). The model predictions suggest a central density that largely exceeds the saturation nuclear density, which is ρ nuc = 3 × 10 14 g/cm 3 . Also the surface density ρ I surpasses ρ nuc . We obtain a mass-radius diagram, corresponding to the boundary density, which is consistent with other observational data.