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)= Re^ζ R, where ζ is a dimensional quantity in squared length units [L²]. 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 { SAX J1748.9-2021}, derived from bursting X-ray binaries located within globular clusters, we determine that ζ is approximately equal to ± 5 km². In particular, the model can create a stable configuration for { SAX J1748.9-2021}, encompassing its geometric and physical characteristics. In f( R) gravity, the Krori-Barua approach links pᵣ and pₜ, which represent the components of the pressures, to (ρ), representing the density, semi-analytically. These relations are described as pᵣ≈ vᵣ² (ρ-ρI) and pₜ≈ vₜ² (ρ-ρII). Here, the expression vᵣ and vₜ represent the radial and tangential sound speeds, respectively. Meanwhile, ρI pertains to the surface density and ρII is derived using the parameters of the model. Notably, within the frame 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 with f( R) with positive ζ, where C has the potential to reach the limit of the black hole asymptotically. The predictions of such model suggest a central energy density which largely exceeds the saturation of nuclear density, which has the value ρnuc = 3× 10¹⁴ g/cm³. Also, the density at the surface ρI surpasses ρnuc.