Eur. Phys. J. C (2024) 84: 521
https://doi.org/10.1140/epjc/s10052-024-12866-8

Regular Article - Theoretical Physics

Constraining $f(\mathcal{R})$ gravity by Pulsar SAX J1748.9-2021 observations

¹ Centre for Theoretical Physics, The British University, P.O. Box 43, 11837, El Sherouk City, Cairo, Egypt
² Dipartimento di Fisica E. Pancini, Universit’a di Napoli Federico II, Complesso Universitario di Monte Sant Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
³ Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138, Naples, Italy
⁴ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Complesso Universitario di Monte Sant Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy

^b capozziello@na.infn.it

Received: 9 March 2024
Accepted: 30 April 2024
Published online: 24 May 2024

Abstract

We discuss spherically symmetric dynamical systems in the framework of a general model of $f(\mathcal{R})$ gravity, i.e. $f(\mathcal{R})=\mathcal{R}{e}^{\zeta \mathcal{R}}$, where $\zeta$ 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 SAX J1748.9-2021, derived from bursting X-ray binaries located within globular clusters, we determine that $\zeta$ is approximately equal to $\pm 5$ km${}^2$. In particular, the model is capable of producing stable configurations for SAX J1748.9-2021, encompassing both its geometric and physical characteristics. We show that, within the framework of $f(\mathcal{R})$ gravity, the Krori–Barua ansatz establishes semi-analytical connections between the radial ($p_r$) and tangential ($p_t$) pressures, and the density ($\rho$). These relations are described as $p_r\approx v_r^2(\rho -{\rho }_I)$ and $p_t\approx v_t^2(\rho -{\rho }_{\mathit{II}})$. In this context, $v_r$ and $v_t$ denote the sound speeds in the radial and tangential directions, respectively. Meanwhile, ${\rho }_I$ pertains to the surface density, and ${\rho }_{\mathit{II}}$ 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 $f(\mathcal{R})$ gravity where $\zeta$ 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 $f(\mathcal{R})$ gravity with $\zeta$ positive, where the compactness has the potential to asymptotically reach the black hole threshold ($C\to 1$). The model predictions suggest a central density that largely exceeds the saturation nuclear density, which is ${\rho }_{\text{nuc}}=3\times {10}^{14}$ g/cm${}^3$. Also the surface density ${\rho }_I$ surpasses ${\rho }_{\text{nuc}}$. We obtain a mass-radius diagram, corresponding to the boundary density, which is consistent with other observational data.