Constraining $f({\cal R})$ gravity by Pulsar {\textit SAX J1748.9-2021} observations
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2024
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| author | Nashed, G. G. L. Capozziello, Salvatore |
| author_facet | Nashed, G. G. L. Capozziello, Salvatore |
| contents | We discuss spherically symmetric dynamical systems in the framework of a general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{ζ{\cal R}}$, 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 {\textit SAX J1748.9-2021}, derived from bursting X-ray binaries located within globular clusters, we determine that $ζ$ is approximately equal to $\pm 5$ km$^2$. In particular, the model can create a stable configuration for {\textit SAX J1748.9-2021}, encompassing its geometric and physical characteristics. In $f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which represent the components of the pressures, to ($ρ$), representing the density, semi-analytically. These relations are described as $p_r\approx v_r^2 (ρ-ρ_{I})$ and $p_t\approx v_t^2 (ρ-ρ_{II})$. Here, the expression $v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively. Meanwhile, $ρ_I$ pertains to the surface density and $ρ_{II}$ is derived using the parameters of the model. Notably, within the frame of $f({\cal R})$ 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 $f({\cal R})$ 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 $ρ_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the surface $ρ_I$ surpasses $ρ_{\text{nuc}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_09590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraining $f({\cal R})$ gravity by Pulsar {\textit SAX J1748.9-2021} observations Nashed, G. G. L. Capozziello, Salvatore General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory We discuss spherically symmetric dynamical systems in the framework of a general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{ζ{\cal R}}$, 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 {\textit SAX J1748.9-2021}, derived from bursting X-ray binaries located within globular clusters, we determine that $ζ$ is approximately equal to $\pm 5$ km$^2$. In particular, the model can create a stable configuration for {\textit SAX J1748.9-2021}, encompassing its geometric and physical characteristics. In $f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which represent the components of the pressures, to ($ρ$), representing the density, semi-analytically. These relations are described as $p_r\approx v_r^2 (ρ-ρ_{I})$ and $p_t\approx v_t^2 (ρ-ρ_{II})$. Here, the expression $v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively. Meanwhile, $ρ_I$ pertains to the surface density and $ρ_{II}$ is derived using the parameters of the model. Notably, within the frame of $f({\cal R})$ 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 $f({\cal R})$ 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 $ρ_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the surface $ρ_I$ surpasses $ρ_{\text{nuc}}$. |
| title | Constraining $f({\cal R})$ gravity by Pulsar {\textit SAX J1748.9-2021} observations |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.09590 |