https://doi.org/10.1140/epjc/s10052-021-09273-8
Regular Article - Theoretical Physics
Anisotropic compact stars in f(R) gravity
1
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, 11837, El Sherouk City, Cairo, Egypt
2
Egyptian Relativity Group (ERG), Cairo University, 12613, Giza, Egypt
3
Dipartimento di Fisica “E. Pancini“, Universitá di Napoli “Federico II”, Complesso Universitario di Monte Sant’ Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
4
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
5
Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138, Naples, Italy
6
Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
Received:
21
March
2021
Accepted:
19
May
2021
Published online:
31
May
2021
We derive a new interior solution for stellar compact objects in 
gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of . After, the time component of the metric potential and the form of 
function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter C which has to be 
for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman–Oppenheimer–Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.
© The Author(s) 2021
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