https://doi.org/10.1140/epjc/s10052-021-09321-3
Regular Article - Theoretical Physics
Anisotropic compact stars in higher-order curvature theory
1
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, 11837, El Sherouk City, Cairo, Egypt
2
Institut de Ciències de l’Espai (ICE-CSIC/IEEC), Campus UAB, c. Can Magrans s/n, 08193, Barcelona, Spain
3
Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
4
Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloníki, Greece
5
Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
Received:
30
April
2021
Accepted:
5
June
2021
Published online:
21
June
2021
In this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the 
type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function 
, which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star 
, which has an estimated mass and radius 
). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
