Structure of neutron star in Rastall gravity
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ORIGINAL ARTICLE
Structure of neutron star in Rastall gravity Ping Xi1
· Qian Hu1 · Gui-nan Zhuang1 · Xin-zhou Li1
Received: 24 June 2020 / Accepted: 1 October 2020 © Springer Nature B.V. 2020
Abstract Using the AV18 equation of state, we numerically calculate the structure of a neutron star in Rastall gravity. The results show that the parameter λ originated from Rastall gravity has a great effect on the mass and the radius of a neutron star. When λ = 1, the Rastall equations of motion can be reduced to those in the general relativity. In terms of the stability condition for the Rastall equation of hydrostatic equilibrium, λ can be divided into two regions: [1, +∞) and (−∞, −1). In these two regions, the maximum mass and radius of a star increase with λ increasing. As λ is large enough in the range of λ 1, the maximum mass and radius tend towards 7.43M and 35.65 km. While λ is small enough in the range of λ < −1, the maximum mass and radius are approximately 7.45M and 35.55 km. It is interesting that the upper maximum mass is 9.76M when λ tends to −1 and the lower maximum mass is 1.65M as λ = 1. Furthermore, when λ ≈ 1.16, there exist two neutron stars with the equal maximum mass, 1.92M , and different radii, 13.28 km and 22.85 km. Keywords Gravitation · The structure of neutron star · Equation of state
B P. Xi
[email protected] Q. Hu [email protected] G.-n. Zhuang [email protected] X.-z. Li [email protected]
1
Department of Physics, Division of Mathematical and Theoretical Physics, Shanghai Normal University, 100 Guilin Road, Shanghai, China
1 Introduction In 1972, Peter Rastall (Rastall (1972, 1976)) proposed a generalized gravity theory of the general relativity (GR), called Rastall gravity. In this theory, the covariant divergence of the energy-momentum tensor is in proportion to the derivative of the Ricci scalar, T μυ ;μ = αR υ (α is an undetermined constant.), which violates the fundamental assumption of GR, the usual conservation law. Without loss of generality, 1−λ (λ is a constant.) as shown in (Oliveira we adopt α ≡ 16πG et al. (2015)). Thus, the equations of motion in Rastall gravity recover the standard field equations in GR in case of λ = 1 or the empty spacetime. Obviously, Rastall gravity doesn’t satisfy the usual conservation law in the curved space-time. It is different from what Visser claimed in (Visser (2018)). In 2019, Moraes and Santos (Mota et al. (2019)) proposed a possible Lagrangian formalism for Rastall gravity based on f (R, T ) gravity (Harko et al. (2011)) and f (R, Lm ) gravity (Harko and Lobo (2010, 2014)), two gravity theories with non-conservation of the energy-momentum tensor. Lately, it is proved that there exists a wormhole throat with normal matter in Rastall gravity (Lobo et al. (2020)). As shown in (Darabi et al. (2018)), Rastall gravity is an “open” theory comparing to GR. Moreover, it is supported by observations for the Universe age, the Hubble parameter, the mass distribution for early-type galaxies and so on (Al-Rawaf and Taha (1996); Li et al. (2019)
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