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Moment of inertia for axisymmetric neutron stars in the standard model extension

Yiming Dong, Zexin Hu, Rui Xu, and Lijing Shao
Phys. Rev. D 108, 104039 – Published 16 November 2023
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  • INTRODUCTION
  • MOI OF SPHERICAL NSs IN GR
  • MOI OF AXISYMMETRIC NSs IN THE SME
  • SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We develop a consistent approach to calculate the moment of inertia (MOI) for axisymmetric neutron stars (NSs) in the Lorentz-violating Standard-Model Extension (SME) framework. To our knowledge, this is the first relativistic MOI calculation for axisymmetric NSs in a Lorentz-violating gravity theory other than deformed, rotating NSs in general relativity. Under Lorentz violation, there is a specific direction in the spacetime, and NSs get stretched or compressed along that direction. When a NS is spinning stationarily along this direction, a conserved angular momentum and the concept of MOI are well defined. In the SME framework, we calculate the partial differential equation governing the rotation and solve it numerically with the finite element method to get the MOI for axisymmetric NSs caused by Lorentz violation. Besides, we study an approximate case where the correction to the MOI is regarded solely from the deformation of the NS and compare it with its counterpart in the Newtonian gravity. Our formalism and the numerical method can be extended to other theories of gravity for static axisymmetric NSs.

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    • Received 6 September 2023
    • Accepted 24 October 2023

    DOI:https://doi.org/10.1103/PhysRevD.108.104039

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Astrophysical studies of gravity
    1. Physical Systems
    Neutron stars & pulsars
    1. Properties
    Lorentz symmetry
    Gravitation, Cosmology & Astrophysics

    Authors & Affiliations

    Yiming Dong1,2, Zexin Hu1,2, Rui Xu3,2, and Lijing Shao2,4,*

    • 1Department of Astronomy, School of Physics, Peking University, Beijing 100871, China
    • 2Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
    • 3Department of Astronomy, Tsinghua University, Beijing 100084, China
    • 4National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China

    • *Corresponding author: lshao@pku.edu.cn

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    Issue

    Vol. 108, Iss. 10 — 15 November 2023

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    Images

    • Figure 1
      Figure 1

      The MOI function of a 1.4M⊙ NS with EOS AP4. The top panel represents the MOI function in GR, IGR, and the MOI in Newtonian gravity, INewton. The middle panel represents the relative difference between IGR and INewton. The bottom panel represents the magnitude of the dimensionless correction factors in Eq. (18). The “Total Factor” is the product of three correction factors.

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    • Figure 2
      Figure 2

      Corrections to the MOIs of NSs caused by Lorentz violation with EOS AP4, as functions of the mass of the NS. The top panel shows the MOI of spherical NSs in GR, IGR. The middle panel shows the absolute correction to the MOI caused by Lorentz violation with s¯zz=10−2. The bottom panel shows the ratio δI/IGR.

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    • Figure 3
      Figure 3

      Corrections to MOIs caused by deformations of NSs with EOS AP4, as functions of the NS mass. The top panel shows the correction to MOI caused by deformations of NSs with s¯zz=10−2. The bottom panel shows the value of k defined in Eq. (60). The gray dashed line represents k=1/3, which is the Newtonian limit for k.

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