Slowly rotating anisotropic relativistic stars (2403.08250v2)
Abstract: The present paper is devoted to a study of the equilibrium configurations of slowly rotating anisotropic stars in the framework of general relativity. For that purpose, we provide the equations of structure where the rotation is treated to second order in the angular velocity. These equations extend those first derived by Hartle for slowly rotating isotropic stars. As an application of the new formalism, we study the rotational properties of Bowers-Liang fluid spheres. A result of particular interest is that the ellipticity and mass quadrupole moment are negative for certain highly anisotropic configurations; thus, such systems are prolate rather than oblate. Furthermore, for configurations with high anisotropy and compactness close to their critical value, quantities like the moment of inertia, change of mass, and mass quadrupole moment approach to the corresponding Kerr black hole values, similar to other ultracompact systems like sub-Buchdahl Schwarzschild stars and analytic rotating gravastars.
- H. A. Buchdahl, Phys. Rev. 116, 1027 (1959).
- M. Ruderman, Annu. Rev. Astron. Astrophys. 10, 427 (1972).
- R. F. Sawyer, Phys. Rev. Lett. 29, 382 (1972).
- S. L. Liebling and C. Palenzuela, Living Rev. Rel. 26, 1 (2023), arXiv:1202.5809 [gr-qc] .
- S. Yazadjiev, Phys. Rev. D 85, 044030 (2012), arXiv:1111.3536 [gr-qc] .
- V. Folomeev and V. Dzhunushaliev, Phys. Rev. D 91, 044040 (2015), arXiv:1501.06275 [gr-qc] .
- L. Herrera and N. O. Santos, Phys. Rept. 286, 53 (1997).
- G. Lemaitre, Annales Soc. Sci. Bruxelles A 53, 51 (1933).
- R. L. Bowers and E. P. T. Liang, Astrophys. J. 188, 657 (1974).
- S. S. Bayin, Phys. Rev. D 26, 1262 (1982).
- M. K. Mak and T. Harko, Proc. Roy. Soc. Lond. A 459, 393 (2003), arXiv:gr-qc/0110103 .
- K. Dev and M. Gleiser, Gen. Rel. Grav. 34, 1793 (2002), arXiv:astro-ph/0012265 .
- W. Hillebrandt and K. O. Steinmetz, Astron. Astrophys. 53, 283 (1976).
- K. Dev and M. Gleiser, Gen. Rel. Grav. 35, 1435 (2003), arXiv:gr-qc/0303077 .
- D. D. Doneva and S. S. Yazadjiev, Phys. Rev. D 85, 124023 (2012), arXiv:1203.3963 [gr-qc] .
- K. Yagi and N. Yunes, Phys. Rev. D 91, 123008 (2015), arXiv:1503.02726 [gr-qc] .
- S. Carloni and D. Vernieri, Phys. Rev. D 97, 124057 (2018), arXiv:1709.03996 [gr-qc] .
- J. B. Hartle, Astrophys. J. 150, 1005 (1967).
- J. B. Hartle and K. S. Thorne, Astrophys. J. 153, 807 (1968).
- M. L. Pattersons and A. Sulaksono, Eur. Phys. J. C 81, 698 (2021).
- P. Beltracchi, Phys. Rev. D 106, 104038 (2022), arXiv:2206.04139 [gr-qc] .
- S. Chandrasekhar and J. C. Miller, Mon. Not. R. Astron. Soc. 167, 63 (1974).
- P. Beltracchi and C. Posada, Class. Quantum Grav. 41, 045001 (2024), arXiv:2305.09544 [gr-qc] .
- N. Uchikata and S. Yoshida, Phys. Rev. D 90, 064042 (2014), arXiv:1506.06478 [gr-qc] .
- N. Uchikata and S. Yoshida, Class. Quantum Grav. 33, 025005 (2016), arXiv:1506.06485 [gr-qc] .
- P. Pani, Phys. Rev. D 92, 124030 (2015), [Erratum: Phys.Rev.D 95, 049902 (2017)], arXiv:1506.06050 [gr-qc] .
- B. Reina and R. Vera, Class. Quantum Grav. 32, 155008 (2015), arXiv:1412.7083 [gr-qc] .
- J. C. Miller, Mon. Not. R. Astron. Soc. 179, 483 (1977).
- K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1916, 424 (1916), arXiv:physics/9912033 [physics.hist-ph] .
- P. O. Mazur and E. Mottola, Class. Quantum Grav. 32, 215024 (2015), arXiv:1501.03806 [gr-qc] .
- B. Reina, Mon. Not. R. Astron. Soc. 455, 4512 (2016), arXiv:1503.07835 [gr-qc] .
- J. B. Hartle and D. H. Sharp, Atrophys. J. 147, 317 (1967).
- P. O. Mazur and E. Mottola, Universe 9, 88 (2023), arXiv:gr-qc/0109035 .
- P. O. Mazur and E. Mottola, Proc. Nat. Acad. Sci. 101, 9545 (2004), arXiv:gr-qc/0407075 .