Non-comoving description of adiabatic radial perturbations of relativistic stars (2405.10359v1)
Abstract: We study adiabatic, radial perturbations of static, self-gravitating perfect fluids within the theory of general relativity employing a new perturbative formalism. We show that by considering a radially static observer, the description of the perturbations can be greatly simplified with respect to the standard comoving treatment. The new perturbation equations can be solved to derive analytic solutions to the problem for a general class of equilibrium solutions. We discuss the thermodynamic description of the fluid under isotropic frame transformations, showing how, in the radially static, non-inertial frame, the stress-energy tensor of the fluid must contain momentum transfer terms. As illustrative examples of the new approach, we study perturbations of equilibrium spacetimes characterized by the Buchdahl I, Heintzmann IIa, Patwardhan-Vaidya IIa, and Tolman VII solutions, computing the first oscillation eigenfrequencies and the associated eigenfunctions. We also analyze the properties of the perturbations of cold neutron stars composed of a perfect fluid verifying the Bethe-Johnson model I equation of state, computing the oscillation eigenfrequencies and the $e$-folding time.
- J. M. Stewart and M. Walker, “Perturbations of Space-Times in General Relativity”, Proc. R. Soc. Lond. A 341, 49 (1974).
- V. Moncrief, “Gravitational perturbations of spherically symmetric systems. I. The exterior problem”, Ann. Phys. 88, 323 (1974).
- C. A. Clarkson and R. K. Barrett, “Covariant perturbations of Schwarzschild black holes”, Class. Quantum Grav. 20, 3855 (2003).
- J. M. Bardeen, “Gauge Invariant Cosmological Perturbations”, Phys. Rev. D 22, 1882 (1980).
- G. F. R. Ellis and M. Bruni, “Covariant and Gauge Invariant Approach to Cosmological Density Fluctuations”, Phys. Rev. D 40, 1804 (1989).
- S. Chandrasekhar, “Dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity”, Phys. Rev. Lett. 12, 114 (1964); Erratum: Phys. Rev. Lett. 12, 437 (1964).
- S. Chandrasekhar, “The dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity”, Astrophysical Journal 140, 417 (1964); Erratum: Astrophysical Journal 140, 1342 (1964).
- G. Chanmugam, “Radial oscillations of zero-temperature white dwarfs and neutron stars below nuclear densities”, Astrophysical Journal 217, 799 (1977).
- D. Gondek, P. Haensel, and J. L. Zdunik, “Radial pulsations and stability of protoneutron stars”, Astron. Astrophys. 325, 217 (1997).
- K. D. Kokkotas and J. Ruoff, “Radial oscillations of relativistic stars”, Astron. Astrophys. 366, 565 (2001).
- P. Luz and S. Carloni, “Gauge invariant perturbations of static spatially compact LRS II spacetimes”, arXiv:2405.05321 [gr-qc].
- P. Luz and S. Carloni,“Adiabatic radial perturbations of relativistic stars: analytic solutions to an old problem”, arXiv:2405.06740 [gr-qc].
- G. Betschart and C. A. Clarkson, “Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes”, Class. Quantum Grav. 21, 5587 (2004).
- C. A. Clarkson, “A covariant approach for perturbations of rotationally symmetric spacetimes”, Phys. Rev. D 76, 104034 (2007).
- G. F. R. Ellis and H. van Elst, “Cosmological models: Cargese lectures 1998”, NATO Sci. Ser. C 541, 1 (1999).
- P. Luz and J. P. S. Lemos, “Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory”, Phys. Rev. D 107, 084004 (2023).
- S. Carloni and D. Vernieri, “Covariant Tolman-Oppenheimer-Volkoff equations. I. The isotropic case”, Phys. Rev. D 97, 124056 (2018).
- S. Carloni and D. Vernieri, “Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case”, Phys. Rev. D 97, 124057 (2018).
- N. F. Naidu, S. Carloni and P. Dunsby, “Two-fluid stellar objects in general relativity: The covariant formulation”, Phys. Rev. D 104, 044014 (2021).
- N. F. Naidu, S. Carloni and P. Dunsby, “Anisotropic two-fluid stellar objects in general relativity”, Phys. Rev. D 106, 124023 (2022).
- P. Luz and S. Carloni, “Static compact objects in Einstein-Cartan theory”, Phys. Rev. D 100, 084037 (2019).
- M. Campbell, S. Carloni, P. K. S. Dunsby and N. F. Naidu, “Reconstructing exact solutions to relativistic stars in f(R)𝑓𝑅f(R)italic_f ( italic_R ) gravity”, arXiv:2403.00070 [gr-qc].
- J. L. Rosa and S. Carloni, “Junction conditions for general LRS spacetimes in the 1+1+21121+1+21 + 1 + 2 covariant formalism”, arXiv:2303.12457 [gr-qc].
- S. Chandrasekhar, “Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity”, Phys. Rev. Lett. 12, 114 (1964).
- W. Israel and J.M. Stewart, “Transient relativistic thermodynamics and kinetic theory”, Annals Phys. 118, 341 (1979).
- H. M. Väth and G. Chanmugam, “Radial oscillations of neutron stars and strange stars”, Astron. Astrophys. 260, 250 (1992).
- M. S. R. Delgaty and K. Lake, “Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations”, Comput. Phys. Commun. 115, 395 (1998).
- P. Haensel and A. Y. Potekhin, “Analytical representations of unified equations of state of neutron-star matter”, Astron. Astrophys. 428, 191 (2004).
- H. A. Bethe and M. B. Johnson, “Dense baryon matter calculations with realistic potentials”, Nucl. Phys. A 230, 1 (1974).
- R. C. Malone, M. B. Johnson and H. A. Bethe, “Neutron star models with realistic high-density equations of state.”, Astrophysical Journal 199, 741 (1975).
- L. Lindblom, “Phase Transitions and the Mass-Radius Curves of Relativistic Stars”, Phys. Rev. D 58, 024008 (1998).