Coupling of radial and nonradial oscillations of relativistic stars: Gauge-invariant formalism

Journal Article · Sat Jan 15 00:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.024022· OSTI ID:20705840

Passamonti, Andrea; Bruni, Marco ^[1]; Gualtieri, Leonardo ^[2]; Sopuerta, Carlos F ^[1]

---

1. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG (United Kingdom)
2. Dipartimento di Fisica 'G. Marconi', Universita di Roma 'La Sapienza' and Sezione INFN ROMA 1, piazzale Aldo Moro 2, I-00185 Rome (Italy)

Linear perturbation theory is appropriate to describe small oscillations of stars, while a mild nonlinearity is still tractable perturbatively but requires one to consider mode coupling, i.e., to take into account second order effects. It is natural to start to look at this problem by considering the coupling between linear radial and nonradial modes. A radial pulsation may be thought of as an important component of an overall mildly nonlinear oscillation, e.g., of a protoneutron star. Radial pulsations of spherical compact objects do not per se emit gravitational waves but, if the coupling between the existing first order radial and nonradial modes is efficient in driving and possibly amplifying the nonradial oscillations, one may expect the appearance of nonlinear harmonics, and gravitational radiation could then be produced to a significant level. More in general, mode coupling typically leads to an interesting phenomenology, thus it is worth investigating in the context of star perturbations. In this paper we develop the relativistic formalism to study the coupling of radial and nonradial first order perturbations of a compact spherical star. From a mathematical point of view, it is convenient to treat the two sets of perturbations as separately parametrized, using a 2-parameter perturbative expansion of the metric, the energy-momentum tensor and Einstein equations in which {lambda} is associated with the radial modes, {epsilon} with the nonradial perturbations, and the {lambda}{epsilon} terms describe the coupling. This approach provides a well-defined framework to consider the gauge dependence of perturbations, allowing us to use {epsilon} order gauge-invariant nonradial variables on the static background and to define new second order {lambda}{epsilon} gauge-invariant variables representing the result of the nonlinear coupling. We present the evolution and constraint equations for our variables outlining the setup for numerical computations, and briefly discuss the surface boundary conditions in terms of the second order {lambda}{epsilon} Lagrangian pressure perturbation.

• OSTI ID: 20705840
• Journal Information: Physical Review. D, Particles Fields, Vol. 71, Issue 2; Other Information: DOI: 10.1103/PhysRevD.71.024022; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
COUPLING
DISTURBANCES
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
GAUGE INVARIANCE
GRAVITATION
GRAVITATIONAL RADIATION
GRAVITATIONAL WAVES
HARMONICS
LAGRANGIAN FUNCTION
NONLINEAR PROBLEMS
PERTURBATION THEORY
PULSATIONS
RELATIVISTIC RANGE