Browsing by Author "Luz, Paulo"
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- Adiabatic radial perturbations of relativistic stars: Analytic solutions to an old problemPublication . Luz, Paulo; Carloni, SanteWe present a new system of equations that fully characterizes adiabatic, radial perturbations of perfect fluid stars within the theory of general relativity. The properties of the system are discussed, and, provided that the equilibrium spacetime verifies some general regularity conditions, analytical solutions for the perturbation variables are found. As illustrative examples, the results are applied to study perturbations of selected classical exact spacetimes, and the first oscillation eigenfrequencies are computed. Exploiting the new formalism, we derive an upper bound for the maximum compactness of stable, perfect fluid stars, which is equation-of-state agnostic and significantly smaller than the Buchdahl bound.
- Gauge invariant perturbations of static spatially compact LRS II spacetimesPublication . Luz, Paulo; Carloni, SanteWe present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by construction covariant and identification gauge invariant and encompass the geometry and the thermodynamics of the fluid sources. The new equations are then applied to the study of isotropic, adiabatic perturbations. We discuss how the choice of frame in which perturbations are described can significantly simplify the mathematical analysis of the problem and show that it is possible to change frames directly from the linear level equations. We find explicitly that the case of isotropic, adiabatic perturbations can be reduced to a singular Sturm–Liouville eigenvalue problem, and lower bounds for the values of the eigenfrequencies can be derived. These results lay the theoretical groundwork to analytically describe linear, isotropic, and adiabatic perturbations of static, spherically symmetric spacetimes
- Noncomoving description of adiabatic radial perturbations of relativistic starsPublication . Luz, Paulo; Carloni, SanteWe 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, noninertial frame, the stressenergy 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.
- The effects of intrinsic spin of matter in relativistic cosmologyPublication . Luz, PauloWe discuss general solutions of the Einstein-Cartan theory sourced by a cosmological perfect fluid composed of particles with intrinsic spin. In the considered model, the metric tensor is described by a general FLRW solution, however, the Weyl tensor might not vanish. The coupling between the intrinsic spin and the Weyl tensor excludes spatially closed solutions, and the universe must either be flat or open. In the open case, it is shown that the magnetic part of the Weyl tensor verifies a wave equation, such that, in a dynamic universe, the intrinsic spin of matter leads to the generation and emission of gravitational waves. The properties of these waves are discussed, with an emphasis on their decay rate at late time. Lastly, we discuss that, in the considered cosmological model, the intrinsic spin of matter contributes to a positive accelerated expansion of the universe.