arXiv subjects
Publications and source records attributed to Paulo M. Sá.
We present and discuss the analytical r-mode solution to the linearized hydrodynamic equations of a slowly rotating, Newtonian, barotropic, non-magnetized, perfect-fluid star in which the gravitational radiation reaction force is present.
We discuss the role of differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly-rotating neutron star. It is shown that the amplitude of the r-mode saturates in a natural way at a value that depends on the amount of differential rotation at the time the instability becomes active. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to a rotation rate that is comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants.
Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly rotating neutron star. It is shown that the amplitude of the r-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r-mode and, consequently, almost none is carried away by gravitational radiation.
Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.
We investigate three-dimensional perfect fluid stars with polytropic equation of state, matched to the exterior three-dimensional black hole geometry of Banados, Teitelboim and Zanelli. A new class of exact solutions for a generic polytropic index is found and analysed.
A general dilaton gravity theory in 1+1 spacetime dimensions with a cosmological constant $λ$ and a new dimensionless parameter $ω$, contains as special cases the constant curvature theory of Teitelboim and Jackiw, the theory equivalent to vacuum planar General Relativity, the first order string theory, and a two-dimensional purely geometrical theory. The equations of this general two-dimensional theory admit several different black holes with various types of singularities. The singularities can be spacelike, timelike or null, and there are even cases without singularities. Evaluation of the ADM mass, as a charge density integral, is possible in some situations, by carefully subtrating the black hole solution from the corresponding linear dilaton at infinity.
General Relativity in three or more dimensions can be obtained by taking the limit $ω\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit $ω\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.
We show that the two-dimensional theory of Teitelboim and Jackiw has a black hole solution, with two surprising properties: first, it has constant curvature, and second, is free of spacetime singularities. The maximally extended spacetime consists of an infinite chain of universes connected by timelike wormholes.