An inverse approach to Einstein's equations for non-conducting fluids

We show that a flow (timelike congruence) in any type $B_{1}$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is written out explicitly for canonical representations of the spacetimes. With the flow determined, we explore an inverse approach to Einstein's equations where a phenomenological fluid interpretation of a spacetime follows directly from the metric irrespective of the choice of coordinates. This approach is pursued for fluids with anisotropic pressure and shear viscosity. In certain degenerate cases this interpretation is shown to be generically not unique. The framework developed allows the study of exact solutions in any frame without transformations. We provide a number of examples, in various coordinates, including spacetimes with and without unique interpretations. The results and algorithmic procedure developed are implemented as a computer algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev

On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system

In this paper we explore the consequences of the recent determination of the mass m=(8.7 +/- 0.8)M_Sun of Cygnus X-1, obtained from the Quasi-Periodic Oscillation (QPO)-photon index correlation scaling, on the orbital and physical properties of the binary system HDE 226868/Cygnus X-1. By using such a result and the latest spectroscopic optical data of the HDE 226868 supergiant star we get M=(24 +/- 5)M_Sun for its mass. It turns out that deviations from the third Kepler law significant at more than 1-sigma level would occur if the inclination i of the system's orbital plane to the plane of the sky falls outside the range 41-56 deg: such deviations cannot be due to the first post-Newtonian (1PN) correction to the orbital period because of its smallness; interpreted in the framework of the Newtonian theory of gravitation as due to the stellar quadrupole mass moment Q, they are unphysical because Q would take unreasonably large values. By conservatively assuming that the third Kepler law is an adequate model for the orbital period we obtain i=(48 +/- 7) deg which yields for the relative semimajor axis a=(42 +/- 9)R_Sun. Our estimate for the Roche's lobe of HDE 226868 is r_M = (21 +/- 6)R_Sun.Comment: Latex2e, 7 pages, 1 table, 4 figures. To appear in ApSS (Astrophysics and Space Science

The impact of the oblateness of Regulus on the motion of its companion

The fast spinning B-star Regulus has recently been found to be orbited by a fainter companion in a close circular path with orbital period P_b = 40.11(2) d. Being its equatorial radius R_e 32% larger than the polar one R_p, Regulus possesses a remarkable quadrupole mass moment Q. We investigate the effects of Q on the orbital period P_b of its companion in order to see if they are measurable, given the present-day level of accuracy in measuring P_b. Conversely, we will look for deviations from the third Kepler law, attributed to the quadrupole mass moment Q of Regulus, to constrain the ratio \gamma=m/M of the system's masses.Comment: LaTex, 6 pages, 5 figures, 1 table. Accepted by Astrophysics and Space Scienc

Scalar wave propagation in topological black hole backgrounds

We consider the evolution of a scalar field coupled to curvature in topological black hole spacetimes. We solve numerically the scalar wave equation with different curvature-coupling constant $\xi$ and show that a rich spectrum of wave propagation is revealed when $\xi$ is introduced. Relations between quasinormal modes and the size of different topological black holes have also been investigated.Comment: 26 pages, 18 figure

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -- the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX