The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.
The conformal gravity fit to observed galactic rotation curves requires γ>0. On the other hand, the conventional method for light deflection by galaxies gives a negative contribution to the Schwarzschild value for γ>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for γ>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R. Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self-similar way as advocated long ago by the Swedish school of astrophysics.
The present paper is an extension of a recent work (Bhattacharya et al. 2010) to the Einstein-Strauss vacuole model with a cosmological constant, where we work out the light deflection by considering perturbations up to order M3 and confirm the light bending obtained previously in their vacuole model by Ishak et al. (2008). We also obtain another local coupling term −5πM2Λ/8 related to Λ, in addition to the one obtained by Sereno (2008, 2009). We argue that the vacuole method for light deflection is exclusively suited to cases where the cosmological constant Λ disappears from the path equation. However, the original Rindler-Ishak method (2007) still applies even if a certain parameter γ of Weyl gravity does not disappear. Here, using an alternative prescription, we obtain the known
term −γR/2, as well as another new local term 3πγM/2 between M and γ. Physical implications are compared, where we argue that the repulsive term −γR/2 can be masked by the Schwarzschild term 2M/R in the halo regime supporting attractive property of the dark matter.
The Einstein evolution of a dust shell universe with spatial spherical symmetry is analyzed. The implicit and parametric solutions of Tolman-Bondi equations are proposed in order to show its agreement with the rectilinear solutions of Kepler's problem. Finally, a complete systematization of Tolman-Bondi models is obtained through the classical Weierstrass approach.
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