Massive merging black holes will be the primary sources of powerful gravitational waves at low frequency, and will permit to test general relativity with candidate galaxies close to a binary black hole merger. In this paper we identify the typical ma
ss ratio of the two black holes but then show that the distance when gravitational radiation becomes the dominant dissipative effect (over dynamical friction) does not depend on the mass ratio. However the dynamical evolution in the gravitational wave emission regime does. For the typical range of mass ratios the final stage of the merger is preceded by a rapid precession and a subsequent spin-flip of the main black hole. This already occurs in the inspiral phase, therefore can be described analytically by post-Newtonian techniques. We then identify the radio galaxies with a super-disk as those in which the rapidly precessing jet produces effectively a powerful wind, entraining the environmental gas to produce the appearance of a thick disk. These specific galaxies are thus candidates for a merger of two black holes to happen in the astronomically near future.
The high value of brane tension has a crucial role in recovering Einsteins general relativity at low energies. In the framework of a recently developed formalism with variable brane tension one can pose the question, whether it was always that high?
In analogy with fluid membranes, in this paper we allow for temperature dependent brane tension, according to the corresponding law established by Eotvos. For cosmological branes this assumption leads to several immediate consequences: (a) The brane Universe was created at a finite temperature $T_{c}$ and scale factor $a_{min}$. (b) Both the brane tension and the 4-dimensional gravitational coupling constant increase with the scale factor from zero to asymptotic values. (c) The 4-dimensional cosmological constant evolves with $a$, starting with a huge negative value, passing through zero, finally reaching a small positive value. Such a scale-factor dependent cosmological constant is able to generate a surplus of attraction at small $a$ (as dark matter does) and a late-time repulsion at large $a$ (dark energy). In the particular toy model discussed here the evolution of the brane tension is compensated by energy interchange between the brane and the fifth dimension, such that the continuity equation holds for the cosmological fluid. The resulting cosmology closely mimics the standard model at late times, a decelerated phase being followed by an accelerated expansion. The energy absorption of the brane drives the 5D space-time towards maximal symmetry, becoming Anti de Sitter.
We give here a new third post-Newtonisn (3PN) spin-spin contribution (in the PN parameter $epsilon $) to the accumulated orbital phase of a compact binary, arising from the spin-orbit precessional motion of the spins. In the equal mass case this cont
ribution vanishes, but LISA sources of merging supermassive binary black holes have typically a mass ratio of 1:10. For such non-equal masses this 3PN correction is periodic in time, with period approximately $epsilon ^{-1}$ times larger than the period of gravitational waves. We derive a renormalized and simpler expression of the spin-spin coefficient at 2PN, as an average over the time-scale of this period of the combined 2PN and 3PN contribution. We also find that for LISA sources the quadrupole-monopole contribution to the phase dominates over the spin-spin contribution, while the self-spin contribution is negligible even for the dominant spin. Finally we define a renormalized total spin coefficient $bar{sigma}$ to be employed in the search for gravitational waves emitted by LISA sources.
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eotvos. This new degree of freedom allows for evolving gravitati
onal and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a Friedmann brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter space-time.
The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is not a representant of
the above class, but contains the static Einstein brane as embedded hypersurface. We prove that the 5d Birkhoff theorem is still satisfied in a weaker sense: the GM space-time is related to the degenerated horizon metric of certain black-hole space-times of the allowed class. This result resembles the connection between the Bertotti-Robinson space-time and the horizon region of the extremal Reissner-Nordstrom space-time in general relativity.
When galaxies collide, dynamical friction drives their central supermassive black holes close enought to each other such that gravitational radiation becomes the leading dissipative effect. Gravitational radiation takes away energy, momentum and angu
lar momentum from the compact binary, such that the black holes finally merge. In the process, the spin of the dominant black hole is reoriented. On observational level, the spins are directly related to the jets, which can be seen at radio frequencies. Images of the X-shaped radio galaxies together with evidence on the age of the jets illustrate that the jets are reoriented, a phenomenon known as spin-flip. Based on the galaxy luminosity statistics we argue here that the typical galaxy encounters involve mass ratios between 1:3 to 1:30 for the central black holes. Based on the spin-orbit precession and gravitational radiation we also argue that for this typical mass ratio in the inspiral phase of the merger the initially dominant orbital angular momentum will become smaller than the spin, which will be reoriented. We prove here that the spin-flip phenomenon typically occurs already in the inspiral phase, and as such is describable by post-Newtonian techniques.
In a recent paper Liu considered the complete Schwarzschild interior and exterior solution in harmonic coordinates. There he argued about the necessity to keep an integration constant, in contrast with previous treatments. The purpose of this comment
is to show that the above conclusion cannot be traced from the matching conditions between the vacuum exterior and the uniform density interior perfect fluid, as claimed.
We develop a Hamiltonian formalism of brane-world gravity, which singles out two preferred, mutually orthogonal directions. One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane. The other is a t
emporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane. They represent the gravitons, a gravi-photon and a gravi-scalar, respectively. From the action we derive the canonical evolution equations and the constraints for these gravitational degrees of freedom both on the brane and outside it. By integrating across the brane, the dynamics also generates the tensorial and scalar projection of the Lanczos equation. The vectorial projection of the Lanczos equation arises in a similar way from the diffeomorphism constraint. Both the graviton and the gravi-scalar are continuous across the brane, however the momentum of the gravi-vector has a jump, related to the energy transport (heat flow) on the brane.
A class of generalized Randall-Sundrum type II (RS) brane-world models with Weyl fluid are confronted with the Gold supernovae data set and BBN constraints. We consider three models with different evolutionary history of the Weyl fluid, characterized
by the parameter $alpha$. For $alpha=0$ the Weyl curvature of the bulk appears as dark radiation on the brane, while for $alpha =2$ and 3 the brane radiates, leaving a Weyl fluid on the brane with energy density decreasing slower than that of (dark) matter. In each case the contribution $Omega_d$ of the Weyl fluid represents but a few percent of the energy content of the Universe. All models fit reasonably well the Gold2006 data. The best fit model for $alpha =0$ is for $Omega_d=0.04$. In order to obey BBN constraints in this model however, the brane had to radiate at earlier times.
