Brane-world cosmology with black strings

We consider the simplest scenario when black strings / cigars penetrate the cosmological brane. As a result, the brane has a Swiss-cheese structure, with Schwarzschild black holes immersed in a Friedmann-Lema\^{\i}tre-Robertson-Walker brane. There is no dark radiation in the model, the cosmological regions of the brane are characterized by a cosmological constant $\Lambda$ and flat spatial sections. Regardless of the value of $\Lambda$, these brane-world universes forever expand and forever decelerate. The totality of source terms in the modified Einstein equation sum up to a dust, establishing a formal equivalence with the general relativistic Einstein-Straus model. However in this brane-world scenario with black strings the evolution of the cosmological fluid strongly depends on $\Lambda$. For $\Lambda \leq 0$ it has positive energy density $\rho$ and negative pressure $p$ and at late times it behaves as in the Einstein-Straus model. For (not too high) positive values of $\Lambda$ the cosmological evolution begins with positive $\rho$ and negative $p$, but this is followed by an epoch with both $\rho$ and $p$ positive. Eventually, $\rho$ becomes negative, while $p$ stays positive. A similar evolution is present for high positive values of $\Lambda$, however in this case the evolution ends in a pressure singularity, accompanied by a regular behaviour of the cosmic acceleration. This is a novel type of singularity appearing in brane-worlds.Comment: 6 pages, 4 figures; expanded version, references added, to appear in Physical Review

Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.

On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case

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.Comment: 13 pages; v2: title amended, to be published in Classical and Quantum Gravit

Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole-magnetic dipole interaction

We study the gravitational radiation reaction in compact binary systems composed of neutron stars with spin and huge magnetic dipole moments (magnetars). The magnetic dipole moments undergo a precessional motion about the respective spins. At sufficiently high values of the magnetic dipole moments, their interaction generates second post-Newtonian order contributions both to the equations of motion and to the gravitational radiation escaping the system. We parametrize the radial motion and average over a radial period in order to find the secular contributions to the energy and magnitude of the orbital angular momentum losses, in the generic case of \textit{eccentric} orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole interactions, here too we deduce the secular evolution of the relative orientations of the orbital angular momentum and spins. These equations, supplemented by the evolution equations for the angles characterizing the orientation of the dipole moments form a first order differential system, which is closed. The circular orbit limit of the energy loss agrees with Ioka and Taniguchi's earlier result

Non-uniform Braneworld Stars: an Exact Solution

The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\cal U}(r)$ is always negative inside the stellar distribution, in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behaviour inside the distribution. Using a Reissner-N\"{o}rdstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.Comment: 22 pages, 3 figures, version to be published in International Journal of Modern Physics D (IJMPD

Spin-spin effects in radiating compact binaries

The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum $\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of $\bar{L}$ and other constants of the motion. Among them, self-interaction spin effects are found, representing the second post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring approximation.Comment: 12 pages, to appear in Phys. Rev.

Asymmetric Swiss-cheese brane-worlds

We study a brane-world cosmological scenario with local inhomogeneities represented by black holes. The brane is asymmetrically embedded into the bulk. The black strings/cigars penetrating the Friedmann brane generate a Swiss-cheese type structure. This universe forever expands and decelerates, as its general relativistic analogue. The evolution of the cosmological fluid however can proceed along four branches, two allowed to have positive energy density, one of them having the symmetric embedding limit. On this branch a future pressure singularity can arise for either (a) a difference in the cosmological constants of the cosmological and black hole brane regions (b) a difference in the left and right bulk cosmological constants. While the behaviour (a) can be avoided by a redefinition of the fluid variables, (b) establishes a critical value of the asymmetry over which the pressure singularity occurs. We introduce the pressure singularity censorship which bounds the degree of asymmetry in the bulk cosmological constant. We also show as a model independent generic feature that the asymmetry source term due to the bulk cosmological constant increases in the early universe. In order to obey the nucleosynthesis constraints, the brane tension should be constrained therefore both from below and from above. With the maximal degree of asymmetry obeying the pressure singularity censorship, the higher limit is 10 times the lower limit. The degree of asymmetry allowed by present cosmological observations is however much less, pushing the upper limit to infinity.Comment: v2: considerably expanded, 19 pages, 8 figures, many new references. Pressure singularity censorship introduced, strict limits on the possible degree of asymmetry derived. v3: model independent analysis shows that the asymmetry bounds the brane tension from above. Limits on the maximal tension set. Version published in JCA

Active Galactic Nuclei with Starbursts: Sources for Ultra High Energy Cosmic Rays

Ultra high energy cosmic ray events presently show a spectrum, which we interpret here as galactic cosmic rays due to a starburst in the radio galaxy Cen A pushed up in energy by the shock of a relativistic jet. The knee feature and the particles with energy immediately higher in galactic cosmic rays then turn into the bulk of ultra high energy cosmic rays. This entails that all ultra high energy cosmic rays are heavy nuclei. This picture is viable if the majority of the observed ultra high energy events come from the radio galaxy Cen A, and are scattered by intergalactic magnetic fields across most of the sky.Comment: 4 pages, 1 figure, proceedings of "High-Energy Gamma-rays and Neutrinos from Extra-Galactic Sources", Heidelber