A conformal scalar dyon black hole solution

An exact solution of Einstein - Maxwell - conformal scalar field equations is given, which is a black hole solution and has three parameters: scalar charge, electric charge, and magnetic charge. Switching off the magnetic charge parameter yields the solution given by Bekenstein. In addition the energy of the conformal scalar dyon black hole is obtained.Comment: 7 pages, Late

Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit

Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulae for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a non trivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional non equatorial images may play an important role in the phenomenology.Comment: 13 pages, 9 figures. Improved version with detailed physical discussio

Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index $n$, on the leading order gravitational waveforms is studied.Comment: 31 pages, 7 figures, typos correcte

Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel and Xu, and the framework established by Carter and Quintana the post Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces also the outer surface boundary conditions are presented. The PN junction condition is an extension of Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page

Edge states of graphene bilayer strip

The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectra of the bilayer strip is computed. The dependence of the edge state band flatness on the bilayer width is found. The density of states at the Fermi level is analytically computed. It is shown that it has the singularity which depends on the width of the bilayer strip. There is also asymmetry in the density of states below and above the Fermi energy.Comment: 9 page

Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition (finite mass gap) between wormhole topology and black hole topology; the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and black hole topology; the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter $p$ is replaced by a 2-vector $\vec{p}$ parametrizing the solutions. We find that $Mass\propto|\vec{p}-\vec{p}_*|^\gamma$ where $\gamma\approx 0.66$. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected.Comment: 15 pages, Latex, 4 figures include

Estimating the parameters of the Sgr A* black hole

The measurement of relativistic effects around the galactic center may allow in the near future to strongly constrain the parameters of the supermassive black hole likely present at the galactic center (Sgr A*). As a by-product of these measurements it would be possible to severely constrain, in addition, also the parameters of the mass-density distributions of both the innermost star cluster and the dark matter clump around the galactic center.Comment: Accepted for publication on General Relativity and Gravitation, 2010. 11 Pages, 1 Figur

Measuring Black Hole Spin in OJ287

We model the binary black hole system OJ287 as a spinning primary and a non-spinning secondary. It is assumed that the primary has an accretion disk which is impacted by the secondary at specific times. These times are identified as major outbursts in the light curve of OJ287. This identification allows an exact solution of the orbit, with very tight error limits. Nine outbursts from both the historical photographic records as well as from recent photometric measurements have been used as fixed points of the solution: 1913, 1947, 1957, 1973, 1983, 1984, 1995, 2005 and 2007 outbursts. This allows the determination of eight parameters of the orbit. Most interesting of these are the primary mass of $1.84\cdot 10^{10} M_\odot$, the secondary mass $1.46\cdot 10^{8} M_\odot$, major axis precession rate $39^\circ.1$ per period, and the eccentricity of the orbit 0.70. The dimensionless spin parameter is $0.28\:\pm\:0.01$ (1 sigma). The last parameter will be more tightly constrained in 2015 when the next outburst is due. The outburst should begin on 15 December 2015 if the spin value is in the middle of this range, on 3 January 2016 if the spin is 0.25, and on 26 November 2015 if the spin is 0.31. We have also tested the possibility that the quadrupole term in the Post Newtonian equations of motion does not exactly follow Einstein's theory: a parameter $q$ is introduced as one of the 8 parameters. Its value is within 30% (1 sigma) of the Einstein's value $q = 1$. This supports the $no-hair theorem$ of black holes within the achievable precision. We have also measured the loss of orbital energy due to gravitational waves. The loss rate is found to agree with Einstein's value with the accuracy of 2% (1 sigma).Comment: 12 pages, 4 figures, IAU26