New Black Hole Solutions in Brans-Dicke Theory of Gravity

Existence check of non-trivial, stationary axisymmetric black hole solutions in Brans-Dicke theory of gravity in different direction from those of Penrose, Thorne and Dykla, and Hawking is performed. Namely, working directly with the known explicit spacetime solutions in Brans-Dicke theory, it is found that non-trivial Kerr-Newman-type black hole solutions different from general relativistic solutions could occur for the generic Brans-Dicke parameter values -5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry scalar hair and can really arise in nature and if they can, what the associated physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.

Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes

An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first derive the general extremal condition for PD spacetimes. This general result could be applied to get the extremal limit in any stationary and axisymmetric spacetimes.Comment: 9 pages, Some special modifications are mad

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio

The evolution of cosmic string loops in Kerr-de Sitter spacetimes

The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can expand and exist except for too small ones.Comment: 8 page

Complex Kerr Geometry and Nonstationary Kerr Solutions

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in PRD), added the relation to twistors and algorithm of numerical computations, English is correcte

A rotating three component perfect fluid source and its junction with empty space-time

The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein's equations. It is shown that these solutions are the familiar static perfect fluid cases commonly derived in curvature coordinates but now endowed with rotation. The resulting solutions are also discussed in the context of T-solutions of Einstein's equations and the vacuum T-solution outside a rotating source is presented. The interior source for these solutions is shown not to be a perfect fluid but rather an anisotropic three component perfect fluid for which the energy momentum tensor is derived. The Schwarzschild interior solution is given as an example of the approach.Comment: 14 page

The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General Relativity and Gravitatio

Effects of acceleration on the collision of particles in the rotating black hole spacetime

We study the collision of two geodesic particles in the accelerating and rotating black hole spacetime and probe the effects of the acceleration of black hole on the center-of-mass energy of the colliding particles and on the high-velocity collision belts. We find that the dependence of the center-of-mass energy on the acceleration in the near event-horizon collision is different from that in the near acceleration-horizon case. Moreover, the presence of the acceleration changes the shape and position of the high-velocity collision belts. Our results show that the acceleration of black holes brings richer physics for the collision of particles.Comment: 7 pages, 2 figures, The corrected version accepted for publication in EPJ

Boundary value problems for the stationary axisymmetric Einstein equations: a disk rotating around a black hole

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.Comment: 46 page

Initial data for a head on collision of two Kerr-like black holes with close limit

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. This family of initial data has the following properties: (i) When the mass parameter of one of them is zero or when the distance between them goes to infinity, it reduces exactly to the Kerr initial data. (ii) When the distance between them is zero, we obtain exactly a Kerr initial data with mass and angular momentum equal to the sum of the mass and angular momentum parameters of each of them. The initial data depends smoothly on the distance, the mass and the angular momentum parameters.Comment: 15 pages, no figures, Latex2