Carlos O. Nicasio

Inspiralling Black holes: The close limit

We calculate an estimate of the gravitational radiation emitted when two equal mass black holes coalesce at the end of their binary inspiral, using several approximations based on considering the holes close to each other. A shortcoming of our method is that it is limited to models forming final holes with slow rotation, but our results clearly suggest a trend for larger angular momenta. We find that about 1% of the mass energy of the pair will emerge as gravitational waves during the final stages of the collision and that a negligible fraction of the angular momentum will be radiated. PACS numbers: 04.30.Db, 04.25.Dm, 04.70.Bw, 97.80.Fk An international network of interferometric gravitational wave (GW) observatories (the LIGO project in the U.S., the VIRGO and GEO projects in Europe, and the TAMA project in Japan [1]) will be capable of detecting gravitational waves in the next few years. This could have revolutionary implications for astronomy since it constitutes a new form of “light” with which to observe the Universe, a form that is better correlated with the bulk motions of matter and is very hard to shield or distort. Gravitational waves were originally predicted by Einstein in 1915 but their theoretical existence was not completely understood until the 1960’s [2] and their direct experimental detection has remained a daunting challenge [3]. One of the most promising sources for detection is the collision of two black holes to form a single, final hole. Such a collision is expected to be the end point of the decaying inspiral for a binary pair of holes. Just how promising such collisions are depends very much on the masses of the colliding holes and is connected with the characteristics of detectors. The sensitivity of the laser interferometric detectors, like LIGO, peaks around 100 Hz. The major determinant of the frequency of GWs produced in a black hole inspiral/collision is M, the mass of the system (and of the final black hole formed). The frequency scales as 1M and is around 10 4 Hz for a 1MO system. The usual black hole candidates are stellar mass holes and supermassive holes (10 6 MO) in the centers of many galaxies. The frequency of GWs from the former candidates would be too high except for the weak radiation from the early inspiral. GWs from supermassive holes would be too low in frequency for Earth based systems but well suited to space based detection. Black holes of 100MO would be ideal as sources and black holes of any mass can in principle exist. But the astrophysical motivation for such “middleweight” holes was weak. Recent observations [4] of x-ray emission from galaxies suggest that some galaxies may contain middleweight holes, perhaps as an evolutionary stage in the formation of supermassive holes. Should such a middleweight hole exist it will produce GWs near the optimal 100 Hz frequency when it collides with compact objects of equal or smaller masses. For two different reasons, we focus here on the collision of roughly equal mass holes. The first is that the power radiated from the collision of holes of masses m1 # m2 scales as m1m2 2 , at least in the case that m1

Gravitational radiation from Schwarzschild black holes: the second-order perturbation formalism

Abstract The perturbation theory of black holes has been useful recently for providing estimates of gravitational radiation from the black-hole collisions. Second-order perturbation theory, relatively undeveloped until recently, has proved to be important both for providing refined estimates and for indicating the range of validity of perturbation theory. Here we review the second-order formalism for perturbations of Schwarzschild spacetimes. The emphasis is on practical methods for carrying out the second-order computations of the outgoing radiation. General issues are illustrated throughout with examples from “close-limit” results, perturbation calculations in which black holes start from the small separation.

Topological properties of single gravisolitons

The possibility of assigning topological properties to gravisolitons has been recently discussed by Belinsky, who considered perturbations of certain diagonal metrics with two commuting Killing vectors. The discussion given by Belinsky relies on the properties of the solitonic part of the projection of the four‐dimensional space–time metric onto the two‐dimensional space spanned by the Killing vectors. In that context, for single soliton perturbations, he finds two types of, in principle, disjoint solutions, characterized respectively by the functions μin and μout, such that one can assign a ‘‘topological charge’’ to the corresponding space–time. In this article we analyze this problem, studying in detail the single soliton perturbation of a Bianchi‐type VI0 background, and prove that when we consider the full four‐dimensional metric, it is possible to construct locally smooth extensions that connect sectors associated to μin to sectors associated to μout. Therefore, the concept of ‘‘topological charge’’ ...

Cylindrical--spherical Einstein--Maxwell solitons

We present an analysis of a family of exact solutions of the Einstein--Maxwell equations, obtained using Alekseevs inverse scattering method. The solutions are simple soliton transformations of a Minkowski background and can be interpreted as cylindrical--spherical electrogravitational waves travelling on a flat background. Although the solutions are locally everywhere regular, the construction of a complete manifold (through appropriate extensions) requires a non-trivial topology, giving rise to the presence of ring-like structures connecting two different asymptotically flat regions. The electrogravitational waves display the kind of phase shift previously described for cylindrical waves. A brief description of the construction procedure is also included.

Gravitational radiation from cosmic string splitting on a Friedmann-Robertson-Walker background

We present exact solutions of Einsteins equations that may be interpreted as representing the splitting of a primordial cosmic string imbedded in a perfect fluid Friedmann-Robertson-Walker (FRW) cosmology. The splitting leads to the creation of a ‘bubble’ whose boundary is given by a gravitational shock wave, expanding from the point of splitting, associated to the motion of the free ends of the string. Inside the bubble we have a perturbed FRW metric. This perturbation is largest near the string ends, producing a sort of ‘wake’ along the path of the free ends, but decreases rapidly with time and the metric approaches the FRW regime locally everywhere inside the bubble. Similar results are shown to hold also for flat vacuum de Sitter space-times.