Detection Strategies for Extreme Mass Ratio Inspirals

The capture of compact stellar remnants by galactic black holes provides a unique laboratory for exploring the near horizon geometry of the Kerr spacetime, or possible departures from general relativity if the central cores prove not to be black holes. The gravitational radiation produced by these Extreme Mass Ratio Inspirals (EMRIs) encodes a detailed map of the black hole geometry, and the detection and characterization of these signals is a major scientific goal for the LISA mission. The waveforms produced are very complex, and the signals need to be coherently tracked for hundreds to thousands of cycles to produce a detection, making EMRI signals one of the most challenging data analysis problems in all of gravitational wave astronomy. Estimates for the number of templates required to perform an exhaustive grid-based matched-filter search for these signals are astronomically large, and far out of reach of current computational resources. Here I describe an alternative approach that employs a hybrid between Genetic Algorithms and Markov Chain Monte Carlo techniques, along with several time saving techniques for computing the likelihood function. This approach has proven effective at the blind extraction of relatively weak EMRI signals from simulated LISA data sets.Comment: 10 pages, 4 figures, Updated for LISA 8 Symposium Proceeding

Forced motion near black holes

We present two methods for integrating forced geodesic equations in the Kerr spacetime, which can accommodate arbitrary forces. As a test case, we compute inspirals under a simple drag force, mimicking the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what is observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would provide clear evidence that the inspiral was occurring in a non-vacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In one method the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a generalization of earlier work by Pound and Poisson for planar forces in a Schwarzschild background.Comment: 28 pages, 2 figures, submitted to Phys. Rev. D; v2 has minor changes for consistency with published version, plus a new section discussing the relative advantages of the two approache

Cosmic Swarms: A search for Supermassive Black Holes in the LISA data stream with a Hybrid Evolutionary Algorithm

We describe a hybrid evolutionary algorithm that can simultaneously search for multiple supermassive black hole binary (SMBHB) inspirals in LISA data. The algorithm mixes evolutionary computation, Metropolis-Hastings methods and Nested Sampling. The inspiral of SMBHBs presents an interesting problem for gravitational wave data analysis since, due to the LISA response function, the sources have a bi-modal sky solution. We show here that it is possible not only to detect multiple SMBHBs in the data stream, but also to investigate simultaneously all the various modes of the global solution. In all cases, the algorithm returns parameter determinations within $5\sigma$ (as estimated from the Fisher Matrix) of the true answer, for both the actual and antipodal sky solutions.Comment: submitted to Classical & Quantum Gravity. 19 pages, 4 figure

Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time

Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics (orbits) in the outer region of a Kerr Black Hole, representing the space time created by a bigger object. In our paper we study the entire class of orbits, both of constant radius (spherical orbits), as well as non-null eccentricity orbits, showing a number of properties on the physical parameters and trajectories. The main result is the determination of the geometrical locus of all the orbits in the space of physical parameters in Kerr space-time. This becomes a powerful tool to know if different orbits can be connected by a continuous change of their physical parameters. A discussion on the influence of different values of the angular momentum of the hole is given. Main results have been obtained by analytical methods.Comment: 26 pages, 12 figure

On asymptotically flat solutions of Einstein's equations periodic in time I. Vacuum and electrovacuum solutions

By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.Comment: 25 pages, 2 figures, published in Class. Quant. Grav

Extreme Mass Ratio Inspirals: LISA's unique probe of black hole gravity

In this review article I attempt to summarise past and present-ongoing-work on the problem of the inspiral of a small body in the gravitational field of a much more massive Kerr black hole. Such extreme mass ratio systems, expected to occur in galactic nuclei, will constitute prime sources of gravitational radiation for the future LISA gravitational radiation detector. The article's main goal is to provide a survey of basic celestial mechanics in Kerr spacetime and calculations of gravitational waveforms and backreaction on the small body's orbital motion, based on the traditional `flux-balance' method and the Teukolsky black hole perturbation formalism.Comment: Invited review article, 45 pages, 23 figure

Spherical Universes with Anisotropic Pressure

Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.Comment: 24 pages, 11 figures, accepted for publication in Classical and Quantum Gravit

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA

Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany