The main purpose of this work is to study the collision of two black holes and the energy loss due to the gravitational waves emitted during this collision in the framework of general relativity. For this purpose we first study plane wave geometries and their collisions. More realistic collisions are the pp-wave collisions. As an analytic treatment of this problem, we investigate the head-on collision of two ultra-relativistic black holes. Treating the problem perturbatively, we extract the news function to compute how much energy is radiated in gravitational waves during the process. We show that the news function vanishes for the solutions obtained meaning that there is no mass-loss at the order of approximation.

One of the most important predictions of General Relativity, Einstein’s theory of gravity, is the existence of gravitational radiation. The strongest source of such radiation is expected to come from the merging of black holes. Upgrades to large ground based interferometric detectors (LIGO, VIRGO, GEO 600) have increased their sensitivity to the point that the first direct observation of a gravitational wave is expected to occur within the next few years. The chance of detection is greatly improved by the use of simulated waveforms which can be used as templates for signal processing. Recent advances in numerical relativity have allowed for long stable evolution of black hole mergers and the generation of expected waveforms. openGR is a modular, open framework black hole evolution code developed at The University of Texas at Austin Center for Relativity. Based on the BSSN (strongly hyperbolic) formulation of Einstein’s equations and the moving puncture method, we are able to model the evolution of a binary black hole system through the merger and extract the gravitational radiation produced. Although we are generally interested in binary interactions, openGR is capable of handling any number of black holes. This work serves as an overview of the capabilities of openGR and a demonstration of the physics it can be used to explore. / text

This thesis deals with two classes of space-time symmetries: emergent symmetries in the near-horizon region of rapidly rotating Kerr black holes and residual gauge symmetries. The main aim of the thesis is to investigate consequences and effects of these symmetries on black holes and gravitational radiation. The first class of symmetries is exploited to address questions of astrophysical relevance for force-free magnetospheres, thin accretion discs, and strong magnetic fields around Kerr black holes. We investigate how the dynamics of electromagnetic and matter fields is constrained by global conformal symmetries of the near-horizon geometry. In the context of force-free electrodynamics, we find exact solutions and classify them according to the highest weight representation of the isometry group. We introduce novel criteria to distinguish physical solutions and deduce bounds on conformal weights of electromagnetic fields. For thin accretion discs, within the Novikov-Thorne model, new properties arise in the high spin regime of the Kerr black hole. We find a novel self-similar solution and we explain the critical behaviour of the observables by symmetry arguments. Afterwards, we study an exact analytic solution to the Einstein-Maxwell theory. It describes a black hole immersed in a strong magnetic field and it shares the same near-horizon geometry of extreme Kerr black holes. We compute its total conserved mass by means of the covariant phase space formalism and study its thermodynamics. The second class of symmetries is considered in order to provide a new definition of gravitational multipole moments by means of Noether charges and by adopting the covariant phase space formalism. We show that such a definition in terms of Noether charges reproduces multipole moments in General Relativity. We propose to apply it to an arbitrary generally covariant metric theory of gravity. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

In this report, we analyze general relativistic effects on celestial bodies, including gravitational strength in different metrics, gravitational radiation, and frame-dragging. We present simulation methods for classical and general relativistic motion, through the use of systems of equations that may be numerically integrated. The amount of energy leaving the system as gravitational radiation is approximated using the quadrupole formula, and by using a binary pair of planetary bodies as an approximation for orbital motion. Here we demonstrate that classical approximations may be suitable in low-mass high-distance scenarios. The eccentricity of an orbit also affects the gravitational radiation and would have to be much less than one for reliable results. It is concluded that frame-dragging effects are negligible for slowly rotating objects only, which is a well-known result.

Boosted black holes play an important role in General Relativity (GR), especially in relation to the binary black hole problem. Solving Einstein vacuum equations in the strong field regime had long been the holy grail of numerical relativity until the significant breakthroughs made in 2005 and 2006. Numerical relativity plays a crucial role in gravitational wave detection by providing numerically generated gravitational waveforms that help search for actual signatures of gravitational radiation exciting laser interferometric detectors such as LIGO, VIRGO and GEO600 here on Earth. Binary black holes orbit each other in an ever tightening adiabatic inspiral caused by energy loss due to gravitational radiation emission. As the orbits shrinks, the holes speed up and eventually move at relativistic speeds in the vicinity of each other (separated by ~ 10M or so where 2M is the Schwarzschild radius). As such, one must abandon the Newtonian notion of a point mass on a circular orbit with tangential velocity and replace it with the concept of black holes, cloaked behind spheroidal event horizons that become distorted due to strong gravity, and further appear distorted because of Lorentz effects from the high orbital velocity. Apparent horizons (AHs) are 2-dimensional boundaries that are trapped surfaces. Conceptually, one can think of them as 'quasi-local' definitions for a black hole horizon. This will be explained in more detail in chapter 2. Apparent horizons are especially important in numerical relativity as they provide a computationally efficient way of describing and locating a black hole horizon. For a stationary spacetime, apparent horizons are 2-dimensional cross-sections of the event horizon, which is itself a 3-dimensional null surface in spacetime. Because an AH is a 2-dimensional cross-section of an event horizon, its area remains invariant under distortions due to Lorentz boosts although its shape changes. This fascinating property of the AH can be attributed to the fact that it is a cross-section of a null surface, which, under the boost, still remains null and the total area does not change. Although this invariance of the area is conceptually easy to see it is less straightforward to derive this result. We present two different ways to show the area invariance. One is based on the spin-boost transformation of the null tetrad and the other a direct coordinate transformation of the boosted metric under the Lorentz boost. Despite yielding identical results the two methods differ significantly and we elaborate on this in much more detail. We furthermore show that the use of the spin-boost transformation is not well-suited for binary black hole spacetime and that the spin-boost is fundamentally different from a Lorentz boost although the transformation equations look very similar. We also provide a way to visualize the distorted horizons and look at the multi-pole moments of these surfaces under small boosts. We finish by summarizing our main results at the end and by commenting on the binding energy of the binary and how the apparent horizon is distorted due to presence of another black hole. / text

While general relativity is a very successful theory of gravity, having thus far passed all observational tests with flying colors, it is thought to be incomplete. Indeed, we lack an ultimate high energy theory in which general relativity and quantum mechanics are both valid. We consider extensions to the action of general relativity, and seek to place constraints on these alternative theories using astrophysical tests. General relativity has been extensively tested in the solar system, but not with precision in strong gravity systems. We discuss constraints that could be placed on alternative theories using neutron stars. We find that we may not be able to distinguish between general relativity and some alternative theories in the spacetimes around black holes. We also discuss constraints from cosmological tests, and show that instabilities can appear.Adding higher-order terms to the action of general relativity can introduce new dynamical degrees of freedom and instabilities. From the standpoint of effective field theory however, these alternative theories are inconsistent because they are not unitary. In an effective field theory, no new degree of freedom is introduced. This also means that extra polarizations of gravitational waves, which are predicted by some alternative theories, would not be present in an effective field theory.We then consider an effective field theoretic formulation for gravitational radiation called Non-Relativistic General Relativity (NRGR). We study the gravitational wave emission in non-relativistic coalescing compact binaries, which are thought to be powerful emitters of gravitational waves. While NRGR is based on the post-newtonian (PN) approximation to general relativity, and should therefore be in complete agreement with other post-newtonian methods, the effective field theory approach provides two major advantages: it provides a consistent framework for the dynamics using a lagrangian formulation; also, one can in principle compute observables to all orders in the orbital velocity in a systematic way. We provide a brief overview of NRGR methods, and present the NRGR calculation of the subleading spin-orbit correction to the newtonian potential.

General relativity (GR) has stood as the most accurate description of gravity for the last 100 years, weathering a barrage of rigorous tests. However, attempts to derive GR from a more fundamental theory or to capture further physical principles at high energies has led to a vast number of alternative gravity theories. The individual examination of each gravity theory is infeasible and as such a systematic method of examining modified gravity theories is a necessity. Studying generic classes of gravity theories allows for general statements about observables to be made independent of explicit models. Take, for example, those models described by the Horndeski action, the most general class of scalar-tensor theory with at most second-order derivatives in the equations of motion, satisfying theoretical constraints. But these constraints alone are not enough for a given modified gravity model to be physically viable and hence worth studying. In particular, observations place incredibly tight constraints on the size of any deviation in the solar system. Hence, any modified gravity would have to mimic GR in such a situation. To accommodate this requirement, many models invoke screening mechanisms which suppress deviations from GR in regions of high density. But these mechanisms really upon non-linear effects and so studying them in complex models is mathematically complex. To constrain the space of actions of Horndeski type to those which pass solar-system tests, a set of conditions on the four free functions of the Horndeski action are derived which indicate whether a specific model embedded in the action possesses a GR limit. For this purpose, a new and surprisingly simple scaling method is developed, identifying dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified gravity action. Solutions to the dominant terms identify regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can determine whether the recovery of Einstein's field equations can be attributed to a genuine screening effect. The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. This is through parameterising common perturbations of the metric found when performing a post-Newtonian expansion. The framework is adapted by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. Screening mechanisms of modified gravity theories can then be incorporated into the PPN framework through further developing the scaling method into a perturbative series. The PPN functions are found through a combination of the scaling method with a post-Newtonian expansion within a screened region. For illustration, we show that both a chameleon and cubic galileon model have a limit where they recover GR. Moreover, we find the effective gravitational constant and all PPN functions for these two theories in the screened limit. To examine how the adapted formalism compares to solar-system tests, we also analyse the Shapiro time delay effect for these two models and find no deviations from GR insofar as the signal path and the perturbing mass reside in a screened region of space. As such, tests based upon the path light rays such as those done by the Cassini mission do not constrain these theories. Finally, gravitational waves have opened up a new regime where gravity can be tested. To this end, we examine how the generation of gravitational waves are affected by theories of gravity with screening to second post-Newtonian (PN) order beyond the quadrupole. This is done for a model of gravity where the black hole binary lies in a screened region, while the space between the binary's neighbourhood and the detector is described by Brans-Dicke theory. We find deviations at both 1.5 and 2 PN order. Deviations of this size can be measured by the Advanced LIGO gravitational wave detector highlighting that our calculation may allow for constraints to be placed on these theories. We model idealised data from the black hole merger signal GW150914 and perform a best fit analysis. The most likely value for the un-screened Brans-Dicke parameter is found to be ω = -1:42, implying on large scales gravity is very modified, incompatible with cosmological results.

Gravitation is the dominant influence in most astrophysical interactions. Weak-field interactions have been extensively studied, but the strong-field regime remains largely unexplored. Gravitational waves (GWs) are an excellent means of accessing strong-field regions. We investigate what we can learn about both astrophysics and gravitation from strong-field tests and, in particular, GWs; we focus upon extreme-mass-ratio (EMR) systems where a small body orbits a much more massive one. EMR bursts, a particular class of GW signals, could be used to determine the properties of massive black holes (MBHs). They could be detectable with a space-borne interferometer from many nearby galaxies, as well as the Galactic centre. Bursts could provide insightful constraints on the MBHs' parameters. These could elucidate the formation history of the MBHs and, by association, their host galaxies. The Galactic centre is the most promising source. Its event rate is determined by the stellar distribution surrounding the MBH; the rate is not high, but we still expect to gain useful astronomical information from bursts. Strong-field tests may reveal deviations from general relativity (GR). We calculate modifications that could be observed assuming metric f(R)-gravity as an effective alternative theory. Gravitational radiation is modified, as are planetary precession rates. Both give a means of testing GR. However, existing laboratory measurements already place tighter constraints on f(R)-gravity, unless there exists a screening effect, such as the chameleon mechanism, which suppresses modifications on small scales. To make precision measurements of astrophysical systems or place exacting bounds on deviations from GR, we must have accurate GW templates. Transient resonances are currently not included in the prescription for generating EMR inspiral waveforms. Their effects can be estimated from asymptotic expansions of the evolving orbital parameters. The quantitative impact on parameter estimation has yet to be calculated, but it appears that it shall be necessary to incorporate resonances when creating inspiral waveforms.

We have released maps and data for five years of observation of the cosmic microwave background with the Wilkinson Microwave Anisotropy Probe (WMAP) and I will review the main results in this talk. A simple 6 parameter cosmological model continues to be an excellent fit to the CMB data and to our data in conjunction with other astrophysical measurements. In particular a running spectral index is not supported by the data, and constraints that the Universe is spatially flat have increased in precision. Increased sensitivity and improvements in our understanding of the instrumental beam shape have allowed us to measure for the first time a cosmic neutrino background. Neutrinos de-coupled from other matter earlier than photons did. While they are expected to have a 2 Kelvin thermal distribution today, they comprised 10% of the energy density of the Universe at the epoch of photon de-coupling. The data also allow tighter constraints on the shape of the inflationary potential via the amplitude of a gravitational wave background new constraints on features of cosmic axions. Recorded at TRIUMF on Thursday April 17, 2008.

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