@phdthesis{Paganini2018,
  author    = {Paganini, Claudio Francesco},
  title     = {The role of trapping in black hole spacetimes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-414686},
  school      = {Universit{\"a}t Potsdam},
  pages     = {v, 138},
  year      = {2018},
  abstract  = {In the here presented work we discuss a series of results that are all in one way or another connected to the phenomenon of trapping in black hole spacetimes. First we present a comprehensive review of the Kerr-Newman-Taub-NUT-de-Sitter family of black hole spacetimes and their most important properties. From there we go into a detailed analysis of the bahaviour of null geodesics in the exterior region of a sub-extremal Kerr spacetime. We show that most well known fundamental properties of null geodesics can be represented in one plot. In particular, one can see immediately that the ergoregion and trapping are separated in phase space. We then consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer. Therefore the topological structure of the trapped set on the celestial sphere of any observer is identical to that in Schwarzschild. We discuss how this is relevant to the black hole stability problem. In a further development of these observations we introduce the notion of what it means for the shadow of two observers to be degenerate. We show that, away from the axis of symmetry, no continuous degeneration exists between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore, except possibly for discrete changes, an observer can, by measuring the black holes shadow, determine the angular momentum and the charge of the black hole under observation, as well as the observer's radial position and angle of elevation above the equatorial plane. Furthermore, his/her relative velocity compared to a standard observer can also be measured. On the other hand, the black hole shadow does not allow for a full parameter resolution in the case of a Kerr-Newman-Taub-NUT black hole, as a continuous degeneration relating specific angular momentum, electric charge, NUT charge and elevation angle exists in this case. We then use the celestial sphere to show that trapping is a generic feature of any black hole spacetime. In the last chapter we then prove a generalization of the mode stability result of Whiting (1989) for the Teukolsky equation for the case of real frequencies. The main result of the last chapter states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation, and was recently used by Shlapentokh-Rothman (2015) for the scalar wave equation.},
  language  = {en}
}
@phdthesis{Cotesta2021,
  author    = {Cotesta, Roberto},
  title     = {Multipolar gravitational waveforms for spinning binary black holes and their impact on source characterization},
  doi       = {10.25932/publishup-50823},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-508236},
  school      = {Universit{\"a}t Potsdam},
  pages     = {XII, 274, LVI},
  year      = {2021},
  abstract  = {In the last five years, gravitational-wave astronomy has gone from a purerly theoretical field into a thriving experimental science. Several gravitational- wave signals, emitted by stellar-mass binary black holes and binary neutron stars, have been detected, and many more are expected in the future as consequence of the planned upgrades in the gravitational-wave detectors. The observation of the gravitational-wave signals from these systems, and the characterization of their sources, heavily relies on the precise models for the emitted gravitational waveforms. To take full advantage of the increased detector sensitivity, it is then necessary to also improve the accuracy of the gravitational-waveform models. In this work, I present an updated version of the waveform models for spinning binary black holes within the effective-one-body formalism. This formalism is based on the notion that the solution to the relativistic two- body problem varies smoothly with the mass ratio of the binary system, from the equal-mass regime to the test-particle limit. For this reason, it provides an elegant method to combine, under a unique framework, the solution to the relativistic two-body problem in different regimes. The main two regimes that are combined under the effective-one-body formalism are the slow-motion, weak field limit (accessible through the post-Newtonian theory), and the extreme mass-ratio regime (described using the black-hole- perturbation theory). This formalism is nevertheless flexible enough to integrate information about the solution to the relativistic two-body problem obtained using other techniques, such as numerical relativity. The novelty of the waveform models presented in this work is the inclusion of beyond-quadupolar terms in the waveforms emitted by spinning binary black holes. In fact, while the time variation of the source quadupole moment is the leading contribution to the waveforms emitted by binary black holes observable by LIGO and Virgo detectors, beyond-quadupolar terms can be important for binary systems with asymmetric masses, large total mass, or observed with large inclination angle with respect to the orbital angular momentum of the binary. For this purpose, I combine the approximate analytic expressions of these beyond-quadupolar terms, with their calculations from numerical relativity, to develop an accurate waveform model including inspiral, merger and ringdown for spinning binary black holes. I first construct this model in the simplified case of black holes with spins aligned with the orbital angular momentum of the binary, then I extend it to the case of generic spin orientations. Finally, I test the accuracy of both these models against a large number of waveforms obtained from numerical relativity. The waveform models I present in this work are the state of the art for spinning binary black holes, without restrictions in the allowed values for the masses and the spins of the system. The measurement of the source properties of a binary system emitting gravitational waves requires to compute O(107 - 109) different waveforms. Since the waveform models mentioned before can require O(1 - 10)s to generate a single waveform, they can be difficult to use in data-analysis studies given the increasing number of sources observed by the LIGO and Virgo detectors. To overcome this obstacle, I use the reduced-order-modeling technique to develop a faster version of the waveform model for black holes with spins aligned to the orbital angular momentum of the binary. This version of the model is as accurate as the original and reduces the time for evaluating a waveform by two orders of magnitude. The waveform models developed in this thesis have been used by the LIGO and Virgo collaborations in the inference of the source parameters of the gravitational-wave signals detected during the second observing run (O2), and first half of the third observing run (O3a) of LIGO and Virgo detectors. Here, I present a study on the source properties of the signals GW170729 and GW190412, for which I have been directly involved in the analysis. In addition, these models have been used by the LIGO and Virgo collaborations to perform tests on General Relativity employing the gravitational-wave signals detected during O3a, and to analyze the population of the observed binary black holes.},
  language  = {en}
}