Frontiers of Gravity: Astrophysical Environments, Ringdown Nonlinearities and the Semiclassical Approximation by Laura Sberna A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2020 c Laura Sberna 2020 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner: Vitor Cardoso Professor, Instituto Superior Tecnico, Departamento de Fsica Supervisor: Neil Turok Higgs Chair of Theoretical Physics, University of Edinburgh Senior Faculty member, Perimeter Institute for Theoretical Physics Professor of Physics, University of Waterloo Internal Members: Latham Boyle Junior Faculty member, Perimeter Institute for Theoretical Physics Robert Mann Professor of Physics, University of Waterloo Internal-External Member: Achim Kempf Professor, Applied Mathematics, University of Waterloo ii Author's Declaration This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions The material presented in this thesis is largely my own, and it includes the portions of co-authored publications to which I made significant contributions. Text taken from publications (pages listed below) is written in the voice of the publication authors. The remaining pages are my original work, written for this thesis. Chapter2 of this thesis consists of material from: publication [63] (pages 14{26), co- authored with A. Caputo, A. Toubiana, S. Babak, E. Barausse, S. Marsat and P. Pani; publication [224] (pages 28{29), co-authored with A. Toubiana, A. Caputo, G. Cusin, S. Marsat, K. Jani, S. Babak, E. Barausse, C. Caprini, P. Pani, A. Sesana and N. Tamanini; publication [212] (pages 29{36, 107{109), co-authored with A. Toubiana and C. Miller. Chapter3 of this thesis consists of ongoing research in collaboration with P. Bosch, W. East and L. Lehner. The numerical data used in Chapter3 was produced by P. Bosch, with code co-authored by P. Bosch, S. Green, L. Lehner and H. Roussille. Chapter4 of this thesis consists of material from the publication [240] (pages 68{80, 110{114), co-authored with Y. Yargic and A. Kempf. iv Abstract Einstein's general relativity is based on a tensorial, nonlinear equation for the spacetime metric. The gravitational interaction is however so weak that, in most circumstances, the equations can be solved perturbatively. This is true in early-time cosmology, for the inspiral of binary systems, and even after black holes merge, releasing the equivalent of multiple solar masses in gravitational waves. In this thesis, we analyze a range of problems that can be addressed assuming a background gravitational field and small fluctuations over it. We will progress from problems where the perturbative hypothesis can be tested and holds, to ones that begin to show nonlinear effects, ending with an application of perturbation theory to quantum gravity, where it is only a working hypothesis. We first analyze the dynamics of black hole binaries immersed in a dense gas environ- ment or interacting with a stellar companion. For binaries in a dense environment, we study the effect of accretion and dynamical friction on the gravitational wave emission. We derive the modification of the gravitational wave phase in the assumption of small accretion rates, and assess whether future gravitational wave observatories could detect this effect. For black holes in a binary with a white dwarf, we identify new evolutionary relations and propose a method to infer the black hole and white dwarf masses and their luminosity distance from the gravitational wave signal alone. Next, we study how isolated black holes react to perturbations, in the simplified setting of spherical symmetry and negative cosmological constant. We show that modes belonging to the linear spectrum can be excited nonlinearly. We further find that nonlinear effects can change the black hole mass at percent level, and that this effect can be explained by the flux of characteristic excitations through the black hole horizon. Finally, we propose a new definition of the semiclassical Einstein equations for cos- mological spacetimes. We propose that the source on the right hand side of the Einstein equations could be the amount of stress-energy above the instantaneous ground state. In this more speculative application, the linear order semiclassical approximation is not guar- anteed to hold. If our hypothesis were confirmed, however, the vacuum stress-energy above the instantaneous ground state would not renormalize the cosmological constant, hinting at a resolution of the longstanding problem connected to its observed value. v Acknowledgements I am grateful to my advisor, Neil Turok. Neil gave me the opportunity to come to Perimeter, together with many opportunities to travel and meet interesting physicists. He also inspired me to aim for the big, fundamental questions in physics and to not be afraid to go against the current, and taught me this through example. I am not sure I always followed his advice but thanks to him, I will keep striving to be a better scientist. I thank Angelika Fertig, Job Feldbrugge and Beatrice Bonga for their collaboration and support. I cherish the endless hours spent on a couch at Perimeter, working on projects that will soon see the light of day. I especially thank Angelika Fertig and Job Feldbrugge for their guidance in my first months as a PhD student. Andrea Caputo deserves the biggest thanks for academic collaboration { and a six- years-strong friendship. Andrea gave me a big push when my research had stalled. He will make for a great supervisor one day (very soon, if you've seen his publication list). Another special thanks goes to Alexandre Toubiana, for our fun collaborations that turned into a friendship, and to Cole Miller, for his amazingly supportive mentorship. I am also indebted to Jean-Luc Lehners for his collaboration and for hosting me at the Albert Einstein Institute on several occasions. Although science shouldn't be about people, working with people is what I enjoy the most about it. I sincerely thank all my close collaborators and mentors: Paolo Pani, Enrico Barausse, William East, Luis Lehner, Latham Boyle, Achim Kempf, Diego Blas, Mikhail Ivanov, Stas Babak, Yigit Yargic, Alice Di Tucci, Pablo Bosch and Enrico Cannizzaro. The international community at Perimeter Institute and in Kitchener-Waterloo made my stay in Canada joyful and unique. I thank Martina Canesi and Luca Dellantonio (my second home away from home), Jinglei Zhang, Alessandro Malus`a,Davide Racco, Flaminia Giacomini and Jan Haase; Angelika Fertig, Nils Wilde, Pablo Bosch, Nayeli Galindo, Beatrice Bonga, Nestor Ortiz, Will and Annie East, Job Feldbrugge and Nynke Niezink; Anna Heffernan and Max Corman; Dani Marcheva, Laura Bernard and Lena Funcke. I am so greatful to have met you all. My PhD started in the hardest time of my life so far. I thank my family, mia madre Maria Rita e mio fratello Francesco, for supporting me in this journey abroad despite our need for each other at home. I would not be who I am today without my family, and my life-long friends Letizia, Federica, Serena, Clara, Fabiana, Caterina, Oliviero and Gianluca, and Marco. vi I thank my partner Stephen Green, for the way we support, encourage and help each other in our academic endeavors. My peace of mind, my plans for the future { and my semi-fluent English { would not exist without him. I love you tortolito. vii To my father, who never tired of my first questions about the Universe viii Table of Contents List of Tables xi List of Figures xiii 1 Introduction: the frontiers of gravity1 1.1 Classical gravity.................................1 1.2 Quantum gravity................................5 1.3 Summary and outline..............................7 2 Astrophysical environments 10 2.1 Black holes in astrophysical environments................... 10 2.2 Mass accretion from the surrounding gas................... 13 2.2.1 Accretion in the gravitational waveform............... 13 2.2.2 First estimate of the effect of accretion................ 18 2.2.3 Fisher matrix and rates........................ 20 2.2.4 Prospects for multimessenger astronomy and conclusions...... 24 2.3 Dynamical friction............................... 26 2.4 Mass transfer from a stellar companion.................... 29 2.4.1 Evolution of mass transferring white dwarf-black hole binaries... 29 2.4.2 Evolutionary tracks relations...................... 33 2.4.3 Parameter estimation with LISA................... 34 2.4.4 Conclusions............................... 37 ix 3 Black hole ringdown 39 3.1 The problem: why so linear?.......................... 39 3.2 An investigation in a simplified setting.................... 43 3.2.1 Scalar field in a Schwarzschild-Anti de Sitter spacetime....... 43 3.2.2 Excitation coefficients and perturbation theory beyond linear order 44 3.2.3 The analysis............................... 49 3.2.4 Results: quasi normal mode perturbations.............. 50 3.2.5 Results: compact pulse perturbations................. 55 3.2.6 Theoretical predictions: area increase................. 57 3.3 Future prospects................................ 61 4 Semiclassical approximation