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Uwaterloo Latex Thesis Template Explorations in black hole chemistry and higher curvature gravity by Robie Hennigar 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, 2018 c Robie Hennigar 2018 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: Don Page Professor, University of Alberta Supervisor: Robert Mann Professor, University of Waterloo Internal Member: Niayesh Afshordi Professor, University of Waterloo Internal-External Member: Achim Kempf Professor, University of Waterloo Committee Member: Robert Myers Professor, Perimeter Institute for Theoretical Physics, University of Waterloo ii 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 This thesis is based on the following published and forthcoming articles. • Chapter3 is based on: { R. A. Hennigar, D. Kubiznak and R. B. Mann, Entropy Inequality Violations from Ultraspinning Black Holes, Phys. Rev. Lett. 115 (2015) 031101, [1411.4309] { R. A. Hennigar, D. Kubiznak, R. B. Mann and N. Musoke, Ultraspinning limits and super-entropic black holes, JHEP 06 (2015) 096, [1504.07529] { R. A. Hennigar, D. Kubiznak, R. B. Mann and N. Musoke, Ultraspinning lim- its and rotating hyperboloid membranes, Nucl. Phys. B903 (2016) 400{417, [1512.02293] • Chapter4 is based on: { R. A. Hennigar and R. B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D95 (2017) 064055, [1610.06675] { R. A. Hennigar, D. Kubiznak and R. B. Mann, Generalized quasitopological gravity, Phys. Rev. D95 (2017) 104042, [1703.01631] { J. Ahmed, R. A. Hennigar, R. B. Mann and M. Mir, Quintessential Quartic Quasi-topological Quartet, JHEP 05 (2017) 134, [1703.11007] { R. A. Hennigar, Criticality for charged black branes, JHEP 09 (2017) 082, [1705.07094] { R. A. Hennigar, M. B. J. Poshteh and R. B. Mann, Shadows, Signals, and Stabil- ity in Einsteinian Cubic Gravity, Phys. Rev. D97 (2018) 064041, [1801.03223] { P. Bueno, P. A. Cano, R. A. Hennigar and R. B. Mann, NUTs and bolts beyond Lovelock, [1808.01671] { P. Bueno, P. A. Cano, R. A. Hennigar and R. B. Mann, Universality of squashed- sphere partition functions, [1808.02052] { R. A. Hennigar, M. Lu and R. B. Mann, Five-dimensional generalized quasi- topological gravities, In preparation, 2018 { M. Mir, R. A. Hennigar, R. B. Mann and J. Ahmed, Chemistry and holography in generalized quasi-topological gravity, In preparation, 2018 iv • Chapter5 is based on: { R. A. Hennigar, R. B. Mann and E. Tjoa, Superfluid Black Holes, Phys. Rev. Lett. 118 (2017) 021301, [1609.02564] { R. A. Hennigar, E. Tjoa and R. B. Mann, Thermodynamics of hairy black holes in Lovelock gravity, JHEP 02 (2017) 070, [1612.06852] { H. Dykaar, R. A. Hennigar and R. B. Mann, Hairy black holes in cubic quasi- topological gravity, JHEP 05 (2017) 045, [1703.01633] • Contributions not included in the thesis: { R. A. Hennigar, W. G. Brenna and R. B. Mann, P v criticality in quasitopological gravity, JHEP 07 (2015) 077, [1505.05517] { R. A. Hennigar and R. B. Mann, Reentrant phase transitions and van der Waals behaviour for hairy black holes, Entropy 17 (2015) 8056{8072, [1509.06798] { R. A. Hennigar, R. B. Mann and S. Mbarek, Thermalon mediated phase transi- tions in Gauss-Bonnet gravity, JHEP 02 (2016) 034, [1512.02611] { R. A. Hennigar, F. McCarthy, A. Ballon and R. B. Mann, Holographic heat engines: general considerations and rotating black holes, Class. Quant. Grav. 34 (2017) 175005, [1704.02314] { L. J. Henderson, R. A. Hennigar, R. B. Mann, A. R. H. Smith and J. Zhang, Harvesting Entanglement from the Black Hole Vacuum, 1712.10018 { P. A. Cano, R. A. Hennigar and H. Marrochio, Complexity Growth Rate in Lovelock Gravity, 1803.02795 v Abstract This thesis has two goals. The primary goal is to communicate two results within the framework of black hole chemistry, while the secondary goal is concerned with higher curvature theories of gravity. Super-entropic black holes will be introduced and discussed. These are new rotating black hole solutions that are asymptotically (locally) anti de Sitter with horizons that are topologically spheres with punctures at the north and south poles. The basic properties of the solutions are discussed, including an analysis of the geometry, geodesics, and black hole thermodynamics. It is found that these are the first black hole solutions to violate the reverse isoperimetric inequality, which was conjectured to bound the entropy of anti de Sitter black holes in terms of the thermodynamic volume. Implications of this result for the inequality are discussed. The second main result is a new phase transition in black hole thermodynamics: the λ-line. This is a line of second order (continuous) phase transitions with no associated first order phase transition. The result is illustrated for black holes in higher curvature gravity | cubic Lovelock theory coupled to real scalar fields. The properties of the black holes exhibiting the transition are discussed and it is shown that there are no obvious pathologies associated with the solutions. The features of the theory that allow for the transition are analyzed and then applied to obtain a further example in cubic quasi-topological gravity. The secondary goal of the thesis is to discuss higher curvature theories of gravity. This serves as a transition between the discussion of super-entropic black holes and λ-lines but also provides an opportunity to discuss recent work in the area. Higher curvature theories are introduced through a study of general theories on static and spherically symmetric spacetimes. It is found that there are three classes of theories that have a single indepen- dent field equation under this restriction: Lovelock gravity, quasi-topological gravity, and generalized quasi-topological gravity, the latter being previously unknown. These theories admit natural generalizations of the Schwarzschild solution, a feature that turns out to be equivalent to a number of other remarkable properties of the field equations and their black hole solutions. The properties of these theories are discussed and their applicability as toy models in gravity and holography is suggested, with emphasis on the previously unknown generalized quasi-topological theories. vi Acknowledgements During my time at the University of Waterloo, I have had the privilege of learning a great deal from very smart people. While I am grateful to all those who have served as a mentor to me in some capacity, I would especially like to single out three individuals. First, is my supervisor Robb Mann who in addition to being an excellent and kind teacher, has always provided superb guidance in both research and professional matters. I owe the very fact that I have been able to study topics in theoretical physics to him | Robb, thanks for responding positively to that email sent to you by a naive little physical chemist who wanted to learn about black holes! Second, I would like to acknowledge Eduardo Mart´ın-Mart´ınez. While I have learned a great deal from Edu concerning relativistic quantum information, I have been particularly inspired by his enthusiasm for science and his dedication to creating a comfortable and effective environment for his students. I hope that if I am lucky enough to one day have a group of my own that I can implement some of the same ideas in my own approach to supervision. Finally, I would like to acknowledge the mythical David Kubizˇn´ak.David was my first collaborator when I was still very new in the field of physics and was always kind to me when I made mistakes. I have learned a lot from David | his careful attention to detail in research, his sense of humour, and his positive yet honest outlook have left lasting impressions on me. Also, I think it is only fitting that, in David's honour, I have submitted this thesis on a Friday. I would like to thank all of the friends, collaborators, and students who have made research and life (though, is there really a distinction at this point?) much more fun: Connor Adair, Jamil Ahmed, Aida Ahmadzadegan, Natacha Altamirano, Alvaro Ballon, Wilson Brenna, Kris Boudreau, Pablo Cano, Alex Chase, Paulina Corona Ugalde, Michael Deveau, Hannah Dykaar, Dan Grimmer, Zhiwei Gu, Laura Henderson, Raines Heath, Christine Kaufhold, Mengqi Lu, Saoussen Mbarek, Fiona McCarthy, Hugo Marrochio, Michael Meiers, Mozhgan Mir, Nathan Musoke, Mohammad Poshteh, Ethan Purdy, Allison Sachs, Turner Silverthorne, Alex Smith, Erickson Tjoa, and Jialin Zhang. Erickson and Hugo get a special bonus thanks for carefully reading drafts of this thesis and providing feedback. I would like to thank my family for their support. My parents, Sharon and Brady, my brother, William, my uncle, Opie, and my grandparents, Edgar and Hazel, and Ella Mae. You have all provided inspiration for my work. Finally, I would like to say thank you to my partner, Emily Lavergne. Your support has had an enormous influence on my well-being during my time in Waterloo. Thank you for listening to me babble about exciting new results, and listening to me complain when everything goes wrong. You have enriched my life. vii Table of contents List of tables xi List of figures xii Notation and conventions xiii 1 Introduction1 1.1 Welcome to anti de Sitter space........................2 1.2 Black hole thermodynamics in anti de Sitter space..............3 1.3 The role of anti de Sitter space in physics...................6 1.4 Plan of the thesis................................8 2 The foundations of black hole chemistry 10 2.1 Black holes and thermodynamics......................
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