Durham E-Theses Black holes, vacuum decay and thermodynamics CUSPINERA-CONTRERAS, JUAN,LEOPOLDO How to cite: CUSPINERA-CONTRERAS, JUAN,LEOPOLDO (2020) Black holes, vacuum decay and thermodynamics, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/13421/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk Black holes, vacuum decay and thermodynamics Juan Leopoldo Cuspinera Contreras A Thesis presented for the degree of Doctor of Philosophy Institute for Particle Physics Phenomenology Department of Physics University of Durham England September 2019 To my family Black holes, vacuum decay and thermodynamics Juan Leopoldo Cuspinera Contreras Submitted for the degree of Doctor of Philosophy September 2019 Abstract In this thesis we study two fairly different aspects of gravity: vacuum decay seeded by black holes and black hole thermodynamics. The first part of this work is devoted to the study of black holes within the (higher dimensional) Randall- Sundrum braneworld scenario and their effect on vacuum decay rates. We argue that, in close parallel to the 4-dimensional case, the decay rate is given by the difference in areas between the seeding and remnant black holes. We follow a brane approach to study the effective equations on the brane and focus on the tidal solution given by Dadhich et al. We solve numerically the equations of motion of a Higgs- like scalar field and obtain its decay rate. We then compare it to the Hawking evaporation rate and find that black holes of certain masses are likely to trigger vacuum decay. Finally, we study decay in the absence of a black hole and determine that, in close analogy to the 4-dimensional case, it is the presence of the black hole that enhances vacuum decay rates. The second part of this thesis discusses the thermodynamics of charged, rotating, accelerating AdS black holes. We impose sensible physical restrictions to the black hole metric and translate them into bounds of the black hole parameter space. We discuss the implications of having an exothermic term in the definition of enthalpy. We then focus on critical black holes, i.e. spacetimes in which at least one of the sides of the black hole's rotation axis has a conical deficit of 2π. Finally, we consider the Penrose process for neutrally charged critical black holes and discuss about the definition of efficiency in this process. Declaration The work in this thesis is based on research carried out at the Institute for Particle Physics Phenomenology, the Department of Physics, at Durham University and funded by the Consejo Nacional de Ciencia y Tecnolog´ıa(CONACyT). No part of this thesis has been submitted elsewhere for any other degree or qualification and it is all my own work unless referenced to the contrary in the text. The results presented have in part already appeared in the following publications: • L. Cuspinera, R. Gregory, K. Marshall and I. G. Moss, Higgs Vacuum Decay from Particle Collisions?, Phys. Rev. D99 (2019) 024046,[1]. In this paper I was instrumental in developing an accurate argument for the calculation of the instanton action and confirmed separately the numerical results obtained. • L. Cuspinera, R. Gregory, K. M. Marshall and I. G. Moss, Higgs Vacuum Decay in a Braneworld, IJMPD (2019) 2050005,[2]. In this project I confirmed, checked and collaborated in the numerical imple- mentation of all the expressions used in this work. • M. Appels, L. Cuspinera, R. Gregory, P. Krtouˇs,D. Kubizˇn´ak, Are Superen- tropic black holes superentropic?,[3]. For this paper I was involved in every part of this work, I led the development of the parameter space and examined the implications of the exotermic term in the enthalpy for a Penrose process of critical black holes. Copyright c 2019 by Juan Leopoldo Cuspinera Contreras. \The copyright of this thesis rests with the author. No quotations from it should be published without the author's prior written consent and information derived from it should be acknowledged". Acknowledgements He aqu´ıel ep´ıtomede cuatro a~nosde trabajo, resumidos en unas cuantas p´aginas dedicadas a mi familia, que comienza en mis padres y mis hermanos. Ustedes son mi pilar y mi ra´ızy con ello son tambi´en gran parte de qui´ensoy y de lo mucho o poco que he podido lograr. Gracias por su apoyo que ha sido mi fuerza en innumerables ocasiones y su por cari~noincondicional, que siempre me ha alentado a continuar en el camino cuando ´esteha sido dif´ıcil. This thesis is the direct result of 4 years of work on physics. During this time I have met wonderful people with whom I'll always be grateful. Of them, I am most thankful to my supervisor Ruth Gregory, who gave me the opportunity to work with her, introduced me to some of the brightest minds in physics and helped me when I went astray in physics or got stuck at an airport. I'd like to thank you for your guidance, your patience to answer some of my questions and for laughing off half a bottle of ketchup in your blouse. I would also like to thank Ian Moss for always having time to discuss our projects, look at some code or organising the annual summer barbecues. Since the first days of my stay at Durham I have always been lucky to find interesting, warm and caring people that became my family away from M´exico. Special thanks to Akash, Mike and Omar with whom I'll forever share some of my dearest memories of the time I lived at Durham (from Capriccio Mondays to Pancake Sundays, beers at HoS, games of chess or Catan, countless old fashions, barbecues and our travels to Canada). I would also like to thank the great people with whom I shared this last year: Emmanuel, Tobi, Glover, Pedro, M´onica,Fernando, Oscar´ and all the people that gave me the opportunity to teach them how to play dominoes. Leaving Durham will be specially hard because of you all but I am sure we will meet again. Per concludere, vorrei dire che questa tesi `ededicata sopratutto a te Carlotta che sei la mia famiglia, quella che nasce spontaneamente da un amore immenso. La tua presenza `estata fondamentale non solo per non impazzire mentre finivo di scrivere questa tesi ma anche perch´ela tua pazienza, la tua cura ed il tuo amore mi hanno reso sempre un po' pi`ufelice. Grazie mille per quella gioia di vita che solo tu mi dai. Adesso mi amor, non ci sono parole che possano esprimere l'emozione di iniziare questa nuova tappa della nostra vita in cui andremo insieme a scoprire il mondo. E` proprio in questo momento di bella incertezza in cui sono sicuro che prendendoti la mano troveremo sempre il nostro posto, la nostra gente e la nostra felicit`a.Ti amo vera e profondamente Cucciolina. Contents Abstractv Declaration vii Acknowledgements ix Contents xi List of Figures xiii 1 Introduction3 1.1 Vacuum decay in quantum mechanics...........................7 1.1.1 Simple Harmonic Oscillator.............................. 10 1.1.2 The bounce........................................... 11 1.2 Vacuum decay in QFT........................................ 15 1.2.1 The thin-wall limit..................................... 21 1.3 Inclusion of gravity........................................... 24 2 Branes 29 2.1 Hypersurfaces................................................ 29 2.2 Lower dimensional decomposition of General Relativity............ 32 2.3 The Randall-Sundrum model................................... 35 2.4 SMS formalism............................................... 39 3 Vacuum Decay in Higher Dimensions 43 3.1 Motivation................................................... 43 3.2 Vacuum decay around higher dimensional black holes.............. 47 3.2.1 Brane-black hole action................................. 50 3.2.2 Tidal black hole bubbles................................ 61 3.3 Vacuum decay on a brane...................................... 73 3.3.1 The Scalar Brane Instanton.............................. 76 3.3.2 Computation of the action............................... 78 3.4 Discussion................................................... 81 4 Critical Black Hole Thermodynamics 85 4.1 Accelerated black holes........................................ 89 4.1.1 The generalized C-metric................................ 89 4.1.2 Coordinate ranges and parametric restrictions.............. 91 4.1.3 The conical defect...................................... 95 4.2 Critical black holes........................................... 97 4.3 Thermodynamics of Critical Black Holes......................... 99 4.3.1 Thermodynamics of accelerated black holes................ 99 4.3.2 Thermodynamics of super-entropic black holes............. 102 4.3.3 The Reverse Isoperimetric Inequality...................... 104 4.3.4 The critical limit....................................... 105 4.4 The Penrose process for critical black holes....................... 106 4.5 Conclusions.................................................. 110 5 Concluding remarks 113 List of Figures 1.1 In the SHO the only solution for a particle to start at the bottom of the potential and remain there is the trivial one................... 11 1.2 Potential energy as a function of position for a quantum mechanical particle in a barrier. Notice that we have plotted −V , which has a false vacuum at q = 0 and an \exit" point q∗ s.t. V (q∗) = 0......... 12 1.3 A quantum field with energy E = 0 described by this potential V will transition from the false vacuum to the true vacuum state by tunnelling from φFV to φc and then evolving classically towards φTV .