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Gravity As an Emergent Phenomenon: Fundamentals and Applications

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Gravity As an Emergent Phenomenon: Fundamentals and Applications Gravity as an emergent phenomenon: fundamentals and applications Ra´ulCarballo Rubio Universidad de Granada Programa de Doctorado en F´ısicay Matem´aticas Escuela de Doctorado de Ciencias, Tecnolog´ıase Ingenier´ıas Granada, 2016 Editor: Universidad de Granada. Tesis Doctorales Autor: Raúl Carballo Rubio ISBN: 978-84-9125-879-7 URI: http://hdl.handle.net/10481/43711 Gravity as an emergent phenomenon: fundamentals and applications Ra´ulCarballo Rubio1 In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Under the supervision of: Carlos Barcel´oSer´on1 Luis Javier Garay Elizondo2;3 1 Instituto de Astrof´ısicade Andaluc´ıa(IAA-CSIC), Glorieta de la Astronom´ıa,18008 Granada, Spain 2 Departamento de F´ısicaTe´oricaII, Universidad Complutense de Madrid, 28040 Madrid, Spain 3 Instituto de Estructura de la Materia (IEM-CSIC), Serrano 121, 28006 Madrid, Spain Consejo Superior de Investigaciones Cient´ıficas Estructuraci´onde contenidos en la memoria Los contenidos exigidos en una tesis doctoral en la Universidad de Granada para los pro- gramas de doctorado regulados por el RD99/2011 se encuentran en la presente memoria estructurados en las siguientes secciones: T´ıtulo Portada Compromiso de respeto de derechos de autor Compromiso de respeto de derechos de autor Resumen Resumen Introducci´on Introduction Objetivos Introduction, Secs. 1.1, 2.1, 3.1 and 4.1 Metodolog´ıa Secs. 1.2, 1.3, 2.2, 4.2, 4.3 and 4.4 Resultados Secs. 1.4, 1.5, 1.6, 2.3, 2.4, 2.5, 3.2, 3.3, 4.5 and 4.6 Conclusiones Secs. 1.7, 2.6, 3.4 and 4.7; Main conclusions and future directions Bibliograf´ıa Bibliography Resumen En esta tesis se ha realizado un estudio de distintos aspectos de la aproximaci´ona la construcci´onde una teor´ıade gravedad cu´antica conocida como gravedad emergente, con el objetivo de analizar preguntas fundamentales en el marco de este programa de investi- gaci´on,as´ıcomo posibles aplicaciones a problemas actuales de la f´ısicate´oricagravitacional. El objetivo principal de este programa de investigaci´ones la identificaci´onde mecanismos que den lugar de manera robusta a las propiedades observadas en la f´ısicade bajas en- erg´ıasconocida, descrita mediante la relatividad general y el modelo est´andarde f´ısica de part´ıculas.Las t´ecnicasutilizadas comprenden desde f´ısicade la materia condensada y sistemas de muchas part´ıculasno relativistas, hasta teor´ıacl´asicay cu´antica de campos (en espaciotiempos planos y curvos), teor´ıasde campos efectivas, geometr´ıaespaciotemporal y relatividad general. En la primera parte de la tesis, dividida en dos cap´ıtulos,se analiza la emergencia de las propiedades emergentes m´asrelevantes para la f´ısicade bajas energ´ıas: la simetr´ıade Lorentz y simetr´ıasinternas. En el primer cap´ıtulose expone en detalle la construcci´on de un modelo en el que se analiza la emergencia de la electrodin´amicacu´antica en una clase de universalidad de sistemas de muchas part´ıculas(fermi´onicasde esp´ın1/2) no rela- tivistas. La raz´onde considerar la interacci´onelectromagn´eticaen lugar de la gravitatoria se debe a la mayor simplicidad de la primera, lo cual hace natural su estudio como paso previo a la comprensi´onde situaciones m´ascomplejas. La elecci´onde modelo no rela- tivista inicial se basa en la aparici´on de puntos de Fermi en su espectro al producirse una transici´ona una fase superfluida. Se hace un uso extenso de t´ecnicasde aproximaci´on que han sido desarrolladas en paralelo al estudio experimental de las fases superfluidas del helio-3, en particular aquellas que presentan puntos de Fermi. En el segundo cap´ıtulo se estudia la propiedad m´asimportante que diferencia la interacci´ongravitatoria respecto de la electromagn´etica: su car´acterno lineal. Se revisa la determinaci´onde los v´ertices de interacci´on caracter´ısticosde la relatividad general mediante el denominado problema de autointeracci´onde gravitones. Por una parte, el inter´esde reexaminar este conocido problema aparece debido a recientes publicaciones que cuestionan la soluci´onest´andaral mismo. Por otra parte, su comprensi´onen detalle es de fundamental importancia para el programa de gravedad emergente. Las conclusiones obtenidas mediante un desarrollo minucioso del problema son comparadas con la extensa literatura al respecto. x Resumen La segunda parte de la tesis versa sobre dos aplicaciones de resultados espec´ıficosde la primera parte, a cada una de las cuales se le dedica un cap´ıtulocompleto. La primera de las aplicaciones concierne al conocido problema de la constance cosmol´ogica. En el cap´ıtulocorrespondiente se explica c´omola emergencia de estructuras relativistas y de la propia interacci´ongravitatoria permitir´ıaevadir el problema. Se demuestra expl´ıcitamente la existencia de una teor´ıade gravedad en la que la constante cosmol´ogicapuede entenderse como cualquier otra constante fundamental en f´ısica,sin incurrir en una tensi´onentre los principios de la relatividad general y las teor´ıas de campos efectivas. Por su parte, la segunda aplicaci´onata~nea la f´ısica de los agujeros negros. En el marco de gravedad emergente, se estudia la formulaci´ongeom´etricade una nueva propuesta que podr´ıaevitar los problemas de p´erdidade informaci´ony de formaci´onde singularidades en agujeros negros. En t´erminoscualitativos, las geometr´ıasconstruidas describen la transici´onentre una geometr´ıade agujero negro y una geometr´ıade agujero blanco en escalas de tiempo cortas, respecto a la escala de tiempo t´ıpica de un agujero negro en evaporaci´on. La discusi´ondetallada de la motivaci´ony las propiedades geom´etricasde esta propuesta es seguida de una exploraci´onde sus posibles implicaciones experimentales. List of publications The research activities reported in this thesis have resulted in the following articles and conference proceedings: Regular articles 12. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Black holes turn white fast, otherwise stay black: no half measures arXiv: [gr-qc/1511.00633] 11. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Where does the physics of extreme gravitational collapse reside? Invited submission to the special issue \Open Questions in Black Hole Physics" of Universe. [gr-qc/1510.04957] 10. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Uncovering the effective spacetime (Lessons from the effective field theory rationale) Honorable Mention in the 2015 GRF Awards for Essays on Gravitation. Int. J. Mod. Phys. D24 (2015) 1544019 [hep-th/1505.05315] 9. Ra´ulCarballo-Rubio Longitudinal diffeomorphisms obstruct the protection of vacuum energy Phys. Rev. D91 (2015) 124071 [gr-qc/1502.05278] 8. Carlos Barcel´o,Ra´ulCarballo-Rubio, Luis J. Garay and Gil Jannes The lifetime problem of evaporating black holes: mutiny or resignation Class. Quant. Grav. 32 (2015) 035012 [gr-qc/1409.1501] 7. Daniel N. Blaschke, Ra´ulCarballo-Rubio and Emil Mottola Fermion pairing and the scalar boson of the 2D conformal anomaly JHEP 1412 (2014) 153 [hep-th/1407.8523] 6. Carlos Barcel´o,Ra´ulCarballo-Rubio, Luis J. Garay and Gil Jannes Electromagnetism as an emergent phenomenon: a step by step guide New J. Phys. 16 (2014) 123028 [gr-qc/1407.6532] xiv List of publications 5. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Mutiny at the white-hole district Honorable Mention in the 2014 GRF Awards for Essays on Gravitation. Int. J. Mod. Phys. D23 (2014) 1442022 [gr-qc/1407.1391] 4. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Absence of cosmological constant problem in special relativistic field theory of gravity arXiv: [gr-qc/1401.2941] 3. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Unimodular gravity and general relativity from graviton self-interactions Phys. Rev. D89 (2014) 124019 [gr-qc/1401.2941] 2. Carlos Barcel´o,Ra´ulCarballo-Rubio, Luis J. Garay and Ricardo G´omez-Escalante Hybrid classical-quantum dynamics asks for hybrid notions Phys. Rev. A86 (2012) 042120 [quant-ph/1206.7036] 1. Carlos Barcel´o,Ra´ulCarballo-Rubio and Luis J. Garay Two formalisms, one renormalized stress-energy tensor Phys. Rev. D85 (2012) 084001 [gr-qc/1112.0489] Contributions to conferences with proceedings (speaker first) 4. Luis J. Garay, Carlos Barcel´o,Ra´ulCarballo-Rubio and Gil Jannes Do stars die too long? To appear in the MG14 proceedings volumes (published by World Scientific). 3. Ra´ulCarballo-Rubio, Carlos Barcel´oand Luis J. Garay Some not-so-common ideas about gravity J. Phys.: Conf. Ser. 626 (2015) 012010 2. Carlos Barcel´o,Ra´ulCarballo-Rubio, Luis J. Garay and Gil Jannes Do transient white holes have a place in nature? J. Phys.: Conf. Ser. 600 (2015) 012033 1. Ra´ulCarballo-Rubio, Carlos Barcel´oand Luis J. Garay Absence of cosmological constant problem in special relativistic field theory of gravity: one-loop renormalization group J. Phys.: Conf. Ser. 600 (2015) 012032 Contents Introduction 5 Notation and conventions 11 I Fundamentals 13 1 Lessons from emergent electrodynamics 15 1.1 Emergence and many-body systems . 15 1.2 An updated Maxwell fluid model . 19 1.3 Model based on Helium{3 . 25 1.3.1 Non-interacting fermions: the Fermi surface . 25 1.3.2 Microscopic (He{3)-like systems . 28 1.3.3 A weakly interacting gas . 29 1.3.4 Condensation and order parameters . 32 1.3.5 Ginzburg-Landau minimization . 33 1.3.6 Fermi points . 35 1.4 Fermion fields . 38 1.4.1 The emergent Dirac equation . 38 1.4.2 Internal observers . 41 1.4.3 The emergence of charge . 42 1.5 Electromagnetic fields . 44 1.5.1 Textures . 45 1.5.2 Kinematical gauge symmetry . 48 1.6 The low-energy effective field theory . 50 1.6.1 Regime of applicability and effective action .
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