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The Large Numbers Hypothesis: Outline of a Self-Similar Quantum
The Large Numbers Hypothesis: Outline of a self-similar quantum-cosmological Model H. GENREITH ∗ Institut f¨ur Geophysik und Meteorologie der Universit¨at zu K¨oln Abstract leads to a scaled quantum of action 3 In 1919 A. Einstein suspected first that gravita- H =Λ h (2) · tional fields could play an essential role in the in order to handle the Universe like an elementary structure of elementary particles. In 1937, P.A.M. particle. Hence the Universe should have an angu- Dirac found a miraculous link between the prop- lar momentum of about H/2π and it can be sus- erties of the visible Universe and elementary par- pected to be a huge rotating black-hole close to its ticles. Both conjectures stayed alive through the Kerr limit, or close to G¨odel’s spin [1, 2, 35, 10], following decades but still no final theory could be which is the value for the rotating cosmological so- derived to this issues. The herein suggested frac- lution to Einstein’s equations of General Relativity. tal model of the Universe gives a consistent expla- The recent discussion regarding the origin of and nation to Dirac’s Large Numbers Hypothesis and destiny of the Universe raises, for example, the combines the conjectures of Einstein and Dirac. question of where the Universe comes from. The main explanation for this is that time and space 1 Introduction were created with the big-bang and therefore the question of where the Universe is embedded or what 1.1 The Large Numbers Hypothesis happened before the creation, is not admissible. -
University of California Santa Cruz Quantum
UNIVERSITY OF CALIFORNIA SANTA CRUZ QUANTUM GRAVITY AND COSMOLOGY A dissertation submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in PHYSICS by Lorenzo Mannelli September 2005 The Dissertation of Lorenzo Mannelli is approved: Professor Tom Banks, Chair Professor Michael Dine Professor Anthony Aguirre Lisa C. Sloan Vice Provost and Dean of Graduate Studies °c 2005 Lorenzo Mannelli Contents List of Figures vi Abstract vii Dedication viii Acknowledgments ix I The Holographic Principle 1 1 Introduction 2 2 Entropy Bounds for Black Holes 6 2.1 Black Holes Thermodynamics ........................ 6 2.1.1 Area Theorem ............................ 7 2.1.2 No-hair Theorem ........................... 7 2.2 Bekenstein Entropy and the Generalized Second Law ........... 8 2.2.1 Hawking Radiation .......................... 10 2.2.2 Bekenstein Bound: Geroch Process . 12 2.2.3 Spherical Entropy Bound: Susskind Process . 12 2.2.4 Relation to the Bekenstein Bound . 13 3 Degrees of Freedom and Entropy 15 3.1 Degrees of Freedom .............................. 15 3.1.1 Fundamental System ......................... 16 3.2 Complexity According to Local Field Theory . 16 3.3 Complexity According to the Spherical Entropy Bound . 18 3.4 Why Local Field Theory Gives the Wrong Answer . 19 4 The Covariant Entropy Bound 20 4.1 Light-Sheets .................................. 20 iii 4.1.1 The Raychaudhuri Equation .................... 20 4.1.2 Orthogonal Null Hypersurfaces ................... 24 4.1.3 Light-sheet Selection ......................... 26 4.1.4 Light-sheet Termination ....................... 28 4.2 Entropy on a Light-Sheet .......................... 29 4.3 Formulation of the Covariant Entropy Bound . 30 5 Quantum Field Theory in Curved Spacetime 32 5.1 Scalar Field Quantization ......................... -
Black Hole Singularity Resolution Via the Modified Raychaudhuri
Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity Keagan Blanchette,a Saurya Das,b Samantha Hergott,a Saeed Rastgoo,a aDepartment of Physics and Astronomy, York University 4700 Keele Street, Toronto, Ontario M3J 1P3 Canada bTheoretical Physics Group and Quantum Alberta, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethhbridge, Alberta T1K 3M4, Canada E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime. arXiv:2011.11815v3 [gr-qc] 21 Apr 2021 Contents 1 Introduction1 2 Interior of the Schwarzschild black hole3 3 Classical dynamics6 3.1 Classical Hamiltonian and equations of motion6 3.2 Classical Raychaudhuri equation 10 4 Effective dynamics and Raychaudhuri equation 11 4.1 ˚µ scheme 14 4.2 µ¯ scheme 17 4.3 µ¯0 scheme 19 5 Discussion and outlook 22 1 Introduction It is well known that General Relativity (GR) predicts that all reasonable spacetimes are singular, and therefore its own demise. While a similar situation in electrodynamics was resolved in quantum electrodynamics, quantum gravity has not been completely formulated yet. One of the primary challenges of candidate theories such as string theory and loop quantum gravity (LQG) is to find a way of resolving the singularities. -
8.962 General Relativity, Spring 2017 Massachusetts Institute of Technology Department of Physics
8.962 General Relativity, Spring 2017 Massachusetts Institute of Technology Department of Physics Lectures by: Alan Guth Notes by: Andrew P. Turner May 26, 2017 1 Lecture 1 (Feb. 8, 2017) 1.1 Why general relativity? Why should we be interested in general relativity? (a) General relativity is the uniquely greatest triumph of analytic reasoning in all of science. Simultaneity is not well-defined in special relativity, and so Newton's laws of gravity become Ill-defined. Using only special relativity and the fact that Newton's theory of gravity works terrestrially, Einstein was able to produce what we now know as general relativity. (b) Understanding gravity has now become an important part of most considerations in funda- mental physics. Historically, it was easy to leave gravity out phenomenologically, because it is a factor of 1038 weaker than the other forces. If one tries to build a quantum field theory from general relativity, it fails to be renormalizable, unlike the quantum field theories for the other fundamental forces. Nowadays, gravity has become an integral part of attempts to extend the standard model. Gravity is also important in the field of cosmology, which became more prominent after the discovery of the cosmic microwave background, progress on calculations of big bang nucleosynthesis, and the introduction of inflationary cosmology. 1.2 Review of Special Relativity The basic assumption of special relativity is as follows: All laws of physics, including the statement that light travels at speed c, hold in any inertial coordinate system. Fur- thermore, any coordinate system that is moving at fixed velocity with respect to an inertial coordinate system is also inertial. -
What Is Gravity and How Is Embedded in Mater Particles Giving Them Mass (Not the Higgs Field)? Stefan Mehedinteanu
What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs field)? Stefan Mehedinteanu To cite this version: Stefan Mehedinteanu. What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs field)?. 2017. hal-01316929v6 HAL Id: hal-01316929 https://hal.archives-ouvertes.fr/hal-01316929v6 Preprint submitted on 23 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License What Is Gravity (Graviton) and How Is Embedded in Mater Particles Giving Them Mass (Not the Higgs Field)? Stefan Mehedinteanu1 1 (retired) Senior Researcher CITON-Romania; E-Mail: [email protected]; [email protected] “When Einstein was asked bout the discovery of new particles, the answer it was: firstly to clarify what is with the electron!” Abstract It will be shown how the Micro-black-holes particles produced at the horizon entry into a number of N 106162 by quantum fluctuation as virtual micro-black holes pairs like e+ e- creation, stay at the base of: the origin and evolution of Universe, the Black Holes (BH) nuclei of galaxies, of the free photons creation of near mass-less as by radiation decay that condensate later at Confinement in to the structure of gauge bosons (gluons) . -
Raychaudhuri and Optical Equations for Null Geodesic Congruences With
Raychaudhuri and optical equations for null geodesic congruences with torsion Simone Speziale1 1 Aix Marseille Univ., Univ. de Toulon, CNRS, CPT, UMR 7332, 13288 Marseille, France October 17, 2018 Abstract We study null geodesic congruences (NGCs) in the presence of spacetime torsion, recovering and extending results in the literature. Only the highest spin irreducible component of torsion gives a proper acceleration with respect to metric NGCs, but at the same time obstructs abreastness of the geodesics. This means that it is necessary to follow the evolution of the drift term in the optical equations, and not just shear, twist and expansion. We show how the optical equations depend on the non-Riemannian components of the curvature, and how they reduce to the metric ones when the highest spin component of torsion vanishes. Contents 1 Introduction 1 2 Metric null geodesic congruences and optical equations 3 2.1 Null geodesic congruences and kinematical quantities . ................. 3 2.2 Dynamics: Raychaudhuri and optical equations . ............. 6 3 Curvature, torsion and their irreducible components 8 4 Torsion-full null geodesic congruences 9 4.1 Kinematical quantities and the congruence’s geometry . ................ 11 arXiv:1808.00952v3 [gr-qc] 16 Oct 2018 5 Raychaudhuri equation with torsion 13 6 Optical equations with torsion 16 7 Comments and conclusions 18 A Newman-Penrose notation 19 1 Introduction Torsion plays an intriguing role in approaches to gravity where the connection is given an indepen- dent status with respect to the metric. This happens for instance in the first-order Palatini and in the Einstein-Cartan versions of general relativity (see [1, 2, 3] for reviews and references therein), and in more elaborated theories with extra gravitational degrees of freedom like the Poincar´egauge 1 theory of gravity, see e.g. -
Analog Raychaudhuri Equation in Mechanics [14]
Analog Raychaudhuri equation in mechanics Rajendra Prasad Bhatt∗, Anushree Roy and Sayan Kar† Department of Physics, Indian Institute of Technology Kharagpur, 721 302, India Abstract Usually, in mechanics, we obtain the trajectory of a particle in a given force field by solving Newton’s second law with chosen initial conditions. In contrast, through our work here, we first demonstrate how one may analyse the behaviour of a suitably defined family of trajectories of a given mechanical system. Such an approach leads us to develop a mechanics analog following the well-known Raychaudhuri equation largely studied in Riemannian geometry and general relativity. The idea of geodesic focusing, which is more familiar to a relativist, appears to be analogous to the meeting of trajectories of a mechanical system within a finite time. Applying our general results to the case of simple pendula, we obtain relevant quantitative consequences. Thereafter, we set up and perform a straightforward experiment based on a system with two pendula. The experimental results on this system are found to tally well with our proposed theoretical model. In summary, the simple theory, as well as the related experiment, provides us with a way to understand the essence of a fairly involved concept in advanced physics from an elementary standpoint. arXiv:2105.04887v1 [gr-qc] 11 May 2021 ∗ Present Address: Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007, India †Electronic address: [email protected], [email protected], [email protected] 1 I. INTRODUCTION Imagine two pendula of the same length hung from a common support. -
Light Rays, Singularities, and All That
Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition . -
Cosmological Matter-Antimatter Asymmetry and Antimatter in the Universe
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server COSMOLOGICAL MATTER-ANTIMATTER ASYMMETRY AND ANTIMATTER IN THE UNIVERSE A.D. DOLGOV INFN, sezione di Ferrara, Via Paradiso, 12 - 44100 Ferrara, Italy and ITEP, Bol. Cheremushkinskaya 25, Moscow 113259, Russia Models of baryogenesis which may lead to astronomically significant amount of antimatter in the universe are reviewed. Observational features are briefly discussed. 1 Introduction Prediction of antimatter by Dirac 1 (1928) and quick subsequent discovery of the first antimatter particle, positron, by Anderson 2 (1933) are among greatest scientific achievements of XX cen- tury. Discovery of antiproton 22 years later 3 was the next step which had opened a whole new world of antiparticles. Now for (almost) every elementary particle a corresponding antiparticle has also been observed. The latter have opposite signs of all associated charges and, according to CPT theorem4, the same masses and, if unstable, life-times. Such symmetry between par- ticles and antiparticles naturally leads to suggestion that the universe as a whole may be also symmetric with respect to transformation from particles to antiparticles and there should exist astronomically large regions consisting of antimatter: anti-stars, clouds of diffuse antimatter, whole anti-galaxies, or even large clusters of anti-galaxies. As Dirac 5 said in his Nobel lecture a: “... we must regard it rather as an accident that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about, these stars being built up mainly of positrons and negative protons. -
An Introduction to Loop Quantum Gravity with Application to Cosmology
DEPARTMENT OF PHYSICS IMPERIAL COLLEGE LONDON MSC DISSERTATION An Introduction to Loop Quantum Gravity with Application to Cosmology Author: Supervisor: Wan Mohamad Husni Wan Mokhtar Prof. Jo~ao Magueijo September 2014 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London Abstract The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce. i Acknowledgement In the name of Allah, the Most Gracious, the Most Merciful. All praise be to Allah for giving me the opportunity to pursue my study of the fundamentals of nature. In particular, I am very grateful for the opportunity to explore loop quantum gravity and its application to cosmology for my MSc dissertation. -
Curriculum Vitae: M. Coleman Miller Date of Birth
Curriculum Vitae: M. Coleman Miller Date of Birth: 6 July 1968 The University of Maryland Place of Birth: Detroit, MI Department of Astronomy Citizenship: USA College Park, MD 20742-2421 E-mail: [email protected] Telephone: (301) 405-1037 FAX: (301) 314-9067 Webpage: http://www.astro.umd.edu/∼miller/ Research Interests Theoretical Astrophysics Computer Simulations and Modeling Physics of Dense Matter Physics in Strong Magnetic Fields General Relativity Gravitational Radiation PlasmaPhysics GravitationalLensing Education 1984 - 1990 California Institute of Technology, Pasadena, California Department: Physics, with Computer Science minor Thesis Topic: Radiation Transfer in Very Strong Magnetic Fields Degrees: M.S. (1986), Ph.D. (1990) (Advisor: E. S. Phinney) National Science Foundation Graduate Fellow, 1984-1987 1980 - 1984 Hillsdale College, Hillsdale, Michigan Major fields: Mathematics and Physics Degree: B.S., Summa Cum Laude (1984) Research Experience 2009 - Professor of Astronomy, University of Maryland 2020 Radboud Excellence Professor, Radboud University, Nijmegen, Netherlands 2017 - 2019 Chair, Maryland Astronomy Center for Theory and Computation 2015 - 2019 Astronomy Director, Joint Space-Science Institute 2013 - 2014 Director, Joint Space-Science Institute 2004 - 2009 Associate Professor of Astronomy, University of Maryland 2004 - 2006 Chair, Maryland Astronomy Center for Theory and Computation 1999 - 2004 Assistant Professor of Astronomy, University of Maryland 1997 - 1999 Member of the AXAF Science Center, Chicago beta test site 1994 - 1997 Compton Gamma-Ray Observatory Fellow, University of Chicago 1993 - 1999 Research Scientist, University of Chicago Constructed the first detailed model of kilohertz QPOs of neutron star low-mass X- ray binaries, investigated gravitational lensing of gamma-ray bursts and galaxies, and performed various studies of accreting black holes and neutron stars. -
Infinite Derivative Gravity: a Ghost and Singularity-Free Theory
Infinite Derivative Gravity: A Ghost and Singularity-free Theory Aindri´uConroy Physics Department of Physics Lancaster University April 2017 A thesis submitted to Lancaster University for the degree of Doctor of Philosophy in the Faculty of Science and Technology arXiv:1704.07211v1 [gr-qc] 24 Apr 2017 Supervised by Dr Anupam Mazumdar Abstract The objective of this thesis is to present a viable extension of general relativity free from cosmological singularities. A viable cosmology, in this sense, is one that is free from ghosts, tachyons or exotic matter, while staying true to the theoretical foundations of General Relativity such as general covariance, as well as observed phenomenon such as the accelerated expansion of the universe and inflationary behaviour at later times. To this end, an infinite derivative extension of relativ- ity is introduced, with the gravitational action derived and the non- linear field equations calculated, before being linearised around both Minkowski space and de Sitter space. The theory is then constrained so as to avoid ghosts and tachyons by appealing to the modified prop- agator, which is also derived. Finally, the Raychaudhuri Equation is employed in order to describe the ghost-free, defocusing behaviour around both Minkowski and de Sitter spacetimes, in the linearised regime. For Eli Acknowledgements Special thanks go to my parents, M´air´ınand Kevin, without whose encouragement, this thesis would not have been possible; to Emily, for her unwavering support; and to Eli, for asking so many questions. I would also like to thank my supervisor Dr Anupam Mazumdar for his guidance, as well as my close collaborators Dr Alexey Koshelev, Dr Tirthabir Biswas and Dr Tomi Koivisto, who I've had the pleasure of working with.