DOCSLIB.ORG

Black Holes Wormholes & the Development of a Dynamic Warp

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Black Holes Wormholes & the Development of a Dynamic Warp Black Holes Wormholes & the Development ofJBIS, a Dynamic Vol. 58, Warp pp.xxx-xxx, Drive Metric 2005 Black Holes Wormholes & The Development of a Dynamic Warp Drive Metric KELVIN F. LONG 20 Fulmer Road, Beckton, London, E16 3TF, UK. Using The General Theory of Relativity the properties of spacetime metrics are introduced in the context of Black Holes and Wormholes. Applying the same mathematical tools the development of a dynamic warp drive metric is then described as a possible solution to the interstellar distance barrier. The large negative energy density calculated from the stress-energy tensor required for a reasonable warp bubble radius is also dis- cussed. By demonstrating some of the historical and successful applications of metrics to astrophysics, this paper is intended to provide an introduction to the theory behind the warp drive and stimulate increased academic consideration of the subject. Keywords: Black holes, wormholes, warp drive, general relativity, metric 1. Background Since the publication of The General Theory of Relativ- ity nearly a century ago our understanding of gravity ρ 0 0 0 and knowledge of astrophysics has undergone a revo- 0 px 0 0 Tµν = [1.2] lution. In particular, the existence of black holes, an 0 0 p 0 y object once considered not worthy of serious consid- 0 0 0 pz eration for the end point of stellar collapse has now become a core area of astrophysical research. Gen- The terms on the left hand side of Eq.(1.1) de- eral Relativity defines the geometrical warpage of scribe the geometry of spacetime in the presence of spacetime within the vicinity of a matter distribution gravity. For empty space Gµν = 0. The Ricci curvature employing coordinate independent tensor equations - tensor Rµν is found from the Riemann curvature ten- a mathematical language capable of handling multiple α sor Rδµν using the process of contraction. The sca- dimensions with ease. General Relativity supplies us lar curvature R is obtained by further contraction of with the differential Einstein field equation for deter- the Ricci tensor mining the metric gµν contained within the Einstein ten- µν sor Gµν from a given stress-energy tensor Tµν - which is R = g Rµν (1.3) the source of gravity. Thus, the spacetime geometry can be obtained once the energy or matter distribution In spacetime straight lines are curves on geodes- is specified, or put another way the Einstein field equa- ics. The curvature caused by the presence of gravity tion specifies how the presence of matter curves manifests itself in the deviation of one geodesic from spacetime. Einstein used the description ‘gravity is a another and two particles or bodies that may initially manifestation of spacetime curvature’. John Wheeler sums be moving through spacetime on parallel and neigh- up general relativity uniquely as “space tells matter how bouring geodesics will be forced apart or closer to- to move, and matter tells space how to curve” [1]. The gether by spacetime curvature. A geodesic can be Einstein field equation was published in 1915 and has defined as a curve that parallel transports its tan- the following form gent vector along itself. 1 8πG The birth of relativity has seen the removal of the Gµν = Rµν − gµν R = − Tµν (1.1) 2 c4 old Newtonian idea of space and time being sepa- rate entities and a union of the two - ‘spacetime’ has Where the components of the stress-energy ten- been affirmed. The proper time τ and proper dis- sor contain the energy density ρ and principal pres- tance s between events (coordinates) are invariant sures px, py, pz. for all observers and can be written as a line element 1 Kelvin F. Long × 30 or metric. This is written depending on whether the solar masses (1Ms ~ 1.989 10 kg) it is not theoreti- time interval is dominant (timelike) τ2 = t2 - x2 or the cally possible for the star to end its life in a cold distance interval is dominant (spacelike) s2 = x2 - t2. degeneracy-supported state, that is where the star We note that for light x = t = 0 (nulllike). The metric is supported by the pressure of an ideal gas of de- can also be expressed in differential tensor form generate electrons (i.e White Dwarf with M<1.4Ms) or where the indices µ,ν goes from 0 to 3. an ideal gas of degenerate neutrons (i.e neutron star with M<3Ms). Instead, a more massive body will un- 33 2 = µ ν dergo complete collapse to form a black hole, where ds ∑∑gµν dx dx (1.4) µν the escape velocity exceeds even the speed of light – hence the name. To describe the events on a plane Where the Einstein summation convention is im- that passes through the centre of a spherically sym- plied by repeated index metric (non-spinning) centre of gravitational attrac- tion one defines the Schwarzschild metric in polar 2 µ ν ds = gµν dx dx (1.5) coordinate form Re-writing this in matrix form − r r 1 ds2 = −1− g dt 2 + 1− g 0 g g g g dx r r 00 01 02 03 (2.1) 1 2 2 2 2 2 g10 g11 g12 g13 dx dr + r (dθ + sin θdφ ) ds2 = [dx0dx1dx2dx3 ] × g g g g 2 20 21 22 23 dx So that the non-zero components of the metric g30 g31 g32 g33 dx3 are (1.6) −1 r r = − − g = − g g00 1 , g11 1 In a four dimensional spacetime (t, x, y, z), the 16 r r component metric is reduced to a symmetric ten = 2 = 2 2 θ g22 r , g33 r sin component metric gµν of signature [-1,+1,+1,+1] or The radius from which even light cannot escape is −1 0 0 0 known as the gravitational radius r and for a mass m g 0 +1 0 0 is given by gµν = (1.7) 0 0 +1 0 = 2Gm 0 0 0 +1 rg (2.2) c 2 Solving for the components of the spacetime met- Where the gravitational constant ric G = 6.673x10-11 m3kg-1s2 2 = − 2 + 2 + 2 + 2 8 -1 ds g00dx0 g11dx1 g22dx2 g33dx3 and the speed of light c = 2.9979x10 ms . Alternatively Eq.(2.2) may be written in geometrodynamic units This specifies the spacetime interval between ≡ ≡ with G c 1 so that rg = 2m. A consequence of events by use of a flat (no curvature present) Eq.(2.1) is that from the perspective of an external Minkowski spacetime. Written in Cartesian coordi- → observer, as the stellar surface r rg, an event hori- nates this is zon is formed such that no events internal to the horizon can be observed from outside, and this in- 2 = − 2 2 + 2 + 2 + 2 (1.8) ds c dt dx dy dz cludes preventing an observer actually seeing the star fall within the event horizon. This gives an ap- In special relativity although the concepts of length pearance of the star being frozen at this radius. Once and time do not remain invariant for different observ- the star has fallen within its gravitational radius t → 0 ers, the quantity ds2 is invariant for all observers. The and r → ∞ thus collapsing to a point of infinite density metric can also be re-written in a more useful polar and forming the black hole singularity. coordinate form as ds2 = −dt 2 + dr 2 + r 2 (dθ 2 + sin2 θdφ 2 ) (1.9) In 1935 Albert Einstein and Nathan Rosen pub- lished a paper [2] which demonstrated one of the 2. Black Holes & Wormholes first mathematical descriptions of a wormhole by performing a coordinate transformation (letting r = For a star with a mass greater than around three u2+2m) on Eq.(2.1) that removed the region contain- 2 Black Holes Wormholes & the Development of a Dynamic Warp Drive Metric ing the curvature singularity. The solution is a math- demonstrated in this paper that these powerful tools ematical representation of physical space by a space can be applied to another problem which is as much of two asymptotically flat sheets (∞, -∞) connected to do with practical ‘future’ engineering as it is a by a bridge (at u = 0) or Schwarzschild wormhole problem of physics - namely that of interstellar travel. with a ‘throat’ at A(u=0)=16pm2. The Schwarzschild wormhole is described by the metric It is clear that with current solid or liquid chemical rocket fuels (i.e Nitrocellulose or Nitroglycerine ho- u 2 mogeneous mixtures and Hydrogen or Kerosene + ds2 = − dt 2 + 4(u 2 + 2m)du2 + (u 2 + 2m)2 dΩ2 u 2 + 2m Oxygen) [8] travel to the nearest stars will take thou- (2.3) sands of years. Alternative proposals are being con- sidered and in particular, NASA’s Breakthrough Pro- Where dΩ2 = dθ2 + sin2 θdφ2 and dr2=4u2du2. The next pulsion Physics Program [9] is looking at (i) propul- steps in the development of a theoretical wormhole sion that requires no propellant mass (ii) propulsion led to further research notably by scientists such as that attains the maximum transit speeds physically John Wheeler in the 1950’s [3] and later by Morris possible (iii) breakthrough methods of energy pro- and Thorne in the 1980’s [4] who constructed a met- duction to power such devices. However, the current ric to describe a spherically symmetric and static and most realistic theoretical proposals attain speeds wormhole with a proper circumference 2πr with the that are only a fraction of the speed of light mainly coordinate r decreasing from -∞ to a minimum value using Newtons action-reaction principle by mass ejection.
Load more

Recommended publications
  • Closed Timelike Curves, Singularities and Causality: a Survey from Gödel to Chronological Protection
    Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection Jean-Pierre Luminet Aix-Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille , France; Centre de Physique Théorique de Marseille (France) Observatoire de Paris, LUTH (France) [email protected] Abstract: I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to save the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role. Keywords: time travel; closed timelike curves; singularities; wormholes; Gödel’s universe; chronological protection; causal dynamical triangulations 1. Introduction In 1949, the mathematician and logician Kurt Gödel, who had previously demonstrated the incompleteness theorems that broke ground in logic, mathematics, and philosophy, became interested in the theory of general relativity of Albert Einstein, of which he became a close colleague at the Institute for Advanced Study at Princeton.
    [Show full text]
  • Tippett 2017 Class. Quantum Grav
    Citation for published version: Tippett, BK & Tsang, D 2017, 'Traversable acausal retrograde domains in spacetime', Classical Quantum Gravity, vol. 34, no. 9, 095006. https://doi.org/10.1088/1361-6382/aa6549 DOI: 10.1088/1361-6382/aa6549 Publication date: 2017 Document Version Peer reviewed version Link to publication Publisher Rights CC BY-NC-ND This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at: https://doi.org/10.1088/1361-6382/aa6549 University of Bath Alternative formats If you require this document in an alternative format, please contact: [email protected] General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 05. Oct. 2021 Classical and Quantum Gravity PAPER Related content - A time machine for free fall into the past Traversable acausal retrograde domains in Davide Fermi and Livio Pizzocchero - The generalized second law implies a spacetime quantum singularity theorem Aron C Wall To cite this article: Benjamin K Tippett and David Tsang 2017 Class.
    [Show full text]
  • Arxiv:0710.4474V1 [Gr-Qc] 24 Oct 2007 I.“Apdie Pctmsadspruia Travel Superluminal and Spacetimes Drive” “Warp III
    Exotic solutions in General Relativity: Traversable wormholes and “warp drive” spacetimes Francisco S. N. Lobo∗ Centro de Astronomia e Astrof´ısica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa, Portugal and Institute of Gravitation & Cosmology, University of Portsmouth, Portsmouth PO1 2EG, UK (Dated: February 2, 2008) The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distri- bution of matter, i.e., a plausible stress-energy tensor, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equa- tion in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely “exotic matter,” involving a stress- energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. Another interesting feature of these spacetimes is that they allow “effective” superluminal travel, although, locally, the speed of light is not surpassed. These solutions are primarily useful as “gedanken-experiments” and as a theoretician’s probe of the foundations of general relativity, and include traversable wormholes and superluminal “warp drive” spacetimes. Thus, one may be tempted to denote these geometries as “exotic” solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves.
    [Show full text]
  • Arxiv:2103.05610V1
    Warp drive basics Miguel Alcubierre ID ∗ Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Circuito Exterior C.U., A.P. 70-543, M´exico D.F. 04510, M´exico Francisco S. N. Lobo ID † Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa, Edif´ıcio C8, Campo Grande, P-1749-016, Lisbon, Portugal A (Dated: LTEX-ed March 11, 2021) “Warp drive” spacetimes and wormhole geometries are useful as “gedanken-experiments” that force us to confront the foundations of general relativity, and among other issues, to precisely formulate the notion of “superluminal” travel and communication. Here we will consider the basic definition and properties of warp drive spacetimes. In particular, we will discuss the violation of the energy conditions associated with these spacetimes, as well as some other interesting properties such as the appearance of horizons for the superluminal case, and the possibility of using a warp drive to create closed timelike curves. Furthermore, due to the horizon problem, an observer in a spaceship cannot create nor control on demand a warp bubble. To contour this difficulty, we discuss a metric introduced by Krasnikov, which also possesses the interesting property in that the time for a round trip, as measured by clocks at the starting point, can be made arbitrarily short. arXiv:2103.05610v1 [gr-qc] 9 Mar 2021 ∗ [email protected] † [email protected] 2 CONTENTS I. Introduction 2 II. Warp drive spacetime 3 A. Alcubierre warp drive 4 B. Superluminal travel in the warp drive 5 C.
    [Show full text]
  • Advanced General Relativity and Quantum Field Theory in Curved Spacetimes
    Advanced General Relativity and Quantum Field Theory in Curved Spacetimes Lecture Notes Stefano Liberati SISSA, IFPU, INFN January 2020 Preface The following notes are made by students of the course of “Advanced General Relativity and Quantum Field Theory in Curved Spacetimes”, which was held at the International School of Advanced Studies (SISSA) of Trieste (Italy) in the year 2017 by professor Stefano Liberati. Being the course directed to PhD students, this work and the notes therein are aimed to inter- ested readers that already have basic knowledge of Special Relativity, General Relativity, Quantum Mechanics and Quantum Field Theory; however, where possible the authors have included all the definitions and concept necessary to understand most of the topics presented. The course is based on di↵erent textbooks and papers; in particular, the first part, about Advanced General Relativity, is based on: “General Relativity” by R. Wald [1] • “Spacetime and Geometry” by S. Carroll [2] • “A Relativist Toolkit” by E. Poisson [3] • “Gravitation” by T. Padmanabhan [4] • while the second part, regarding Quantum Field Theory in Curved Spacetime, is based on “Quantum Fields in Curved Space” by N. C. Birrell and P. C. W. Davies [5] • “Vacuum E↵ects in strong fields” by A. A. Grib, S. G. Mamayev and V. M. Mostepanenko [6] • “Introduction to Quantum E↵ects in Gravity”, by V. F Mukhanov and S. Winitzki [7] • Where necessary, some other details could have been taken from paper and reviews in the standard literature, that will be listed where needed and in the Bibliography. Every possible mistake present in these notes are due to misunderstandings and imprecisions of which only the authors of the following works must be considered responsible.
    [Show full text]
  • STATIC and DYNAMIC TRAVERSABLE WORMHOLES By
    STATIC AND DYNAMIC TRAVERSABLE WORMHOLES by JAROSLAW PAWEL ADAMIAK submitted in part fulfilment of the requirements for the degree of MASTER OF SCIENCE in the subject APPLIED MATHEMATICS at the UNIVERSITY OF SOUTH AFRICA SUPERVISOR: PROF N T BISHOP JOINT SUPERVISOR: PROF W M LESAME JANUARY 2005 Abstract The aim of this work is to discuss the effects found in static and dynamic wormholes that occur as a solution of Einstein equations in general relativity. The ground is prepared by presentation of “faster than light” effects, historical perspective, worm- hole definition and contemporary directions in wormhole research. Then the focus is narrowed to Morris-Thorne framework for static spherically symmetric wormhole. Energy conditions being a fundamental component in wormhole physics are discussed in detail, their definition, most common violations and attempts to exotic matter quantification. Two types of dynamic wormholes, evolving and rotating, together with their variations are considered. Computer algebra and Cartan calculus are used to obtain detailed solutions. i Contents 1 Introduction 1 1.1 Faster Than Light Mechanisms . 1 1.2 Historical Perspective . 9 1.3 Concept of a Wormhole . 12 1.4 Current State of Research . 15 2 Morris-Thorne Framework 20 2.1 Desired Properties of Traversable Wormhole . 20 2.2 Metric and Einstein Field Equations . 22 2.3 Traversability Conditions . 26 2.4 Wormhole Examples . 31 2.4.1 Zero radial tides . 32 2.4.2 Zero density . 34 3 Energy Conditions 36 3.1 Pointwise and Averaged Energy Conditions . 36 3.2 Violations . 41 ii CONTENTS iii 3.3 Quantification of exotic matter .
    [Show full text]
  • Traversable Achronal Retrograde Domains in Spacetime
    Traversable Achronal Retrograde Domains In Spacetime Doctor Benjamin K. Tippett Gallifrey Polytechnic Institute Doctor David Tsang Gallifrey Institute of Technology (GalTech) (Dated: October 25, 2013) There are many spacetime geometries in general relativity which contain closed timelike curves. A layperson might say that retrograde time travel is possible in such spacetimes. To date no one has discovered a spacetime geometry which emulates what a layperson would describe as a time machine. The purpose of this paper is to propose such a space-time geometry. In our geometry, a bubble of curvature travels along a closed trajectory. The inside of the bubble is Rindler spacetime, and the exterior is Minkowski spacetime. Accelerating observers inside of the bubble travel along closed timelike curves. The walls of the bubble are generated with matter which violates the classical energy conditions. We refer to such a bubble as a Traversable Achronal Retrograde Domain In Spacetime. I. INTRODUCTION t A. Exotic spacetimes x How would one go about building a time machine? Let us begin with considering exactly what one might mean by “time machine?” H.G. Wells (and his successors) might de- scribe an apparatus which could convey people “backwards in time”. That is to say, convey them from their current location in spacetime to a point within their own causal past. If we de- scribe spacetime as a river-bed, and the passage of time as our unrelenting flow along our collective worldlines towards our B future; a time machine would carry us back up-stream. Let us A describe such motion as retrograde time travel.
    [Show full text]
  • Traversable Acausal Retrograde Domains in Spacetime
    Traversable Acausal Retrograde Domains In Spacetime Ben Tippett, UBCO CCGRRA 2016 “Time Travel” Closed Timelike Curves Timelike curves which are closed t “The Time Machine” HG Wells 1895 Popular Geometries with Closed Timelike Curves • Gödel 1949 • angular momentum cosmology • Tipler 1974 • infinite rotating cylinder • Tomimatsu Sato 1973 • weird rotating kerr thing • Friedman, Morris et al. 1990 • wormholes + twin paradox Piecemeal Refutation of Closed Timelike Curves • Gödel 1949 • angular momentum cosmology Asymptotically • Tipler 1974 weird • infinite rotating cylinder • Tomimatsu Sato 1973 • weird rotating kerr thing • Friedman, Morris et al. 1990 • wormholes + twin paradox Piecemeal Refutation of Closed Timelike Curves • Gödel 1949 • angular momentum cosmology Asymptotically • Tipler 1974 weird • infinite rotating cylinder • Tomimatsu Sato 1973 How do we even • weird rotating kerr thing make this thing? • Friedman, Morris et al. 1990 • wormholes + twin paradox Piecemeal Refutation of Closed Timelike Curves • Gödel 1949 • angular momentum cosmology Asymptotically • Tipler 1974 weird • infinite rotating cylinder • Tomimatsu Sato 1973 How do we even • weird rotating kerr thing make this thing? • Friedman, Morris et al. 1990 • wormholes + twin paradox Unphysicality of Morris-Thorne Wormhole • Violates Topological Censorship • Friedman, Schleich, Witt 1993 • Exotic Matter Required • Compactly Generated Cauchy Horizon • Unstable to perturbations Morris, Thorne, Yutsever 1988 General Refutations of CTC • Manifold is not time Orientable • Convenient
    [Show full text]
  • Zen and the Art of Space-Time Manufacturing
    The Journal’s name will be set by the publisher DOI: will be set by the publisher c Owned by the authors, published by EDP Sciences, 2018 Zen and the Art of Space-Time Manufacturing Orfeu Bertolami1,2,a 1Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto 2Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa Abstract. We present a general discussion about the so-called emergent properties and discuss whether space-time and gravity can be regarded as emergent features of under- lying more fundamental structures. Finally, we discuss some ideas about the multiverse, and speculate on how our universe might arise from the multiverse. 1 Introduction The reductionist approach has shown to be extremely useful to unravel the fundamental building blocks of matter and has lead to fecund discoveries in physics, chemistry and biology. It is a method that focus not only on the most elementary building blocks of matter, but also on the interactions that bind this basic pieces at a given scale of energy. The reductionist approach aims fundamentally to explain the complexity of Nature by the motion and interaction of elementary building blocks. It is an approach does not preclude the existence of the so-called emergent properties or phenomena, even though it is clearly based on the assumption that these phenomena can be entirely explained by the underlying interactions between the elementary building blocks. Some claim that the reductionist perspective can be more than a theoretical and a methodological procedure and can acquire an onto- arXiv:1303.2381v1 [gr-qc] 10 Mar 2013 logical dimension, if reality itself, can be decomposed in a minimum set of entities (see e.g.
    [Show full text]
  • A Time Machine Allowing Travel to the Past by Free Fall
    A time machine allowing travel to the past by free fall Livio Pizzocchero Dipartimento di Matematica, Universit`a degli Studi di Milano and Istituto Nazionale di Fisica Nucleare, Sezione di Milano TMF 2019, Torino, September 2019 Based on joint work with Davide Fermi (Classical and Quantum Gravity 35 (2018), 165003, 42 pp) Livio Pizzocchero Free fall into the past 1 / 24 Background and motivations • Time machines := spacetimes with closed timelike curves (CTCs). Literature on this topic, and on the (somehow related) subject of spacetimes with superluminal trajectories: Van Stockum (1938); G¨odel (1949); Kerr (1963); Misner (1963); Tipler (1974); Morris, Thorne and Yurtsever (1988); Gott (1991); Alcubierre (1994); Ori (1993,1995,2007), Ori and Soen (1994); Li (1994); Low (1995); Everett, Everett and Roman (1996-97); Krasnikov (1998); Tippet and Tsang (2017); Mallary, Khanna and Price (2017); Fermi and P (2018); Fermi (2018); Krasnikov (2018); ... Analysis of problematic aspects: Friedman, Morris, Novikov, Echeverria, Klinkhammer, Thorne, Yurtsever (1990); Deutsch (1991); Deser, Jackiw and ’t Hooft (1992); Hawking (1992); Ford and Roman (1995); Krasnikov (1998,2014,2018); Olum (1998); Visser (2003); Maeda, Ishibashi and Narita (1998), Lobo (2008); ... Livio Pizzocchero Free fall into the past 2 / 24 • Typical issues affecting spacetimes with CTCs: Infinitely extended structures (dust cylinders, cosmic strings, ... ) . Naked curvature singularities, or CTCs beyond event horizons. Huge tidal accelerations experienced along CTCs . Violations of energy conditions( ECs); large, negative energy densities. I Still, some quantum systems do violate the ECs (e.g., Casimir effect) . I Ori 2007 time machine: ECs fulfilled, perhaps singularities/horizons. • Chronology protection conjecture: quantum backreactions forbid CTCs.
    [Show full text]
  • Advanced General Relativity and Quantum Field Theory in Curved Spacetimes
    Advanced General Relativity and Quantum Field Theory in Curved Spacetimes Lecture Notes Stefano Liberati SISSA, IFPU, INFN January 2020 Preface The following notes are made by students of the course of \Advanced General Relativity and Quantum Field Theory in Curved Spacetimes", which was held at the International School of Advanced Studies (SISSA) of Trieste (Italy) in the year 2017 by professor Stefano Liberati. Being the course directed to PhD students, this work and the notes therein are aimed to inter- ested readers that already have basic knowledge of Special Relativity, General Relativity, Quantum Mechanics and Quantum Field Theory; however, where possible the authors have included all the definitions and concept necessary to understand most of the topics presented. The course is based on different textbooks and papers; in particular, the first part, about Advanced General Relativity, is based on: • \General Relativity" by R. Wald [1] • \Spacetime and Geometry" by S. Carroll [2] • \A Relativist Toolkit" by E. Poisson [3] • \Gravitation" by T. Padmanabhan [4] while the second part, regarding Quantum Field Theory in Curved Spacetime, is based on • \Quantum Fields in Curved Space" by N. C. Birrell and P. C. W. Davies [5] • \Vacuum Effects in strong fields” by A. A. Grib, S. G. Mamayev and V. M. Mostepanenko [6] • \Introduction to Quantum Effects in Gravity", by V. F Mukhanov and S. Winitzki [7] Where necessary, some other details could have been taken from paper and reviews in the standard literature, that will be listed where needed and in the Bibliography. Every possible mistake present in these notes are due to misunderstandings and imprecisions of which only the authors of the following works must be considered responsible.
    [Show full text]
  • Los Alamos National Laboratory Alamos, New Mexico 87545
    LOS Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36 TITLE: HYPER-FAST INTERSTELLAR TRAVEL VIA A MODIFICATION OF SPACETIME GEOMETRY AUmOR(S): Arkady Kheyfets, NC State University Warner Miller, T-6 k SUBM~TED TO: NASA Lewis Research Center Meeting, "Breakthrough Propulsion Physics," 12- 14 August 1997, Cleveland, OH -3 0- cma3 'I- By acceptance of this article, the publisher recognizes that the US. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for US. Government purposes. The Los Alarnos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Alamos National Laboratory Los Alamos, New Mexico 87545 FORM NO. 836 R4 ST. NO. 2629 5/81 STER DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof.
    [Show full text]