Black Holes - No Need to Be Afraid! Transcript
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Plasma Physics and Pulsars
Plasma Physics and Pulsars On the evolution of compact o bjects and plasma physics in weak and strong gravitational and electromagnetic fields by Anouk Ehreiser supervised by Axel Jessner, Maria Massi and Li Kejia as part of an internship at the Max Planck Institute for Radioastronomy, Bonn March 2010 2 This composition was written as part of two internships at the Max Planck Institute for Radioastronomy in April 2009 at the Radiotelescope in Effelsberg and in February/March 2010 at the Institute in Bonn. I am very grateful for the support, expertise and patience of Axel Jessner, Maria Massi and Li Kejia, who supervised my internship and introduced me to the basic concepts and the current research in the field. Contents I. Life-cycle of stars 1. Formation and inner structure 2. Gravitational collapse and supernova 3. Star remnants II. Properties of Compact Objects 1. White Dwarfs 2. Neutron Stars 3. Black Holes 4. Hypothetical Quark Stars 5. Relativistic Effects III. Plasma Physics 1. Essentials 2. Single Particle Motion in a magnetic field 3. Interaction of plasma flows with magnetic fields – the aurora as an example IV. Pulsars 1. The Discovery of Pulsars 2. Basic Features of Pulsar Signals 3. Theoretical models for the Pulsar Magnetosphere and Emission Mechanism 4. Towards a Dynamical Model of Pulsar Electrodynamics References 3 Plasma Physics and Pulsars I. The life-cycle of stars 1. Formation and inner structure Stars are formed in molecular clouds in the interstellar medium, which consist mostly of molecular hydrogen (primordial elements made a few minutes after the beginning of the universe) and dust. -
Arxiv:0905.1355V2 [Gr-Qc] 4 Sep 2009 Edrt 1 O Ealdrve) Nti Otx,Re- Context, Been Has As This Collapse in Denoted Gravitational of Review)
Can accretion disk properties distinguish gravastars from black holes? Tiberiu Harko∗ Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong Zolt´an Kov´acs† Max-Planck-Institute f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany and Department of Experimental Physics, University of Szeged, D´om T´er 9, Szeged 6720, Hungary Francisco S. N. Lobo‡ Centro de F´ısica Te´orica e Computacional, Faculdade de Ciˆencias da Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa, Portugal (Dated: September 4, 2009) Gravastars, hypothetic astrophysical objects, consisting of a dark energy condensate surrounded by a strongly correlated thin shell of anisotropic matter, have been proposed as an alternative to the standard black hole picture of general relativity. Observationally distinguishing between astrophysical black holes and gravastars is a major challenge for this latter theoretical model. This due to the fact that in static gravastars large stability regions (of the transition layer of these configurations) exist that are sufficiently close to the expected position of the event horizon, so that it would be difficult to distinguish the exterior geometry of gravastars from an astrophysical black hole. However, in the context of stationary and axially symmetrical geometries, a possibility of distinguishing gravastars from black holes is through the comparative study of thin accretion disks around rotating gravastars and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around slowly rotating gravastars, with all the metric tensor components estimated up to the second order in the angular velocity. -
Hawking Radiation
a brief history of andreas müller student seminar theory group max camenzind lsw heidelberg mpia & lsw january 2004 http://www.lsw.uni-heidelberg.de/users/amueller talktalk organisationorganisation basics ☺ standard knowledge advanced knowledge edge of knowledge and verifiability mindmind mapmap whatwhat isis aa blackblack hole?hole? black escape velocity c hole singularity in space-time notion „black hole“ from relativist john archibald wheeler (1968), but first speculation from geologist and astronomer john michell (1783) ☺ blackblack holesholes inin relativityrelativity solutions of the vacuum field equations of einsteins general relativity (1915) Gµν = 0 some history: schwarzschild 1916 (static, neutral) reissner-nordstrøm 1918 (static, electrically charged) kerr 1963 (rotating, neutral) kerr-newman 1965 (rotating, charged) all are petrov type-d space-times plug-in metric gµν to verify solution ;-) ☺ black hole mass hidden in (point or ring) singularity blackblack holesholes havehave nono hairhair!! schwarzschild {M} reissner-nordstrom {M,Q} kerr {M,a} kerr-newman {M,a,Q} wheeler: no-hair theorem ☺ blackblack holesholes –– schwarzschildschwarzschild vs.vs. kerrkerr ☺ blackblack holesholes –– kerrkerr inin boyerboyer--lindquistlindquist black hole mass M spin parameter a lapse function delta potential generalized radius sigma potential frame-dragging frequency cylindrical radius blackblack holehole topologytopology blackblack holehole –– characteristiccharacteristic radiiradii G = M = c = 1 blackblack holehole -- -
Scattering on Compact Body Spacetimes
Scattering on compact body spacetimes Thomas Paul Stratton A thesis submitted for the degree of Doctor of Philosophy School of Mathematics and Statistics University of Sheffield March 2020 Summary In this thesis we study the propagation of scalar and gravitational waves on compact body spacetimes. In particular, we consider spacetimes that model neutron stars, black holes, and other speculative exotic compact objects such as black holes with near horizon modifications. We focus on the behaviour of time-independent perturbations, and the scattering of plane waves. First, we consider scattering by a generic compact body. We recap the scattering theory for scalar and gravitational waves, using a metric perturbation formalism for the latter. We derive the scattering and absorption cross sections using the partial-wave approach, and discuss some approximations. The theory of this chapter is applied to specific examples in the remainder of the thesis. The next chapter is an investigation of scalar plane wave scattering by a constant density star. We compute the scattering cross section numerically, and discuss a semiclassical, high-frequency analysis, as well as a geometric optics approach. The semiclassical results are compared to the numerics, and used to gain some physical insight into the scattering cross section interference pattern. We then generalise to stellar models with a polytropic equation of state, and gravitational plane wave scattering. This entails solving the metric per- turbation problem for the interior of a star, which we accomplish numerically. We also consider the near field scattering profile for a scalar wave, and the cor- respondence to ray scattering and the formation of a downstream cusp caustic. -
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 . -
Lecture 24. Degenerate Fermi Gas (Ch
Lecture 24. Degenerate Fermi Gas (Ch. 7) We will consider the gas of fermions in the degenerate regime, where the density n exceeds by far the quantum density nQ, or, in terms of energies, where the Fermi energy exceeds by far the temperature. We have seen that for such a gas μ is positive, and we’ll confine our attention to the limit in which μ is close to its T=0 value, the Fermi energy EF. ~ kBT μ/EF 1 1 kBT/EF occupancy T=0 (with respect to E ) F The most important degenerate Fermi gas is 1 the electron gas in metals and in white dwarf nε()(),, T= f ε T = stars. Another case is the neutron star, whose ε⎛ − μ⎞ exp⎜ ⎟ +1 density is so high that the neutron gas is ⎝kB T⎠ degenerate. Degenerate Fermi Gas in Metals empty states ε We consider the mobile electrons in the conduction EF conduction band which can participate in the charge transport. The band energy is measured from the bottom of the conduction 0 band. When the metal atoms are brought together, valence their outer electrons break away and can move freely band through the solid. In good metals with the concentration ~ 1 electron/ion, the density of electrons in the electron states electron states conduction band n ~ 1 electron per (0.2 nm)3 ~ 1029 in an isolated in metal electrons/m3 . atom The electrons are prevented from escaping from the metal by the net Coulomb attraction to the positive ions; the energy required for an electron to escape (the work function) is typically a few eV. -
Condensation of Bosons with Several Degrees of Freedom Condensación De Bosones Con Varios Grados De Libertad
Condensation of bosons with several degrees of freedom Condensación de bosones con varios grados de libertad Trabajo presentado por Rafael Delgado López1 para optar al título de Máster en Física Fundamental bajo la dirección del Dr. Pedro Bargueño de Retes2 y del Prof. Fernando Sols Lucia3 Universidad Complutense de Madrid Junio de 2013 Calificación obtenida: 10 (MH) 1 [email protected], Dep. Física Teórica I, Universidad Complutense de Madrid 2 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid 3 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid Abstract The condensation of the spinless ideal charged Bose gas in the presence of a magnetic field is revisited as a first step to tackle the more complex case of a molecular condensate, where several degrees of freedom have to be taken into account. In the charged bose gas, the conventional approach is extended to include the macroscopic occupation of excited kinetic states lying in the lowest Landau level, which plays an essential role in the case of large magnetic fields. In that limit, signatures of two diffuse phase transitions (crossovers) appear in the specific heat. In particular, at temperatures lower than the cyclotron frequency, the system behaves as an effectively one-dimensional free boson system, with the specific heat equal to (1/2) NkB and a gradual condensation at lower temperatures. In the molecular case, which is currently in progress, we have studied the condensation of rotational levels in a two–dimensional trap within the Bogoliubov approximation, showing that multi–step condensation also occurs. -
Linear Stability of Slowly Rotating Kerr Black Holes
LINEAR STABILITY OF SLOWLY ROTATING KERR BLACK HOLES DIETRICH HAFNER,¨ PETER HINTZ, AND ANDRAS´ VASY Abstract. We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation. Our proof rests on a robust general framework, based on recent advances in microlocal analysis and non-elliptic Fredholm theory, for the analysis of resolvents of operators on asymptotically flat spaces. With the mode stability of the Schwarzschild metric as well as of certain scalar and 1-form wave operators on the Schwarzschild spacetime as an input, we establish the linear stability of slowly rotating Kerr black holes using perturbative arguments; in particular, our proof does not make any use of special algebraic properties of the Kerr metric. The heart of the paper is a detailed description of the resolvent of the linearization of a suitable hyperbolic gauge-fixed Einstein operator at low energies. As in previous work by the second and third authors on the nonlinear stability of cosmological black holes, constraint damping plays an important role. Here, it eliminates certain pathological generalized zero energy states; it also ensures that solutions of our hyperbolic formulation of the linearized Einstein equations have the stated asymptotics and decay for general initial data and forcing terms, which is a useful feature in nonlinear and numerical applications. -
Exploring Fundamental Physics with Neutron Stars
EXPLORING FUNDAMENTAL PHYSICS WITH NEUTRON STARS PIERRE M. PIZZOCHERO Dipartimento di Fisica, Università degli Studi di Milano, and Istituto Nazionale di Fisica Nucleare, sezione di Milano, Via Celoria 16, 20133 Milano, Italy ABSTRACT In this lecture, we give a First introduction to neutron stars, based on Fundamental physical principles. AFter outlining their outstanding macroscopic properties, as obtained From observations, we inFer the extreme conditions oF matter in their interiors. We then describe two crucial physical phenomena which characterize compact stars, namely the gravitational stability of strongly degenerate matter and the neutronization of nuclear matter with increasing density, and explain how the Formation and properties of neutron stars are a direct consequence oF the extreme compression of matter under strong gravity. Finally, we describe how multi-wavelength observations of diFFerent external macroscopic Features (e.g. maximum mass, surface temperature, pulsar glitches) can give invaluable inFormation about the exotic internal microscopic scenario: super-dense, isospin-asymmetric, superFluid, bulk hadronic matter (probably deconFined in the most central regions) which can be Found nowhere else in the Universe. Indeed, neutrons stars represent a unique probe to study the properties of the low-temperature, high-density sector of the QCD phase diagram. Moreover, binary systems of compact stars allow to make extremely precise measurements of the properties of curved space-time in the strong Field regime, as well as being efFicient sources oF gravitational waves. I – INTRODUCTION Neutron stars are probably the most exotic objects in the Universe: indeed, they present extreme and quite unique properties both in their macrophysics, controlled by the long-range gravitational and electromagnetic interactions, and in their microphysics, controlled by the short-range weak and strong nuclear interactions. -
What Is a Black Hole?
National Aeronautics and Space Administration Can black holes be used to travel through spacetime? Where are black holes located? It’s a science fiction cliché to use black holes to travel through space. Dive into one, the story goes, Black holes are everywhere! As far as astronomers can tell, there are prob- and you can pop out somewhere else in the Universe, having traveled thousands of light years in the blink of an eye. ably millions of black holes in our Milky Way Galaxy alone. That may sound like a lot, but the nearest one discovered is still 1600 light years away — a But that’s fiction. In reality, this probably won’t work. Black holes twist space and time, in a sense punching a hole in the fabric of the pretty fair distance, about 16 quadrillion kilometers! That’s certainly too far Universe. There is a theory that if this happens, a black hole can form a tunnel in space called a wormhole (because it’s like a tunnel away to affect us. The giant black hole in the center of the Galaxy is even formed by a worm as it eats its way through an apple). If you enter a wormhole, you’ll pop out someplace else far away, not needing to farther away: at a distance of 26,000 light years, we’re in no danger of travel through the actual intervening distance. being sucked into the vortex. The neutron star companion While wormholes appear to be possible mathematically, they would be violently unstable, or need to be made of theoretical For a black hole to be dangerous, it would have to be very close, probably of a black hole spirals in and is destroyed as it merges with the forms of matter which may not occur in nature. -
Neutron(Stars(( Degenerate(Compact(Objects(
Neutron(Stars(( Accre.ng(Compact(Objects6(( see(Chapters(13(and(14(in(Longair((( Degenerate(Compact(Objects( • The(determina.on(of(the( internal(structures(of(white( dwarfs(and(neutron(stars( depends(upon(detailed( knowledge(of(the(equa.on(of( state(of(the(degenerate( electron(and(neutron(gases( Degneracy(and(All(That6(Longair(pg(395(sec(13.2.1%( • In(white&dwarfs,(internal(pressure(support(is(provided(by(electron( degeneracy(pressure(and(their(masses(are(roughly(the(mass(of(the( Sun(or(less( • the(density(at(which(degeneracy(occurs(in(the(non6rela.vis.c(limit(is( propor.onal(to(T&3/2( • This(is(a(quantum(effect:(Heisenberg(uncertainty(says(that δpδx>h/2π# • Thus(when(things(are(squeezed(together(and(δx(gets(smaller((the( momentum,(p,(increases,(par.cles(move(faster(and(thus(have(more( pressure( • (Consider(a(box6(with(a(number(density,n,(of(par.cles(are(hiSng(the( wall;the(number(of(par.cles(hiSng(the(wall(per(unit(.me(and(area(is( 1/2nv(( • the(momentum(per(unit(.me(and(unit(area((Pressure)(transferred(to( the(wall(is(2nvp;(P~nvp=(n/m)p2((m(is(mass(of(par.cle)( Degeneracy6(con.nued( • The(average(distance(between(par.cles(is(the(cube(root(of(the( number(density(and(if(the(momentum(is(calculated(from(the( Uncertainty(principle(p~h/(2πδx)~hn1/3# • and(thus(P=h2n5/3/m6(if(we(define(ma[er(density(as(ρ=[n/m](then( • (P~(ρ5/3(%independent%of%temperature%% • Dimensional(analysis(gives(the(central(pressure(as%P~GM2/r4( • If(we(equate(these(we(get(r~M61/3(e.q%a%degenerate%star%gets%smaller% as%it%gets%more%massive%% • At(higher(densi.es(the(material(gets('rela.vis.c'(e.g.(the(veloci.es( -
Computing Neutron Capture Rates in Neutron-Degenerate Matter †
universe Article Computing Neutron Capture Rates in Neutron-Degenerate Matter † Bryn Knight and Liliana Caballero * Department of Physics, University of Guelph, Guelph, ON N1G 2W1, Canada; [email protected] * Correspondence: [email protected] † This paper is based on the talk at the 7th International Conference on New Frontiers in Physics (ICNFP 2018), Crete, Greece, 4–12 July 2018. Received: 28 November 2018; Accepted: 16 January 2019; Published: 18 January 2019 Abstract: Neutron captures are likely to occur in the crust of accreting neutron stars (NSs). Their rate depends on the thermodynamic state of neutrons in the crust. At high densities, neutrons are degenerate. We find degeneracy corrections to neutron capture rates off nuclei, using cross sections evaluated with the reaction code TALYS. We numerically integrate the relevant cross sections over the statistical distribution functions of neutrons at thermodynamic conditions present in the NS crust. We compare our results to analytical calculations of these corrections based on a power-law behavior of the cross section. We find that although an analytical integration can simplify the calculation and incorporation of the results for nucleosynthesis networks, there are uncertainties caused by departures of the cross section from the power-law approach at energies close to the neutron chemical potential. These deviations produce non-negligible corrections that can be important in the NS crust. Keywords: neutron capture; neutron stars; degenerate matter; nuclear reactions 1. Introduction X-ray burst and superburst observations are attributed to accreting neutron stars (NSs) (see, e.g., [1,2]). In such a scenario, a NS drags matter from a companion star.