Numerical Relativity in Spherical Polar Coordinates: Calculations with the BSSN Formulation
|
|
- Douglas Dalton
- 5 years ago
- Views:
Transcription
1 Numerical Relativity in Spherical Polar Coordinates: Calculations with the BSSN Formulation Pedro Montero Max-Planck Institute for Astrophysics Garching (Germany) 28/01/13 in collaboration with T.Baumgarte, I. Cordero-Carrion and E. Mueller [arxiv: v1; to appear in Phys. Rev. D]
2 Outline - Astrophysical motivation - Spherical polar coordinates and numerical relativity - BSSN covariant formulation and treatment of singular terms - Partially implicit Runge-Kutta method (PIRK) - Numerical examples: Weak gravitational waves Rotating relativistic stars Schwarzschild black hole - Conclusions 2
3 Most 3-dimensional numerical relativity codes use Cartesian coordinates. While Cartesian coordinates have many desirable properties, there are astrophysical problems for which spherical polar coordinates are better suited: Accretion onto BHs Collapse of massive stars (SN 1987A) An alternative approach is the use of multi-patch applications 3
4 Implementing a numerical relativity code in spherical polar coordinates possess several challenges: 1) The original version of the BSSN formulation explicitly assumes Cartesian coordinates. This has been resolved by Brown (2009) who introduced a covariant formulation of the BSSN equations. This formulation is well suited for curvilinear coordinate systems 2) Another challenge is introduced by the coordinate singularities at the origin and at the axis in spherical polar coordinates. 4
5 Coordinate singularities at the origin and at the axis introduce singular terms in the equations which is a source of numerical problems. One problem arises because of the presence of terms that behave like 1/r in the equations near the origin at r=0 Analytically, regularity of the data (metric) ensures that these terms cancel exactly but on the numerical level is a source of numerical instabilities. Similar problem appears near the axis with terms like 1/sin(θ) 5
6 Methods to handle these problems 1) Specific gauge choice (i.e. polar/aereal gauges) [Bardeen & Piran 1983; Choptuik 1991]. Disadvantage: restricts the gauge freedom; which is one of the main ingredients in successful evolutions in numerical relativity 2) Regularization method by imposing appropiate parity regularity conditions and local flatness. [Acubierre et al. 2005, Ruiz et al. 2007, Alcubierre et al. 2011] Disadvantage: these are not easy to implement (introduce auxiliary variables and new evolution equations) 6
7 3) Partially Implicit Runge-Kutta methods: Proposed by Cordero-Carrion et al.(2012) for the solution of the hyperbolic part in the Fully Constrained Formalism of Einstein eqs. PM & Cordero-Carrion,(2012) applied successfully the PIRK method to the BSSN eqs. in spherical coordinates under the assumption of spherical symmetry without the need for regularization at the origin r=0. Terms behaving like 1/r close to r=0 can be numerically interpreted as stiff terms. Advantages: - keep the gauge freedom (use 1+log, Gamma-driver) - No need for a regularization scheme at origin or axis - Simple implementation 7
8 Implementing the BSSN equations Shibata&Nakamura 1995, Baumgarte&Shapiro 1998, and Brown 2009 (covariant form) Singular terms (e.g. like 1/r) 8
9 We assume the background metric to be the flat metric is spherical polar coordinates r,θ,φ Conformal metric We treat singular terms analytically by scaling out appropriate powers of r and sinθ Rescaled connection vector We write all evolution equations in terms of h ij, λ i etc... 9
10 We compute derivatives of the spatial metric as follows: Which is written in terms of h ij We compute derivatives of h ij numerically while all r and sinθ terms are treated analytically 10
11 2 nd order PIRK method Consider a system of PDEs We assume the L 1 and L 3 differential operators contain only regular terms, whereas L 2 contains the singular terms (i) u is evolved explicitly (ii) v is evolved taking into account the updated value of u for the evaluation of the L 2 operator 11
12 Computational cost is comparable to explicit methods (no need for analytical or numerical inversion) Source terms in the PIRK operators for the extrinsic curvature evolution equation: 12
13 Numerical grid Cell-centered grid covering the region 0<r<r max 0<θ<π and 0<ϕ<2π 13
14 Numerical implementation - Fourth-order finite difference approximation for spatial derivatives. - Second-order PIRK method to evolve in time the hyperbolic equations. - Kreiss-Oliger dissipation term to avoid high frequency noise. - Cell-centered grid to avoid that the location of the puncture at the origin coincides with a grid point in simulations involving a BH. - Outgoing wave boundary conditions at the outer boundary.. 14
15 I. Weak gravitational waves: axisymmetric waves Small amplitude waves on a flat Minkowski background (l=2,m=0) Results for a numerical grid with (40N,10N,2) with N=1,2 and 4. Outer boundary at r=8.0 1+log gauge condition for the lapse and vanishing shift. h rr for N=4 simulation at θ=1.61 and ϕ=4.71 Crosses: numerical result Solid line: analytical solution L2-norm of the error rescaled by a factor N 4 15
16 II. Weak gravitational waves: nonaxisymmetric waves Small amplitude waves on a flat Minkowski background (l=2,m=2) Results for a numerical grid with (40,32,64) and outer boundary at r=4.0 1+log gauge condition for the lapse and vanishing shift. h rr for N=4 simulation at θ=1.62 and ϕ=3.19 Crosses: numerical result Solid line: analytical solution Convergence rate is close to 4 th order 16
17 III. Hydro-without-hydro: rotating relativistic stars Stable relativistic star (Γ=2) rotating at 92% of the allowed massshedding limit. (M~0.85M max and r p /r eq ~0.7) Results for a numerical grid with (48,32,2) and outer boundary at r=25m 1+log gauge condition for the lapse and Gamma-driver condition for the shift. Snapshots of the conformal exponent and the lapse at The initial time and after two spin periods along the pole and the equator. Both profiles remain very similar to the initial data. 17
18 IV. Schwarzschild trumpet initial data Time independent slicing of Schwarzschild spacetime that satisfies our 1+log slicing condition. Numerical grid of size (160N,2,2) with N=1,2,4 and 8, with outer boundary at r=16m. 2 nd order convergence 18
19 V. Schwarzschild wormhole initial data Conformal factor: Pre-collapsed lapse: Numerical grid of size (10240,2,2) with outer boundary at r=256m. Coordinate transition from wormhole initial data to timeindependent trumpet data. We plot conformal exponent, lapse and radial orthonormal component of the shift as a function of the gauge-invariant areal radius R 19
20 V. Schwarzschild wormhole initial data Maximum of the radial shift for different grid sizes (1280N,2,2) for N=1,2,4 and 8 Profiles of the violations of the Hamiltonian constraint at time t=79m. Results are rescaled with N 2. 20
21 Conclusions - Presented a new numerical relativity code that solves the BSSN equations in spherical polar coordinates without any symmetry assumption. -A key ingredient is the PIRK scheme to integrate the evolution equations in time which allows us to avoid the need for a regularization at the origin or the axis - Obtained the expected stability and convergence of the code - Current developments: AH finder, hydrodynamics, GW extraction and microphysics. 21
EXCISION TECHNIQUE IN CONSTRAINED FORMULATIONS OF EINSTEIN EQUATIONS
EXCISION TECHNIQUE IN CONSTRAINED FORMULATIONS OF EINSTEIN EQUATIONS Journée Gravitation et Physique Fondamentale Meudon, 27 May 2014 Isabel Cordero-Carrión Laboratoire Univers et Théories (LUTh), Observatory
More informationIntroduction to Numerical Relativity I. Erik Schnetter, Pohang, July 2007
Introduction to Numerical Relativity I Erik Schnetter, Pohang, July 2007 Lectures Overview I. The Einstein Equations (Formulations and Gauge Conditions) II. Analysis Methods (Horizons and Gravitational
More informationStudies of self-gravitating tori around black holes and of self-gravitating rings
Studies of self-gravitating tori around black holes and of self-gravitating rings Pedro Montero Max Planck Institute for Astrophysics Garching (Germany) Collaborators: Jose Antonio Font (U. Valencia) Masaru
More informationFirst order BSSN formulation of Einstein s field equations
David Brown 1 Peter Diener 2 3 Jan Hesthaven 4 Frank Herrmann 3 Abdul Mroué 5 Olivier Sarbach 6 Erik Schnetter 7 Manuel Tiglio 3 Michael Wagman 4 1 North Carolina State University 2 Louisiana State University
More informationToward Binary Black Hole Simulations in Numerical Relativity
Toward Binary Black Hole Simulations in Numerical Relativity Frans Pretorius California Institute of Technology BIRS Workshop on Numerical Relativity Banff, April 19 2005 Outline generalized harmonic coordinates
More informationarxiv: v1 [gr-qc] 12 Apr 2016
Multi-horizon and Critical Behavior in Gravitational Collapse of Massless Scalar Zhoujian Cao,, Rong-Gen Cai, 2, 3, 2, 3, and Run-Qiu Yang Institute of Applied Mathematics, Academy of Mathematics and Systems
More informationImproved constrained scheme for the Einstein equations: An approach to the uniqueness issue
Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue Jérôme Novak (Jerome.Novak@obspm.fr) Laboratoire Univers et Théories (LUTH) CNRS / Observatoire de Paris / Université
More informationCONTENTS. 1. Introduction. 2. General Relativistic Hydrodynamics. 3. Collapse of Differentially Rotating Stars. 4. Summary
Collapse of Differentially Rotating Supermassive Stars: Post Black Hole Formation Stage Motoyuki Saijo (Rikkyo University, Japan) Ian Hawke (University of Southampton, UK) CONTENTS 1. Introduction 2. General
More informationMHD simulation for merger of binary neutron stars in numerical relativity
MHD simulation for merger of binary neutron stars in numerical relativity M. SHIBATA (Yukawa Institute for Theoretical Physics, Kyoto University) In collaboration with K. Kiuchi, L. Baiotti, & Y. Sekiguchi
More informationCalculating Accurate Waveforms for LIGO and LISA Data Analysis
Calculating Accurate Waveforms for LIGO and LISA Data Analysis Lee Lindblom Theoretical Astrophysics, Caltech HEPL-KIPAC Seminar, Stanford 17 November 2009 Results from the Caltech/Cornell Numerical Relativity
More informationGeneralized Harmonic Gauge Drivers
Generalized Harmonic Gauge Drivers Lee Lindblom Caltech Collaborators: Keith Matthews, Oliver Rinne, and Mark Scheel GR18 Sydney, Australia 13 July 2007 Gauge conditions are specified in the GH Einstein
More informationThe ECHO code: from classical MHD to GRMHD in dynamical spacetimes
The ECHO code: from classical MHD to GRMHD in dynamical spacetimes Luca Del Zanna Dipartimento di Fisica e Astronomia Università di Firenze Main collaborators: N. Bucciantini, O. Zanotti, S. Landi 09/09/2011
More informationKadath: a spectral solver and its application to black hole spacetimes
Kadath: a spectral solver and its application to black hole spacetimes Philippe Grandclément Laboratoire de l Univers et de ses Théories (LUTH) CNRS / Observatoire de Paris F-92195 Meudon, France philippe.grandclement@obspm.fr
More informationA Numerical Study of Boson Star Binaries
A Numerical Study of Boson Star Binaries Bruno C. Mundim with Matthew W. Choptuik (UBC) 12th Eastern Gravity Meeting Center for Computational Relativity and Gravitation Rochester Institute of Technology
More informationDYNAMICS OF MIXED BINARIES
DYNAMICS OF MIXED BINARIES Luciano Rezzolla Albert Einstein Institute, Golm, Germany In collaboration with Frank Löffler & Marcus Ansorg [Phys. Rev. D 74 104018 (2006)] SISSA (Trieste, Italy), AEI (Golm,
More informationNumerical Relativity
Numerical Relativity Mark A. Scheel Walter Burke Institute for Theoretical Physics Caltech July 7, 2015 Mark A. Scheel Numerical Relativity July 7, 2015 1 / 34 Outline: Motivation 3+1 split and ADM equations
More informationAnalytic Kerr Solution for Puncture Evolution
Analytic Kerr Solution for Puncture Evolution Jon Allen Maximal slicing of a spacetime with a single Kerr black hole is analyzed. It is shown that for all spin parameters, a limiting hypersurface forms
More informationBachelor Thesis. General Relativity: An alternative derivation of the Kruskal-Schwarzschild solution
Bachelor Thesis General Relativity: An alternative derivation of the Kruskal-Schwarzschild solution Author: Samo Jordan Supervisor: Prof. Markus Heusler Institute of Theoretical Physics, University of
More informationProject 2: Gravitational collapse in the spherically symmetric Einstein-Klein-Gordon system
Project 2: Gravitational collapse in the spherically symmetric Einstein-Klein-Gordon system Frans Pretorius and Richard Price July 19, 2009 1 Introduction In this project we will study the dynamics of
More informationA Hyperbolic Solver for Black Hole Initial Data in Numerical Relativity
Marshall University Marshall Digital Scholar Physics Faculty Research Physics Spring 4-18-2016 A Hyperbolic Solver for Black Hole Initial Data in Numerical Relativity Maria Babiuc-Hamilton Marshall University,
More informationGeneral Relativity and Cosmology Mock exam
Physikalisches Institut Mock Exam Universität Bonn 29. June 2011 Theoretische Physik SS 2011 General Relativity and Cosmology Mock exam Priv. Doz. Dr. S. Förste Exercise 1: Overview Give short answers
More informationSyllabus. Course Number PHY Pre-requisites General Relativity (PHY 6938) Dr. Pedro Marronetti - Charles E. Schmidt College of Science
Syllabus Course Name Numerical Relativity Course Number PHY 7566 Pre-requisites General Relativity (PHY 6938) Instructor Dr. Pedro Marronetti - Charles E. Schmidt College of Science Classroom SE 435 Room
More informationBlack-hole binary inspiral and merger in scalar-tensor theory of gravity
Black-hole binary inspiral and merger in scalar-tensor theory of gravity U. Sperhake DAMTP, University of Cambridge General Relativity Seminar, DAMTP, University of Cambridge 24 th January 2014 U. Sperhake
More informationSolving Einstein s equations with dual coordinate frames
PHYSICAL REVIEW D 74, 104006 (2006) Solving Einstein s equations with dual coordinate frames Mark A. Scheel, 1 Harald P. Pfeiffer, 1 Lee Lindblom, 1 Lawrence E. Kidder, 2 Oliver Rinne, 1 and Saul A. Teukolsky
More informationarxiv: v2 [gr-qc] 30 Nov 2017
Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries Kenneth A. Dennison 1 and Thomas W. Baumgarte 1 1 Department of Physics and Astronomy, Bowdoin College, Brunswick, ME 04011,
More informationGeneral-Relativistic Simulations of Stellar Collapse and The Formation of Stellar-Mass Black Holes
General-Relativistic Simulations of Stellar Collapse and The Formation of Stellar-Mass Black Holes Christian D. Ott, TAPIR, Caltech cott@tapir.caltech.edu Work in Collaboration with: Evan O Connor, Fang
More informationarxiv: v2 [gr-qc] 3 Mar 2015
Trumpet Slices in Kerr Spacetimes Kenneth A. Dennison, 1 Thomas W. Baumgarte, 1 Pedro J. Montero 1 Department of Physics Astronomy, Bowdoin College, Brunswick, ME 04011, USA Max-Planck-Institut für Astrophysik,
More informationTurduckening black holes: an analytical and computational study
Turduckening black holes: an analytical and computational study David Brown, 1 Peter Diener, 2, 3 Olivier Sarbach, 4 Erik Schnetter, 3, 2 and Manuel Tiglio 5, 6 1 Department of Physics, North Carolina
More informationNumerical Simulation of Orbiting Black Holes
Bernd Brügmann Penn State, 1/29/2004 Numerical Simulation of Orbiting Black Holes BB, Wolfgang Tichy, Nina Jansen (gr-qc/0312112) New: + evolutions last for one orbital time scale for close but still separate
More informationTheory. V H Satheeshkumar. XXVII Texas Symposium, Dallas, TX December 8 13, 2013
Department of Physics Baylor University Waco, TX 76798-7316, based on my paper with J Greenwald, J Lenells and A Wang Phys. Rev. D 88 (2013) 024044 with XXVII Texas Symposium, Dallas, TX December 8 13,
More informationGravitational Waves from Supernova Core Collapse: Current state and future prospects
Gravitational Waves from Core Collapse Harald Dimmelmeier harrydee@mpa-garching.mpg.de Gravitational Waves from Supernova Core Collapse: Current state and future prospects Work done with E. Müller (MPA)
More informationA Holographic Description of Black Hole Singularities. Gary Horowitz UC Santa Barbara
A Holographic Description of Black Hole Singularities Gary Horowitz UC Santa Barbara Global event horizons do not exist in quantum gravity: String theory predicts that quantum gravity is holographic:
More informationBlack Hole Formation in Randall-Sundrum II Braneworlds
Black Hole Formation in Randall-Sundrum II Braneworlds Matt Choptuik CIFAR Cosmology & Gravity Program Dept of Physics & Astronomy, UBC Workshop on Numerical and Mathematical Relativity Oppurg, DE September
More informationarxiv: v1 [gr-qc] 6 Nov 2009
Gowdy waves as a test-bed for constraint-preserving boundary conditions C. Bona and C. Bona-Casas Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca, Spain. Institute for Applied
More informationGeneral Relativity and Gravitational Waveforms
General Relativity and Gravitational Waveforms Deirdre Shoemaker Center for Relativistic Astrophysics School of Physics Georgia Institute of Technology Kavli Summer Program in Astrophysics 2017 Astrophysics
More informationAdjusted ADM systems and their expected stability properties 1
Adjusted ADM systems and their expected stability properties 1 Hisa-aki Shinkai 1 and Gen Yoneda 2 shinkai@atlas.riken.go.jp, yoneda@mn.waseda.ac.jp 1 Computational Science Division, Institute of Physical
More informationarxiv: v2 [gr-qc] 20 Aug 2008
NADA: A new code for studying self-gravitating tori around black holes Pedro J. Montero, 1 José A. Font, 1 and Masaru Shibata 2 1 Departamento de Astronomía y Astrofísica, Universidad de Valencia, Dr.
More informationGeneralized Harmonic Evolutions of Binary Black Hole Spacetimes
Generalized Harmonic Evolutions of Binary Black Hole Spacetimes Lee Lindblom California Institute of Technology AMS Meeting :: New Orleans :: 7 January 2007 Lee Lindblom (Caltech) Generalized Harmonic
More informationSolving Einstein s Equations: PDE Issues
Solving Einstein s Equations: PDE Issues Lee Lindblom Theoretical Astrophysics, Caltech Mathematical and Numerical General Relativity Seminar University of California at San Diego 22 September 2011 Lee
More informationQuantum Gravity and Black Holes
Quantum Gravity and Black Holes Viqar Husain March 30, 2007 Outline Classical setting Quantum theory Gravitational collapse in quantum gravity Summary/Outlook Role of metrics In conventional theories the
More informationCausality, hyperbolicity, and shock formation in Lovelock theories
Causality, hyperbolicity, and shock formation in Lovelock theories Harvey Reall DAMTP, Cambridge University HSR, N. Tanahashi and B. Way, arxiv:1406.3379, 1409.3874 G. Papallo, HSR arxiv:1508.05303 Lovelock
More informationSENR: A Super-Efficient Numerical Relativity Code for the Age of Gravitational Wave Astrophysics. Zachariah B. Etienne Ian Ruchlin
SENR: A Super-Efficient Numerical Relativity Code for the Age of Gravitational Wave Astrophysics Zachariah B. Etienne Ian Ruchlin in collaboration with Thomas W. Baumgarte Moore's Law Is Slowing Down Intel
More informationWhat happens at the horizon of an extreme black hole?
What happens at the horizon of an extreme black hole? Harvey Reall DAMTP, Cambridge University Lucietti and HSR arxiv:1208.1437 Lucietti, Murata, HSR and Tanahashi arxiv:1212.2557 Murata, HSR and Tanahashi,
More informationFirst structure equation
First structure equation Spin connection Let us consider the differential of the vielbvein it is not a Lorentz vector. Introduce the spin connection connection one form The quantity transforms as a vector
More informationOptimal constraint projection for hyperbolic evolution systems
PHYSICAL REVIEW D, VOLUME 70, 084017 Optimal constraint projection for hyperbolic evolution systems Michael Holst, 1,2 Lee Lindblom, 1 Robert Owen, 1 Harald P. Pfeiffer, 1 Mark A. Scheel, 1 and Lawrence
More informationThe Schwarzschild Metric
The Schwarzschild Metric The Schwarzschild metric describes the distortion of spacetime in a vacuum around a spherically symmetric massive body with both zero angular momentum and electric charge. It is
More informationarxiv:gr-qc/ v2 8 Jan 2001
The 3D Grazing Collision of Two Black Holes Miguel Alcubierre (1), Werner Benger (1,2), Bernd Brügmann (1), Gerd Lanfermann (1), Lars Nerger (1), Edward Seidel (1,3), and Ryoji Takahashi (1) (1) Max-Planck-Institut
More informationarxiv: v1 [gr-qc] 2 Feb 2015
arxiv:1502.00424v1 [gr-qc] 2 Feb 2015 Valiente Kroon s obstructions to smoothness at infinity James Grant Department of Mathematics, University of Surrey, Paul Tod Mathematical Institute University of
More informationCurvilinear coordinates
C Curvilinear coordinates The distance between two points Euclidean space takes the simplest form (2-4) in Cartesian coordinates. The geometry of concrete physical problems may make non-cartesian coordinates
More informationAn exact solution for 2+1 dimensional critical collapse
An exact solution for + dimensional critical collapse David Garfinkle Department of Physics, Oakland University, Rochester, Michigan 839 We find an exact solution in closed form for the critical collapse
More informationBlack Holes, Integrable Systems and Soft Hair
Ricardo Troncoso Black Holes, Integrable Systems and Soft Hair based on arxiv: 1605.04490 [hep-th] In collaboration with : A. Pérez and D. Tempo Centro de Estudios Científicos (CECs) Valdivia, Chile Introduction
More informationExcision boundary conditions for black-hole initial data
PHYSICAL REVIEW D, VOLUME 70, 104016 Excision boundary conditions for black-hole initial data Gregory B. Cook* Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, USA Harald
More informationIntroduction to Black Hole Thermodynamics. Satoshi Iso (KEK)
Introduction to Black Hole Thermodynamics Satoshi Iso (KEK) Plan of the talk [1] Overview of BH thermodynamics causal structure of horizon Hawking radiation stringy picture of BH entropy [2] Hawking radiation
More informationA Simple, Direct Finite Differencing of the Einstein Equations
A Simple, Direct Finite Differencing of the Einstein Equations Travis M. Garrett Louisiana State University (Dated: 2008.11.12) We investigate a simple variation of the Generalized Harmonic method for
More informationKerr black hole and rotating wormhole
Kerr Fest (Christchurch, August 26-28, 2004) Kerr black hole and rotating wormhole Sung-Won Kim(Ewha Womans Univ.) August 27, 2004 INTRODUCTION STATIC WORMHOLE ROTATING WORMHOLE KERR METRIC SUMMARY AND
More informationColliding black holes
Colliding black holes U. Sperhake DAMTP, University of Cambridge Holographic vistas on Gravity and Strings Kyoto, 26 th May 2014 U. Sperhake (DAMTP, University of Cambridge) Colliding black holes 26/05/2014
More informationTowards general-relativistic pulsar magnetospheres
Towards general-relativistic pulsar magnetospheres Jérôme Pétri Observatoire Astronomique de Strasbourg, Université de Strasbourg, France. Physics of Neutron Stars, Saint-Petersbourg, 29/7/2014 Jérôme
More informationarxiv:astro-ph/ v1 19 Nov 2006
Non-axisymmetric instability and fragmentation of general relativistic quasi-toroidal stars Burkhard Zink, 1, 2 Nikolaos Stergioulas, 3 Ian Hawke, 4 Christian D. Ott, 5, 6 Erik Schnetter, 1, 5 and Ewald
More informationBlack Hole-Neutron Star Binaries in General Relativity. Thomas Baumgarte Bowdoin College
Black Hole-Neutron Star Binaries in General Relativity Thomas Baumgarte Bowdoin College Keisuke Taniguchi, Joshua Faber, Stu Shapiro University of Illinois Numerical Relativity Solve Einstein s equations
More informationResearch Center for the Early Universe (RESCEU) Department of Physics. Jun ichi Yokoyama
Research Center for the Early Universe (RESCEU) Department of Physics Jun ichi Yokoyama time size Today 13.8Gyr Why is Our Universe Big, dark energy Old, and full of structures? galaxy formation All of
More informationThe nonlinear dynamical stability of infrared modifications of gravity
The nonlinear dynamical stability of infrared modifications of gravity Aug 2014 In collaboration with Richard Brito, Vitor Cardoso and Matthew Johnson Why Study Modifications to Gravity? General relativity
More informationGetting The Spin Right In Black-Hole Binaries
Getting The Spin Right In Black-Hole Binaries Gregory B. Cook Wake Forest University July 25, 2005 Abstract We will take a detailed look at the issues involved in setting the spin of a black hole during
More informationarxiv:gr-qc/ v2 30 Jan 2005
Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole Luca Baiotti, 1 Ian Hawke, 2 Pedro J. Montero, 1 Frank Löffler, 2 Luciano Rezzolla, 1, 3 Nikolaos Stergioulas,
More informationRotating black hole surrounded by self-gravitating torus in the puncture framework
PHYSICAL REVIEW D 76, 6435 (7) Rotating black hole surrounded by self-gravitating torus in the puncture framework Masaru Shibata Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro,
More informationSag A Mass.notebook. September 26, ' x 8' visual image of the exact center of the Milky Way
8' x 8' visual image of the exact center of the Milky Way The actual center is blocked by dust and is not visible. At the distance to the center (26,000 ly), this image would span 60 ly. This is the FOV
More informationEinstein Toolkit Workshop. Joshua Faber Apr
Einstein Toolkit Workshop Joshua Faber Apr 05 2012 Outline Space, time, and special relativity The metric tensor and geometry Curvature Geodesics Einstein s equations The Stress-energy tensor 3+1 formalisms
More informationWave Extraction in Higher Dimensional Numerical Relativity
Wave Extraction in Higher Dimensional Numerical Relativity William Cook with U. Sperhake, P. Figueras. DAMTP University of Cambridge VIII Black Holes Workshop December 22nd, 2015 Overview 1 Motivation
More informationYukawa Institute Workshop Strings and Fields Developments in String Theory and Quantum Field Theory. Conic D-branes
Yukawa Institute Workshop Strings and Fields Developments in String Theory and Quantum Field Theory Conic D-branes Shunichiro Kinoshita (Chuo University) K. Hashimoto (Osaka), K. Murata (Keio) Based on
More informationPinhole Cam Visualisations of Accretion Disks around Kerr BH
Pinhole Camera Visualisations of Accretion Disks around Kerr Black Holes March 22nd, 2016 Contents 1 General relativity Einstein equations and equations of motion 2 Tetrads Defining the pinhole camera
More informationGeneral Relativity in AdS
General Relativity in AdS Akihiro Ishibashi 3 July 2013 KIAS-YITP joint workshop 1-5 July 2013, Kyoto Based on work 2012 w/ Kengo Maeda w/ Norihiro Iizuka, Kengo Maeda - work in progress Plan 1. Classical
More informationDo semiclassical zero temperature black holes exist?
Do semiclassical zero temperature black holes exist? Paul R. Anderson Department of Physics, Wake Forest University, Winston-Salem, North Carolina 7109 William A. Hiscock, Brett E. Taylor Department of
More informationMixed Black Hole - Neutron Star Simulations with Whisky
Mixed Black Hole - Neutron Star Simulations with Whisky Roland Haas (Georgia Tech) Center for Relativistic Astrophysics Collaborators: Tanja Bode, Jim Healy, Pablo Laguna, Deirdre Shoemaker Oct 06, 2009
More informationElectromagnetic Counterparts to Gravitational Wave Detections: Bridging the Gap between Theory and Observation
Electromagnetic Counterparts to Gravitational Wave Detections: Bridging the Gap between Theory and Observation Prof. Zach Etienne, West Virginia University 4 km General Relativity, Briefly Special Relativity:
More informationNew Numerical Code for Black Hole Initial Data
Marshall University Marshall Digital Scholar Physics Faculty Research Physics Summer 6-2017 New Numerical Code for Black Hole Initial Data Maria Babiuc-Hamilton Marshall University, babiuc@marshall.edu
More informationClassical and Quantum Dynamics in a Black Hole Background. Chris Doran
Classical and Quantum Dynamics in a Black Hole Background Chris Doran Thanks etc. Work in collaboration with Anthony Lasenby Steve Gull Jonathan Pritchard Alejandro Caceres Anthony Challinor Ian Hinder
More informationOptimal Constraint Projection for Hyperbolic Evolution Systems
Optimal Constraint Projection for Hyperbolic Evolution Systems Michael Holst 1,2, Lee Lindblom 1, Robert Owen 1, Harald P. Pfeiffer 1, Mark A. Scheel 1, and Lawrence E. Kidder 3 1 Theoretical Astrophysics
More informationBBH coalescence in the small mass ratio limit: Marrying black hole perturbation theory and PN knowledge
BBH coalescence in the small mass ratio limit: Marrying black hole perturbation theory and PN knowledge Alessandro Nagar INFN (Italy) and IHES (France) Small mass limit: Nagar Damour Tartaglia 2006 Damour
More informationIntroduction to isolated horizons in numerical relativity
Introduction to isolated horizons in numerical relativity Olaf Dreyer* Perimeter Institute for Theoretical Physics, 35 King Street North, Waterloo, Ontario, Canada N2J 2W9 Badri Krishnan and Deirdre Shoemaker
More informationAbsorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates
Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates Jérôme Novak, Silvano Bonazzola arxiv:gr-qc/0203102v2 29 Apr 2004 Laboratoire de l Univers
More informationarxiv:gr-qc/ v2 18 Jul 2002
Gauge conditions for long-term numerical black hole evolutions without excision Miguel Alcubierre (1,2), Bernd Brügmann (1), Peter Diener (1), Michael Koppitz (1), Denis Pollney (1), Edward Seidel (1,3),
More informationChapter 21. The Kerr solution The Kerr metric in Boyer-Lindquist coordinates
Chapter 21 The Kerr solution As shown in Chapter 10, the solution of Einstein s equations describing the exterior of an isolated, spherically symmetric, static object is quite simple. Indeed, the Schwarzschild
More informationCollapse of Kaluza-Klein Bubbles. Abstract. Kaluza-Klein theory admits \bubble" congurations, in which the
UMDGR{94{089 gr{qc/940307 Collapse of Kaluza-Klein Bubbles Steven Corley and Ted Jacobson 2 Department of Physics, University of Maryland, College Park, MD 20742{4 Abstract Kaluza-Klein theory admits \bubble"
More informationBackreaction as an explanation for Dark Energy?
Backreaction as an explanation for Dark Energy? with some remarks on cosmological perturbation theory James M. Bardeen University of Washington The Very Early Universe 5 Years On Cambridge, December 17,
More informationFormation and evolution of BH and accretion disk in Collapsar
Formation and evolution of BH and accretion disk in Collapsar Yuichiro Sekiguchi National Astronomical Observatory of Japan arxiv : 1009.5303 Motivation Collapsar model of GRB Central engine : Black hole
More informationNew Model of massive spin-2 particle
New Model of massive spin-2 particle Based on Phys.Rev. D90 (2014) 043006, Y.O, S. Akagi, S. Nojiri Phys.Rev. D90 (2014) 123013, S. Akagi, Y.O, S. Nojiri Yuichi Ohara QG lab. Nagoya univ. Introduction
More informationApplying black hole perturbation theory to numerically generated. spacetimes
Applying black hole perturbation theory to numerically generated spacetimes Andrew M. Abrahams Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 arxiv:gr-qc/9508059v1
More informationBondi-Sachs Formulation of General Relativity (GR) and the Vertices of the Null Cones
Bondi-Sachs Formulation of General Relativity (GR) and the Vertices of the Null Cones Thomas Mädler Observatoire de Paris/Meudon, Max Planck Institut for Astrophysics Sept 10, 2012 - IAP seminar Astrophysical
More informationLevel sets of the lapse function in static GR
Level sets of the lapse function in static GR Carla Cederbaum Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany September 4, 2014 Abstract We present a novel
More informationarxiv: v2 [gr-qc] 6 Apr 2008
Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation arxiv:0804.0628v2 [gr-qc] 6 Apr 2008 Mark Hannam, 1, 2 Sascha Husa, 3 Frank Ohme, 1 Bernd Brügmann, 1 and Niall Ó
More informationCharge, geometry, and effective mass in the Kerr- Newman solution to the Einstein field equations
Charge, geometry, and effective mass in the Kerr- Newman solution to the Einstein field equations Gerald E. Marsh Argonne National Laboratory (Ret) 5433 East View Park Chicago, IL 60615 E-mail: gemarsh@uchicago.edu
More informationTO GET SCHWARZSCHILD BLACKHOLE SOLUTION USING MATHEMATICA FOR COMPULSORY COURSE WORK PAPER PHY 601
TO GET SCHWARZSCHILD BLACKHOLE SOLUTION USING MATHEMATICA FOR COMPULSORY COURSE WORK PAPER PHY 601 PRESENTED BY: DEOBRAT SINGH RESEARCH SCHOLAR DEPARTMENT OF PHYSICS AND ASTROPHYSICS UNIVERSITY OF DELHI
More informationUmbilic cylinders in General Relativity or the very weird path of trapped photons
Umbilic cylinders in General Relativity or the very weird path of trapped photons Carla Cederbaum Universität Tübingen European Women in Mathematics @ Schloss Rauischholzhausen 2015 Carla Cederbaum (Tübingen)
More informationEinstein Double Field Equations
Einstein Double Field Equations Stephen Angus Ewha Woman s University based on arxiv:1804.00964 in collaboration with Kyoungho Cho and Jeong-Hyuck Park (Sogang Univ.) KIAS Workshop on Fields, Strings and
More informationSolving PDEs Numerically on Manifolds with Arbitrary Spatial Topologies
Solving PDEs Numerically on Manifolds with Arbitrary Spatial Topologies Lee Lindblom Theoretical Astrophysics, Caltech Center for Astrophysics and Space Sciences, UC San Diego. Collaborators: Béla Szilágyi,
More informationThe imaginary part of the GR action and the large-spin 4-simplex amplitude
The imaginary part of the GR action and the large-spin 4-simplex amplitude Yasha Neiman Penn State University 1303.4752 with N. Bodendorfer; also based on 1212.2922, 1301.7041. May 7, 2013 Yasha Neiman
More informationBraneworlds: gravity & cosmology. David Langlois APC & IAP, Paris
Braneworlds: gravity & cosmology David Langlois APC & IAP, Paris Outline Introduction Extra dimensions and gravity Large (flat) extra dimensions Warped extra dimensions Homogeneous brane cosmology Brane
More informationOn the Hawking Wormhole Horizon Entropy
ESI The Erwin Schrödinger International Boltzmanngasse 9 Institute for Mathematical Physics A-1090 Wien, Austria On the Hawking Wormhole Horizon Entropy Hristu Culetu Vienna, Preprint ESI 1760 (2005) December
More informationTrapped ghost wormholes and regular black holes. The stability problem
Trapped ghost wormholes and regular black holes. The stability problem Kirill Bronnikov in collab. with Sergei Bolokhov, Arislan Makhmudov, Milena Skvortsova (VNIIMS, Moscow; RUDN University, Moscow; MEPhI,
More informationThreshold of singularity formation in the semilinear wave equation
PHYSICAL REVIEW D 71, 044019 (2005) Threshold of singularity formation in the semilinear wave equation Steven L. Liebling Department of Physics, Long Island University-C.W. Post Campus, Brookville, New
More informationA UNIFIED TREATMENT OF GRAVITATIONAL COLLAPSE IN GENERAL RELATIVITY
A UNIFIED TREATMENT OF GRAVITATIONAL COLLAPSE IN GENERAL RELATIVITY & Anthony Lun Fourth Aegean Summer School on Black Holes Mytilene, Island of Lesvos 17/9/2007 CONTENTS Junction Conditions Standard approach
More information