Numerical Relativity as a Tool for Computing GW Generation (2/2) 
Numerical Relativity as a Tool for Computing GW Generation (2/2) by Caltech / Kip Thorne
Video Lecture 34 of 69
Copyright Information: This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen. The full course, including this and many other lecture videos, exercises, solutions to exercises, and lists of relevant reading, are available on the web at http://elmer.caltech.edu/ph237/
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Date Added: March 19, 2010

Lecture Description

Numerical Relativity as a Tool for Computing GW Generation -- Week 10, Lecture 18 [by Marc Scheel]

A. Motivation: Sources that require numerical relativity for their analysis

  1. Binary black hole mergers

a. Relevance to LIGO & partners, and to LISA
b. Estimated event rates for LIGO-I, LIGO-II and LISA
c. Inspiral, merger, and ringdown; estimated wave strengths from each
d. Rich physics expected in mergers: strong, nonlinear effects; spin-spin and spin-orbit coupling; angular-momentum hangup
e. Importance of simulating mergers as foundation for interpreting observations

       2. Tidal disruption of NS by a BH companion
             a. Estimated event rate for LIGO-II
             b. Information carried by waves: NS structure and equation of state
             c. Possible connection to gamma ray bursts
             d. Importance of simulations for interpreting observations

       3. Some other sources: NS/NS mergers, cosmic string vibrations, brane excitations in early universe
       4. The necessity to use numerical relativity in simulations of these sources

B. Mathematical underpinnings of numerical relativity

  1. 3+1 decomposition of spacetime into space plus time
  2. Initial data must satisfy "constraint equations"
  3. Evolve via "dynamical Einstein equations"
  4. Gauge freedom
  5. Analogy with electromagnetic theory

C. Mathematical details

  1. Spacetime slicing; lapse, shift, and 3-metric; extrinsic curvature
  2. Hamiltonian constraint equation
  3. Momentum constraint equations
  4. Dynamical equations
  5. Choices of lapse and shift

D. Current state of the art in numerical relativity; current efforts on BH/BH inspiral & merger

Course Index

  1. The Nature of Gravitational Waves
  2. Gravitational Waves Data Analysis
  3. Gravitational Wave Sources in Neutron Stars
  4. Introduction to General Relativity: Tidal Gravity
  5. Mathematics of General Relativity: Tensor Algebra
  6. Mathematics of General Relativity: Tensor Differentiation
  7. Introduction to General Relativity (4/5)
  8. Introduction to General Relativity (5/5)
  9. Weak Gravitational Waves in Flat Spacetime (1/6)
  10. Weak Gravitational Waves in Flat Spacetime (2/6)
  11. Weak Gravitational Waves in Flat Spacetime (3/6)
  12. Weak Gravitational Waves in Flat Spacetime (4/6)
  13. Weak Gravitational Waves in Flat Spacetime (5/6)
  14. Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
  15. Propagation of Gravitational Waves Through Curved Spacetime (2/5)
  16. Propagation of Gravitational Waves Through Curved Spacetime (3/5)
  17. Propagation of Gravitational Waves Through Curved Spacetime (4/5)
  18. Propagation of Gravitational Waves Through Curved Spacetime (5/5)
  19. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
  20. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
  21. Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
  22. Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
  23. Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
  24. Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
  25. Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
  26. Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
  27. Supermassive Black Holes and their Gravitational Waves (1/3)
  28. Supermassive Black Holes and their Gravitational Waves (2/3)
  29. Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
  30. Gravitational Waves from Inflation (2/2)
  31. Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
  32. Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
  33. Numerical Relativity as a Tool for Computing GW Generation (1/2)
  34. Numerical Relativity as a Tool for Computing GW Generation (2/2)
  35. The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
  36. The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
  37. The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
  38. The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
  39. Overview of Real LIGO Interferometers (1/2)
  40. Overview of Real LIGO Interferometers (2/2)
  41. Thermal Noise in LIGO Interferometers and its Control (1/2)
  42. Thermal Noise in LIGO Interferometers and its Control (2/2)
  43. Control Systems and Laser Frequency Stabilization (1/2)
  44. Control Systems and Laser Frequency Stabilization (2/2)
  45. Interferometer Simulations and Lock Acquisition in LIGO
  46. Seismic Isolation in Earth-Based Interferometers
  47. Quantum Optical noise in GW Interferometers (1/2)
  48. Quantum Optical noise in GW Interferometers (2/2)
  49. LIGO data analysis (1/2)
  50. LIGO data analysis (2/2)
  51. The Long-Term Future of LIGO: Facility Limits
  52. The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
  53. Large Experimental Science and LIGO as an Example (1/2)
  54. Large Experimental Science and LIGO as an Example (2/2)
  55. Resonant-Mass GW Detectors for the HF Band (1/2)
  56. Resonant-Mass GW Detectors for the HF Band (2/2)
  57. CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
  58. Doppler tracking of spacecraft for GW detection in the low frequency band
  59. Pulsar timing for GW detection in the very low frequency band
  60. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
  61. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
  62. LISA's Lasers and Optics (1/2)
  63. LISA's Lasers and Optics (2/2)
  64. Time-Delay Interferometry [TDI] for LISA (1/2)
  65. Time-Delay Interferometry [TDI] for LISA (2/2)
  66. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
  67. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
  68. The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
  69. GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization

Course Description

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.

Resources:

Credits:
Lectures by Thorne and Guest Lecturers*
Video of lectures by Bondarescu and Chen
Homework problems by Thorne and Guest Lecturers
Homework solutions by Bondarescu and Chen

*John Armstrong (JPL), Barry Barish, Erik Black, Alessandra Buonanno, Yanbei Chen, Riccardo De Salvo, Ronald Drever, Matt Evans, William Folkner (JPL), William Hamilton (LSU), Mark Kamionkowski, Albert Lazzarini, Lee Lindblom, Sterl Phinney, Mark Scheel, Bonny Schumaker (JPL), Robert Spero (JPL), Alan Weinstein, Phil Willems.

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