**COURSE DESCRIPTION**

This course is an introduction to all major aspects of gravitational waves:

- Their physical and mathematical descriptions;
- Their generation, propagation and interaction withdetectors;
- Their astrophysical sources (the big bang, early-universe phenomena, binary stars, black holes, supernovae, neutron stars, …); and
- Gravitational wave detectors (their design, underlying physics, noise and noise control, and data analysis) with emphasis on earth-based interferometers (LIGO, VIRGO, GEO600, TAMA) and space-based interferometers (LISA), but also including resonant-mass detectors, doppler tracking of spacecraft, pulsar timing, and polarization of the cosmic microwave background.

The course is divided in

A. Gravitational-wave theory and sources

B. Gravitational-wave detectors

## PART A: GRAVITATIONAL-WAVE THEORY AND SOURCES

**1- Overview of Gravitational-Wave Science ** – slides, assignments and solutions

- The nature of gravitational waves (slides, assignment, solutions)
- The GW spectrum: HF, LF, VLF, ELF bands
- Detection techniques (slides)
- GW data analysis
- GW sources and science (slides, assignment, solutions)

Lecturer Kip Thorne: **“Overview of Gravitational-Wave Science (1/3)”**

Lecturer Kip Thorne: **“Overview of Gravitational-Wave Science (2/3)”**

Lecturer Kip Thorne: **“Overview of Gravitational-Wave Science (3/3)”**

**2- Introduction to General Relativity** – assignments and solutions

- Tidal gravity in Newtonian theory
- The mathematics underlying general relativity
- The Einstein field equations

Lecturer Kip Thorne: **“Introduction to General Relativity (1/5)”**

Lecturer Kip Thorne: **“Introduction to General Relativity (2/5)”**

Lecturer Kip Thorne: **“Introduction to General Relativity (3/5)”**

Lecturer Kip Thorne: **“Introduction to General Relativity (4/5)”**

Lecturer Kip Thorne: **“Introduction to General Relativity (5/5)”**

**3- Weak Gravitational Waves in Flat Spacetime** – assignments and solutions

- Wave equation for Riemann tensor
- Transverse-traceless GW field, + and x polarizations
- GW’s tidal forces (relative motion of freely falling particles)
- Metric perturbations, TT gauge and other gauges
- Proper reference frame of an observer
- Physical measurements of GW’s in a proper reference frame
- Generation of GW’s: The linearized Einstein field equations
- Projecting out the TT GW field
- Slow-motion, weak-stress approximation for GW sources
- The quadrupole formula for GW generation

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (1/6)”**

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (2/6)”**

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (3/6)”**

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (4/6)”**

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (5/6)”**

Lecturer Kip Thorne: **“Weak Gravitational Waves in Flat Spacetime (6/6)”**

**4- Propagation of Gravitational Waves Through Curved Spacetime** – assignments and solutions

- Short wavelength approximation; two-lenghscale expansion
- Curved-spacetime wave equation for Riemann tensor
- Solution of wave equation via eikonal approximation (geometric optics) – Foundations
- Geometric optics – Details
- Propagation of GW’s through homogeneous matter

Lecturer Kip Thorne: **“Propagation of Gravitational Waves Through Curved Spacetime (1/4)”**

Lecturer Kip Thorne: **“Propagation of Gravitational Waves Through Curved Spacetime (2/4)”**

Lecturer Kip Thorne: **“Propagation of Gravitational Waves Through Curved Spacetime (3/4)”**

Lecturer Kip Thorne: **“Propagation of Gravitational Waves Through Curved Spacetime (4/4)”**

**5- Generation of GWs by Slow-Motion Sources in Curved Spacetime**

- Strong-field region, weak-field near zone, local wave zone, distant wave zone
- Multipolar expansions of metric perturbation in weak-field near zone and local wave zone
- Application to a binary star system with circular orbit

Lecturer Kip Thorne: **“Generation of GWs by Slow-Motion Sources in Curved Spacetime (1/2)”**

Lecturer Kip Thorne: **“Generation of GWs by Slow-Motion Sources in Curved Spacetime (2/2)”**

**6- Astrophysical Phenomenology of Binary-Star GW Sources** – slides, assignments and solutions, complementary reading: “An overview of gravitational-wave sources”, by Cutler and Thorne 2002

- GW’s from Binary Star Systems
- Issues relevant to estimating numbers of binary GW sources and their merger rates
- Estimates of numbers of binary GW sources and inspiral/merger rates
- Estimates of numbers of binary GW sources for LISA and inspiral/merger rates for LIGO

Lecturer Sterl Phinney: **“Astrophysical Phenomenology of Binary-Star GW Sources (1/5)”**

Lecturer Sterl Phinney: **“Astrophysical Phenomenology of Binary-Star GW Sources (2/5)”**

Lecturer Sterl Phinney: **“Astrophysical Phenomenology of Binary-Star GW Sources (3/5)”**

Lecturer Sterl Phinney: **“Astrophysical Phenomenology of Binary-Star GW Sources (4/5)”**

Lecturer Kip Thorne: **“Astrophysical Phenomenology of Binary-Star GW Sources (5/5)”**

**7- Binary Inspiral: Post-Newtonian Gravitational Waveforms for LIGO and Its Partners**

- Matched-filtering data analysis to detect inspiral waves
- Foundations for post-Newtonian approximations to General Relativity
- Post-Newtonian inspiral waveforms for circular orbits and vanishing spins
- Expansion parameter
- Phase evolution governed by energy balance
- Waveform in time domain
- Waveform in frequency domain, via stationary-phase approximation
- Influence of spin-orbit and spin-spin coupling: Orbital and spin precession; waveform modulation
- Innermost stable circular orbit (ISCO) and transition from inspiral to plunge
- The IBBH problem: failure of post-Newtonian waveforms in late inspiral; methods to deal with this

Lecturer Alessandra Buonanno: **“Binary Inspiral: Post-Newtonian Waveforms (1/1)”**

**8- Supermassive Black Holes and their Gravitational Waves** – assignments and solutions

- Astrophysical phenomenology of SMBH’s in galactic nuclei
- Mergers of galaxies
- Evolution of SMBH binary
- Capture and inspiral of stars by a SMBH
- Gravitational waves from SMBH binary inspiral, as measured by LISA
- GW’s from inspiral of a compact star (or BH) into a SMBH

Lecturer Sterl Phinney: **“Supermassive Black Holes and their Gravitational Waves (1/4)”**

Lecturer Sterl Phinney: **“Supermassive Black Holes and their Gravitational Waves (2/4)”**

Lecturer Kip Thorne: **“Supermassive Black Holes and their Gravitational Waves (3/4)”**

Lecturer Kip Thorne: **“Supermassive Black Holes and their Gravitational Waves (4/4)”**

**9- GW’s from Big Bang: Amplification of Vacuum Fluctuations by Inflation**

- Basic idea: same as parametric amplification of classical waves
- Mathematical details

**10- GW’s from Neutron-Star Rotation and Pulsation** – assignments

- GW’s from a structurally deformed, rotating NS
- GW’s from pulsations in a rotating NS

Lecturer Lee Lindblom: **“GW’s from Neutron-Star Rotation and Pulsation (1/2)”**

Lecturer Lee Lindblom: **“GW’s from Neutron-Star Rotation and Pulsation (2/2)”**

**11- Numerical Relativity as a Tool for Computing GW Generation**

- Motivation: Sources that require numerical relativity for their analysis
- Mathematical underpinnings of numerical relativity
- Mathematical details
- Current state of the art in numerical relativity; current efforts on BH/BH inspiral & merger

Lecturer Marc Scheel: **“Numerical Relativity as a Tool for Computing GW Generation (1/2)”**

Lecturer Marc Scheel: **“Numerical Relativity as a Tool for Computing GW Generation (2/2)”**

## PART B: GRAVITATIONAL-WAVE DETECTORS

**1- The Physics Underlying Earth-Based GW Interferometers** – assignments and solutions

- Idealized Interferometer: Conceptual design and crude analysis
- General relativity: Proper reference frame of an accelerated observer
- Optics
- Statistical Physics: The theory of random processes

Lecturer Kip Thorne: **“The Physics Underlying Earth-Based GW Interferometers (1/4)”**

Lecturer Kip Thorne: **“The Physics Underlying Earth-Based GW Interferometers (2/4)”**

Lecturer Kip Thorne: **“The Physics Underlying Earth-Based GW Interferometers (3/4)”**

Lecturer Kip Thorne: **“The Physics Underlying Earth-Based GW Interferometers (4/4)”**

**2- Overview of Real LIGO Interferometers** – assignments and solutions, additional reading: PhD of Martin Regehr

- Overview of noise sources & how they are controlled
- Optics
- Suspensions for mirrors and other optical elements

Lecturer Alan Weinstein: **“Overview of Real LIGO Interferometers (1/2)”**

Lecturer Alan Weinstein: **“Overview of Real LIGO Interferometers (2/2)”**

**3- Thermal Noise in LIGO Interferometers and its Control**

- Motivation: Brownian motion of a dust grain buffeted by molecules of an ideal gas
- Fluctuation-dissipation theorem
- Damped pendulum: suspension thermal noise derived from fluctuation-dissipation theorem
- Dissipation in a LIGO test mass or suspension described via imaginary part of generalized elastic modulus
- Dissipation/fluctuation processes for a LIGO test mass

Lecturer Phil Willems: **“Thermal Noise in LIGO Interferometers and its Control (1/2)”**

Lecturer Phil Willems: **“Thermal Noise in LIGO Interferometers and its Control (2/2)”**

**4- Control Systems and Laser Frequency Stabilization** – assignments and solutions

- Introduction
- General, linear control theory
- Laser frequency stabilization via locking to eigenmode of an optical cavity: an example of linear control theory

Lecturer Erik Black: **“Control Systems and Laser Frequency Stabilization (1/2)”**

Lecturer Erik Black: **“Control Systems and Laser Frequency Stabilization (2/2)”**

**5- Interferometer Simulations and Lock Acquisition in LIGO** – slides

- Simulations of all or part of a LIGO interferometer
- Lock acquisition in LIGO-I

Lecturer Matt Evans: **“Interferometer Simulations and Lock Acquisition in LIGO (1/1)”**

**6- Seismic Isolation in Earth-Based Interferometers** – slides

- Seismic attenuation requirements
- Principals of seismic attenuation
- The Virgo isolation system as an example
- The need for seismic attenuation in all six degrees of freedom
- Vertical attenuation: the most serious problem
- Creep in stressed elements of isolation system
- Mechanical resonances in isolation system

Lecturer Riccardo De Salvo: **“Seismic Isolation in Earth-Based Interferometers (1/1)”**

**7 – Quantum Optical Noise in LIGO Interferometers** – slides, assignments and solutions

- Introduction: review of interferometers and their sensitivities; references on quantum optical noise; the experimental challenge: prevent quantum properties of detector and light (the “probe”) from affecting the GW information we seek
- Quantum optical noise in conventional interferometers (LIGO-I, TAMA, VIRGO)
- Free-mass standard quantum limit [SQL] (for conventional interferometers)
- Ways to beat the SQL
- Quantum optical noise in signal-recycled interferometers (LIGO-II)
- Other noise sources and total noise in LIGO-II; the severity of thermoelastic noise
- Beyond LIGO-II: How to improve the sensitivity further without radical changes of interferometer’s optical topology
- Beyond LIGO-II: New optical topologies

Lecturers Alessandra Buonano and Yanbei Chen: **“Quantum Optical Noise in LIGO Interferometers (1/2)”**

Lecturers Alessandra Buonano and Yanbei Chen: **“Quantum Optical Noise in LIGO Interferometers (2/2)”**

**8 – LIGO Data Analysis** – slides, assignments and solutions

- The context: LIGO-I noise curve and anticipated signal strengths
- LIGO data attributes
- Some signal processing theory and methods
- Optimal filtering for parametrizable waveforms
- Stochastic background searches
- Hypothesis testing: maximum likelihood; Baysean statistics; false alarm probability compared with detection probability
- Searching for (transient) bursts of GW’s
- Analysis of data from a network of detectors

Lecturer Albert Lazzarini: **“LIGO Data Analysis (1/2)”**

Lecturer Albert Lazzarini: **“LIGO Data Analysis (2/2)”**

**9 – The Long-Term Future of LIGO: Facility Limits, and Techniques for Improving on LIGO-II** – slides, assignments and solutions

- Facilities Limits (limits on sensitivity due to the LIGO environment, vacuum system, …)
- Techniques for Improving on LIGO-II

Lecturer Kip Thorne: **“The Long-Term Future of LIGO (1/2)”**

Lecturer Ronald W.P. Drever: **“The Long-Term Future of LIGO (2/2)”**

**10 – Large Experimental Science, with LIGO as an Example** – slides

- Introduction and Overview: Small science contrasted with large science, in the US
- How to create an effective research environment in a large science project; how to maintain flexibility, with experiment driven by science and ideas
- Long-range (decades-long) strategic planning
- Strategic (long-range) planning in high-energy physics
- LIGO organization and construction
- LIGO status

Lecturer Barry Barish: **“Large Experimental Science, with LIGO as an Example (1/2)”**

Lecturer Barry Barish: **“Large Experimental Science, with LIGO as an Example (2/2)”**

**11 – Resonant-Mass (“Bar”) GW Detectors for the HF Band ** – slides

- Historical remarks; Joseph Weber’s pioneering contributions; others’ contributions
- Basic elements of a resonant-mass detector, and how it works
- The full mechanical-electrical system for the LSU detector Allegro
- Experience with Allegro
- Prospects to search for a stochastic background using Allegro and the Livingston LIGO interferometer
- TIGA and Spherical Bars: Looking toward the future
- IGEC: The international network of bar detectors (*)
- Some results from the LSU detector Allegro
- Prospects for future improvements:
- Identifying a GW burst amidst noise: an audio analogy
- Spherical detectors: current status and plans — in Italy, Netherlands and Brazil; projected sensitivity compared with Advanced LIGO (LIGO-II)

Lecturer William O. Hamilton: **“Resonant-Mass (“Bar”) GW Detectors for the HF Band (1/2)”**

Lecturer William O. Hamilton: **“Resonant-Mass (“Bar”) GW Detectors for the HF Band (2/2)”**

(*) CaJAGWR Seminar: William O. Hamilton (LSU) slides

Speaker William O. Hamilton: **“CaJAGWR Seminar”**

**12 – Doppler Tracking of Spacecraft for GW Detection in the LF Band ** – slides

- The doppler-tracking method of GW detection
- Doppler-tracking observations to date: about 160 hours total from 1980 through 1997 on 8 spacecraft, including one three-spacecraft experiment
- Data analysis for various types of signals
- Cassini: the current-generation observatory
- Beyond Cassini

Lecturer John Armstrong: **“Doppler Tracking of Spacecraft for GW Detection in the LF Band (1/1)”**

**13 – Pulsar Timing for GW Detection in the VLF Band**

- Introduction: comparison of wave bands and detection sensitivities
- The basic principles of pulsar-timing searches for GW’s
- Best past sensitivities
- Most promising source: Stochastic background from superposition of waves from many supermassive black hole binaries, with masses

Lecturer Kip Thorne: **“Pulsar Timing for GW Detection in the VLF Band (1/1)”**

**14 – LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design** – slides, assignments and solutions

- The context: Noise curves and GW sources for LISA and for LIGO; white-dwarf / white-dwarf background noise for LISA
- History of ideas for a LISA type GW detector: 1978 – 1998; motivations for changes of conceptual design as time passed
- Noise estimates for current LISA design
- Spacecraft formation and orbits; influence of time-varying arm lengths
- Overview of spacecraft and launch
- Payload [science module] on each spacecraft
- Thermal and laser noise
- Disturbance-Reduction System [DRS] (Drag-free system)
- LISA test flight

Lecturer William Folkner: **“LISA for GW Detection in LF Band: Conceptual Design (1/2)”**

Lecturer William Folkner: **“LISA for GW Detection in LF Band: Conceptual Design (2/2)”**

**15 – LISA’s Lasers and Optics** – slides

- Introduction: Comparison and contrast of LISA and LIGO
- LISA’s light beams
- Detection of incoming beam
- Three-spacecraft phase-monitoring system (current baseline design)
- Laser frequency noise and its control
- Time-delay interferometry [TDI] as a way to remove laser frequency noise
- Noise due to fluctuations in pointing of laser beams

Lecturer Robert Spero: **“LISA’s Lasers and Optics (1/2)”**

Lecturer Robert Spero: **“LISA’s Lasers and Optics (2/2)”**

**16 – Time-Delay Interferometry [TDI] for LISA** – slides

- The context
- Basic idea of TDI
- Details of TDI
- Computation of LISA sensitivity to periodic waves — sensitivity averaged over sky and over GW polarizations
- Uses of TDI
- Practical problems
- Summary

Lecturer John Armstrong: **“Time-Delay Interferometry for LISA (1/2)”**

Lecturer John Armstrong: **“Time-Delay Interferometry for LISA (2/2)”**

**17 – LISA’s Disturbance Reduction System [DRS] (Drag-Free System)** – slides

- Review of LISA: concept, orbit, spacecraft, optics, baseline parameters that affect the DRS
- Requirements and general approach
- The DRS control system (system to control proof-mass and spacecraft degrees of freedom)
- Disturbance sources; their magnitudes; implications for DRS design and control-system parameters
- Capacitive readout & actuation systems: Heritage and ground demonstrations to date; importance of tests on the ground as well as in space; torsion-pendulum facility for ground tests
- Baseline design of DRS system and alternative options

Lecturer Bonny Schumaker: **“LISA’s Disturbance Reduction System [DRS] (Drag-Free System) (1/2)”**

Lecturer Bonny Schumaker: **“LISA’s Disturbance Reduction System [DRS] (Drag-Free System) (2/2)”**

**18 – The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA**

- Scientific goal for a post-LISA mission: detect and study waves from inflation and other processes in the very early universe
- BBO conceptual design
- Parameters
- How noises scale with parameters
- Discussion

Lecturer William M. Folkner: **“The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA (1/1)”**

**19 – GWs from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization **

- The Cosmic Microwave Background [CMB]
- Inflation: basic ideas
- GW production by inflation
- Influence of inflationary GWs on CMB
- Prospects to detect CMB polarization and its nonvanishing curl, and thereby measure energy scale of inflation

Lecturer Marc Kamionkowski: **“GWs from Inflation (1/1)”**

**A NOTE:**

This is an online course on gravitational waves as imparted in Caltech in 2002. Some years ago I converted the original mov videos to theora because they are smaller in size and faster to load but now that YouTube can be played without flash, it is more convenient to host them there, and I have done so after asking Kip. The ordering of the lectures follows the logical flow. The original order of the lectures was dictated in part by the availability of the guest lecturers.

I am grateful to Pau Amaro-Seoane for creating and organizing this mirror site for the 2002 Caltech Gravitational Wave Course. This site makes the course more accessible to people in Europe, and provides the films of lectures in a much improved, compressed format.

In the years since my colleagues and I produced this course, it has been used by a large number of people around the world. I am gratified by the reception it has had.

– Kip Thorne, Caltech, 20 April 2009