6. Gravitational Waves

Question 1

What is LIGO?

Answer 1

Two Michelson interferometers in Louisiana and Washington State

Question 2

How do Michelson interferometers work?

Answer 2

A beam is split perpendicularly
- These beams are then reflected off of a mirror which could feel the effects of GR
- The beam is recombined at the bottom

Question 3

What is VIRGO?

Answer 3

A third instrument in Northern Italy in addition to the LIGO collaboration

Question 4

Describe what would be observed when detecting Gravitational Waves in the LIGO experiment

Answer 4

• Sine type wave which slowly gets larger in amplitude and higher in frequency as the BHs in spiral
• Very high amplitude and frequency for a short duration during the merger
• No signal after the merger has completed; “Ring Down”

Question 5

Describe the chirp waveform

Answer 5

Something that gradually increases, then quickly increases for a very short duration

Question 6

How do we linearise general relativity?

Answer 6

Make a coordinate transform from x^mu -> y^mu + e^mu

Question 7

What must be remembered about the coordinate transform for linearising GR?

Answer 7

It is purely a coordiante transform
- There is no physical change in the space time itself

Question 8

When is a transformation pure gauge?

Answer 8

When the perturbation is equal to the symmetric derivative of the function
- Space time is flat and Minkowski

Question 9

State the 4 properties of gravitational waves

Answer 9

1. Travel at the speed of light
2. Transverse
3. 2 Lineraly independent polarisations
4. Spin 2 excitation

Question 10

What is the spin of a photon?

Answer 10

1

Question 11

What is the value of the Ricci tensor in a vacuum and away from masses, and why?

Answer 11

It is 0
- It represents the curvature of space time, which would be flat in the presence of no mass

Question 12

What does spin describe?

Answer 12

Spin characterises the reponse/behaviour of things under rotations

Question 13

What is the spin of the graviton?

Answer 13

2

Question 14

What is the 00 component of the stres energy momentum tensor equal to?

Answer 14

The energy density

Question 15

What are the basic features of the mass quadrupole formula?

Answer 15

Mass quadrupole = second moment of the mass density
- Sources of grav waves must have time varying mass quadrupole moments as it contains the second order derivative of time

Question 16

What properties must a source have to generate gravitational waves

Answer 16

Must have a very large moment of inertia that is rapidly changing
- Individual spinning stars or axissymmetric objects are not good sources

Question 17

Describe the properties of a basic binary system

Answer 17

You ahve two equal mass stars with a circular orbit around their common centre of mass

Question 18

What are the three main consequences when looking at the amplitude of gravitational waves from binary systems?

Answer 18

• Amplitude is truly tiny
• Frequency of the radiation is twice that of the source (spin 2)
• Polarisation depends on viewing angle. When viewing face on (from x axis) the waves are right circularised

Question 19

Describe the inspiraling process

Answer 19

• Gravitational waves transport energy away from the source
• As energy is conserved, the system loses energy
• It is a runaway process