6. Gravitational Waves Flashcards
What is LIGO?
Two Michelson interferometers in Louisiana and Washington State
How do Michelson interferometers work?
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
What is VIRGO?
A third instrument in Northern Italy in addition to the LIGO collaboration
Describe what would be observed when detecting Gravitational Waves in the LIGO experiment
- 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”
Describe the chirp waveform
Something that gradually increases, then quickly increases for a very short duration
How do we linearise general relativity?
Make a coordinate transform from x^mu -> y^mu + e^mu
What must be remembered about the coordinate transform for linearising GR?
It is purely a coordiante transform
- There is no physical change in the space time itself
When is a transformation pure gauge?
When the perturbation is equal to the symmetric derivative of the function
- Space time is flat and Minkowski
State the 4 properties of gravitational waves
- Travel at the speed of light
- Transverse
- 2 Lineraly independent polarisations
- Spin 2 excitation
What is the spin of a photon?
1
What is the value of the Ricci tensor in a vacuum and away from masses, and why?
It is 0
- It represents the curvature of space time, which would be flat in the presence of no mass
What does spin describe?
Spin characterises the reponse/behaviour of things under rotations
What is the spin of the graviton?
2
What is the 00 component of the stres energy momentum tensor equal to?
The energy density
What are the basic features of the mass quadrupole formula?
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
What properties must a source have to generate gravitational waves
Must have a very large moment of inertia that is rapidly changing
- Individual spinning stars or axissymmetric objects are not good sources
Describe the properties of a basic binary system
You ahve two equal mass stars with a circular orbit around their common centre of mass
What are the three main consequences when looking at the amplitude of gravitational waves from binary systems?
- 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
Describe the inspiraling process
- Gravitational waves transport energy away from the source
- As energy is conserved, the system loses energy
- It is a runaway process
