Gravitational Waves
Homework 5 Questions?
Homework 5 due Thursday (start of class) Final on Monday, December 15, 1:30 pm Review sessions next week (days?) Dec 4: Gravity and the Universe Dec 9: Inside Black Holes Dec 11: Review (and Wormholes?) Read BR Ch 10, Thorne Ch 10
Uncharged black holes
Uncharged black holes
• Zero angular momentum (no spin) “Schwarzschild” black hole event horizon radius: Possible black hole processes:
!
!
Rs =
2GM
c2
!
• Spinning (“Kerr”) black hole: event horizon radius decreases a€s angular momentum increases.
• add mass (e.g. two black holes merge) !
!
size of event horizon increases
• extract spin energy (e.g. for a black hole in a magnetic field)
size of event horizon increases
Uncharged black holes
In classical GR, processes that decrease the size of the event horizon are not possible…
• (obvious) can’t make horizon smaller by removing mass The area of the event horizon of a black hole can stay the same or increase, but can never decrease with time The entropy of an isolated physical system can stay the same or increase, but can never decrease with time !
• (not obvious) can spin up a black hole, but only by adding mass / energy so the horizon increases
Hawking: not just “similar” but equivalent! When effects of quantum mechanics are included, a black hole event horizon:
• has a temperature • has an entropy just like a “regular” thermodynamic system
The area of a black hole plays a “similar” role to entropy (Jacob Bekenstein)
Hawking radiation
For a one Solar mass black hole:
• T = 60 billionths of a degree (60 nano K) (scales as 1/M) !
• evaporation time 1.5 x 1066 yr (scales as M3)
No observable effects for known astronomical black holes
Q & A Time!
Testing Einstein
!
• with gravitational waves !
• with observations of the Universe !
• with thought experiments inside the horizon
Gravitational waves
Recap: prediction of general relativity, masses in non-‐uniform motion close to the speed of light excite waves in space time !
No waves from spherical or axisymmetric sources !
Strong waves from binaries involving compact objects: neutron stars and black holes
Gravitational waves
Know these waves exist from binary pulsar, but have not detected them directly !
Existing observations probe velocities v << c
Gravitational waves
Gravitational waves
Key properties:
• strength – expressed as fractional distortion of space caused by wave: e.g. if the wave caused a 1 cm distortion to a 1 m rod, h = 0.01. Depends on source, distance. (h is called the “dimensionless strain”) time
!
• travel at the speed of light • alternately compress and stretch space as they pass – key to their direct detection
e.g. two neutron stars with an orbital separation of 100 km
2π
d3
Orbital period: P =
= 2π
Ω
G(M1 + M 2 )
About 0.01 s Neutron star mergers produce waves with f ~ 100 Hz – kHz in final stages (1 Hz = 1 Hertz = 1 per second)
• frequency – number of crests of the wave that pass each second… depends on the source
How close is the nearest neutron star binary that will merge this year? !
Closest separation Galactic binaries will merge via gravitational radiation in about 100 Myr !
Estimate the rate per galaxy as ~10 per Myr, i.e. need to watch 100,000 galaxies to catch 1 each year !
There are about 0.01 galaxies per cubic Mpc (1 Mpc ~ 3.3 Million light years) Want volume ~10 million Mpc3, so d ~ 200 Mpc
Distortion of space at Earth from NS-‐NS merger at few hundred Mpc is very weak
Fractional displacement at 100 Hz: h ~ 10-‐23 Much less than diameter of proton over many km
LIGO – Laser Interferometer Gravitational Wave Observatory
Two instruments in Washington and Louisiana
But measureable – we think! Use lasers to measure shifts in the length of two arms at right angles over time:
Laser interferometer: can approach the ultimate sensitivity set by quantum uncertainty principle
Sensitivity achieved in initial operations reached design goal, but only good enough to see NS-‐NS mergers out to ~15 Mpc… not enough !
No signals seen !
Currently being upgraded: Advanced LIGO expected to start operating within next couple of years
Expect first direct detection of gravitational waves
Sources: • neutron star binaries • neutron star – black hole binaries • supernova explosions (?) • asymmetric rotating neutron stars (?) • new classes of sources!
Mergers of supermassive black holes would also emit gravitational waves
Final orbital periods ~hour, so much lower frequency Not accessible from the ground
LISA – proposed mission to detect gravitational waves in space using laser interferometry between three free-‐flying spacecraft
Spacecraft would orbit in a rotating triangular configuration about the Sun
Look for: supermassive BH binary mergers, inspiral of stellar mass BHs into supermassive ones
Status: • “LISA Pathfinder” mission to demonstrate technology due to launch in 2015 !
• No decision to proceed on full LISA (2030s)
Goal: observe the inspiral, merger and ringdown as two black holes merge • can predict waveform accurately • ringdown is when the new hole loses its “hair” • test No-‐Hair theorem for GR, GR in the regime of strong fields
Gravity and the Universe
Test general relativity via: • Solar System / lab tests • Binary pulsars • Black hole mergers (future) • Cosmology – evolution of the Universe
Gravitational time dilation observable directly by changing the height of best atomic clocks by as little as a foot!