Gravitational waves

Gravitational waves

Lecture about gravitational waves targeted at undergraduate students and first year grad students in physics and astronomy. Prepared and taught by Prof. Rodrigo Nemmen at IAG USP.

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

https://blackholegroup.org

C5ca9433e528fd5739fa9555f7193dac?s=128

Rodrigo Nemmen

July 25, 2018
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Transcript

  1. 3.

    Electrodynamics accelerated charges produce electromagnetic radiation Gravitation accelerated masses produce

    gravitational radiation 1 μ 0 E × B c c hμν electromagnetic wave gravitational wave
  2. 4.

    The Elegant Universe. Crédito: Nova Accelerated masses produce wave of

    disturbance in spacetime curvature Gravitational waves
  3. 6.
  4. 7.

    PSR 1913+16: A binary system of pulsars (Hulse & Taylor

    pulsar) precisely determined orbital parameters r = 5 kpc M1 = M2 = 1.4 Msun
  5. 8.

    GWs emitted by binary system Accelerated masses emit GWs System

    loses energy Distance between two bodies shrinks
  6. 9.

    GWs GWs emitted by binary system Accelerated masses emit GWs

    System loses energy Distance between two bodies shrinks NS NS NS NS Distance Period
  7. 10.

    Hulse & Taylor pulsars r = 5Kpc, M1 ≈ M2

    ≈ 1.4M⊙ , T = 7h45min fGW = 7 × 10−5 Hz GR prediction h ∼ 10−23 · T = − 2.4 × 10−12 sec/sec Orbital shrinkage due to GW radiation τ = 3.5 × 108yr timescale for coalescence
  8. 11.

    First evidence of existence of GWs Weisberg & Taylor (2005)

    GR prediction observations Monumental discovery in 1974 by Hulse & Taylor
  9. 12.
  10. 13.

    Linearized gravitational waves Far away from the source, r ≫

    M, gμν ≈ ημν Gravitational wave (GW) will be weak (space empty of matter) Einstein equation can be linearized and solved giving simpler solutions
  11. 14.

    Weak gravitational field gμν = ημν + hμν Minkowski metric

    Perturbation hμν = Aμν eikα xα Solution: plane wave traveling with c wave vector GW amplitude Einstein equation Rμν = 0 Ricci curvature (in vacuum) Reduces to wave equation ( ∂2 ∂t2 − ∇2 ) hμν = □ hμν = 0 Linearized gravitational waves
  12. 15.

    hμν = Aμν eikα xα Plane wave wave vector GW

    amplitude Properties of linear GWs Transverse waves Aμν kμ = 0 kμ kμ = 0 Null wave vector: GWs move like light-rays homework
  13. 16.

    Polarization of GWs Aμν = h+ Aμν + + h×

    Aμν × Wave moving in the z-direction = 0 0 0 0 0 h+ h× 0 0 h× −h+ 0 0 0 0 0 two polarizations Aμν + = 0 0 0 0 0 1 0 0 0 0 −1 0 0 0 0 0 Aμν × = 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 Polarization components
  14. 18.

    Effect of GWs on test particles x y z L0

    ds2 = gμν dxμdxν ⇒ L = ∫ gμν dxμdxν = ∫ g11 dx = L0 [1 + 1 2 h11 (t,0)] ∴ ΔL L0 = 1 2 h11 (t,0) strain produced by GW Particles oscillate after GW passes ⟂ k homework
  15. 19.

    Example 1: periodic wave ΔL L0 = 1 2 h(t,0)

    h(t − z) = a sin[ω(t − z) + ϕ] x y z L0 GW propagating in z-direction ΔL L0 = a 2 sin[ωt + ϕ]
  16. 21.

    Example 2: wave packet ΔL L0 = 1 2 h(t,0)

    h(t − z) = a exp [ − (t − z)2 σ2 ] x y z L0 GW propagating in z-direction ΔL L0 = a 2 exp [ − (t − z)2 σ2 ]
  17. 22.

    Example 3: Change in distance between two masses due to

    GW x y z L0 ΔL L0 = h 2 ΔL = hL0 2 = 10−21 × 2 km = 2 × 10−18 m ~ 1 proton radii L0 = 4 km h = 10−21
  18. 26.

    black hole neutron star neutron star neutron star GW sources

    High mass concentrations + Extreme accelerations star supermassive black hole GWs
  19. 27.
  20. 28.

    Strain = h(t) ≡ Δx L Δx = 10−21 ×

    4 km = 4 × 10−18 m a v v a = 3 proton radii Numerically solve Einstein’s field equation Rμν − 1 2 gμν R = 8πG c4 Tμν spacetime curvature = constant× matter-energy
  21. 29.
  22. 31.

    Importance of GW detection “I liken this to the first

    time we pointed a telescope at the sky, […] people realized there was something to see out there, but didn’t foresee the huge, incredible range of possibilities that exist in the universe.” Janna Levin
  23. 32.

    Importance of GW detection 100-yr wait for this: new astronomy

    Direct, unabsorbed information about dynamics/ mass of relativistic sources
 Black holes really do exist!
  24. 36.
  25. 40.

    A “kilonova” is born lighter elements (lanthanide-poor) heavier elements (lanthanide-rich)

    (UV) (NIR) cf. also Cowperthwaite+2017 place where neutron stars merged
  26. 41.
  27. 42.

    Importance of GW170817 Birth of multimessenger astronomy: photons + gravitons

    Short gamma-ray bursts are due to neutron star collisions Neutron star collisions seem to produce most of the gold in the universe (lanthanides)