Gravitational waves - Speaker Deck

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Rodrigo Nemmen IAG USP Gravitational Waves blackholegroup.org @nemmen

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1916 1918 https://einsteinpapers.press.princeton.edu

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Electrodynamics accelerated charges produce electromagnetic radiation Gravitation accelerated masses produce gravitational radiation 1 μ 0 E × B c c hμν electromagnetic wave gravitational wave

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The Elegant Universe. Crédito: Nova Accelerated masses produce wave of disturbance in spacetime curvature Gravitational waves

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LIGO’s was ﬁrst direct detection of GWs But before LIGO we already knew GWs existed!

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PSR 1913+16: A binary system of pulsars (Hulse & Taylor pulsar) precisely determined orbital parameters r = 5 kpc M1 = M2 = 1.4 Msun

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GWs emitted by binary system Accelerated masses emit GWs System loses energy Distance between two bodies shrinks

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GWs GWs emitted by binary system Accelerated masses emit GWs System loses energy Distance between two bodies shrinks NS NS NS NS Distance Period

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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

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First evidence of existence of GWs Weisberg & Taylor (2005) GR prediction observations Monumental discovery in 1974 by Hulse & Taylor

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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

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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

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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

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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

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GW polarization x y

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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

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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]

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https://www.youtube.com/watch?v=aVFf8UcX1A8 x y z ⊙

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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 ]

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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

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https://www.youtube.com/watch?v=RzZgFKoIfQI Michelson- Morley interferometer

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https://www.youtube.com/watch?v=RzZgFKoIfQI

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LIGO Observatory at Livingston, Louisiana 4 km

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black hole neutron star neutron star neutron star GW sources High mass concentrations + Extreme accelerations star supermassive black hole GWs

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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

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Abbott+2015, PRL

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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

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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!

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https://www.nobelprize.org/prizes/physics/2017/weiss/lecture/

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A moment long-awaited…

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Birth of multimessenger astronomy: GWs and EM radiation from same source

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Rezzolla+2011

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Rezzolla+2011

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Diaz+2017 10 hours after GW signal: A strange optical glow appears

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A “kilonova” is born lighter elements (lanthanide-poor) heavier elements (lanthanide-rich) (UV) (NIR) cf. also Cowperthwaite+2017 place where neutron stars merged

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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)