Gravitational Waves

Question 1

What are gravitational waves?

Answer 1

Ripples in spacetime curvature that propagate at the speed of light.

Question 2

What causes gravitational waves?

Answer 2

Accelerating mass distributions, especially non-spherically symmetric ones.

Question 3

What is the linearized Einstein equation?

Answer 3

□h̄{μν} = -16πG T{μν}, where h̄ is the trace-reversed perturbation.

Question 4

What is the weak-field approximation?

Answer 4

Assumes g_{μν} = η_{μν} + h_{μν}, with |h_{μν}| ≪ 1.

Question 5

What gauge is used in gravitational wave analysis?

Answer 5

The Lorenz gauge: ∂^μ h̄_{μν} = 0.

Question 6

What is the transverse-traceless (TT) gauge?

Answer 6

A gauge where waves are purely spatial, transverse to propagation, and traceless.

Question 7

What components remain in TT gauge?

Answer 7

Only h_{11} = -h_{22} and h_{12} = h_{21} — two polarization modes.

Question 8

What are the two polarizations of GWs?

Answer 8

Plus (+) and cross (×) modes.

Question 9

What is the wave equation in vacuum?

Answer 9

□h̄_{μν} = 0 — wave equation for free space.

Question 10

What is the speed of gravitational waves?

Answer 10

The speed of light, c.

Question 11

What type of sources emit strong GWs?

Answer 11

Binary mergers, asymmetric supernovae, neutron stars.

Question 12

What is the quadrupole formula?

Answer 12

P = (G/5c⁵) ⟨…Q_{ij}⟩² — power radiated depends on the third time derivative of quadrupole moment.

Question 13

Why are monopole and dipole radiation absent in GR?

Answer 13

Due to mass-energy conservation and momentum conservation.

Question 14

What is the energy carried by GWs?

Answer 14

They carry energy, momentum, and angular momentum away from the system.

Question 15

What happens to binaries due to GW emission?

Answer 15

Their orbits shrink — inspiral over time.

Question 16

What is an example of GW detection evidence?

Answer 16

Hulse-Taylor binary pulsar — orbital decay matches GR predictions.

Question 17

How are GWs detected?

Answer 17

Using interferometers like LIGO and Virgo.

Question 18

What is the effect of GWs on test particles?

Answer 18

They stretch and squeeze space perpendicular to propagation.

Question 19

What is a GW waveform?

Answer 19

A time-varying strain pattern, e.g., chirp from inspiral events.

Question 20

What is the strain h in GW detection?

Answer 20

h = ΔL / L — relative change in length between two points.

Question 21

What does chirp mean in GW signals?

Answer 21

Frequency and amplitude increase as inspiral proceeds.

Question 22

What is the observational signature of GWs?

Answer 22

Time-dependent strain in interferometer arms.

Question 23

What are the units of GW strain?

Answer 23

Dimensionless (ΔL/L).

Question 24

What frequencies do LIGO-type detectors observe?

Answer 24

~10 Hz to ~kHz — stellar mass binary mergers.

Question 25

What is the LISA detector?

Answer 25

A planned space-based interferometer for low-frequency GWs.

Question 26

Why is the TT gauge useful?

Answer 26

It simplifies the wave equation and reveals physical polarizations.

Question 27

What is the energy flux of a GW?

Answer 27

Proportional to ⟨(∂_t h_{ij})²⟩ — averaged over time.

Question 28

What are stochastic backgrounds?

Answer 28

Random GW noise from early universe or unresolved sources.

Question 29

Can GWs interact with matter?

Answer 29

Very weakly — they pass through matter nearly undisturbed.

Question 30

What is the geodesic deviation equation used for in GW detection?

Answer 30

Describes relative acceleration of nearby test particles.

Question 31

What happens to spacetime in a GW?

Answer 31

It oscillates, changing distances between points.

Question 32

What is the difference between gravitational and electromagnetic waves?

Answer 32

GWs are tensor (spin-2) waves; EM are vector (spin-1).

Question 33

Can black holes emit GWs?

Answer 33

Yes — especially during merger and ringdown phases.

Question 34

What is a ringdown?

Answer 34

The final stage of a merger, where the black hole settles into a stable state.

Question 35

What is back-reaction in GW physics?

Answer 35

The effect of GW emission on the source's dynamics.

Question 36

What is the TT projection operator?

Answer 36

Projects general perturbations into transverse-traceless components.

Question 37

Why is gravitational radiation quadrupolar?

Answer 37

Mass conservation rules out monopole, and momentum conservation rules out dipole.

Question 38

What does polarization tell us about a GW source?

Answer 38

Orientation, inclination, and nature of motion (e.g., orbit vs spin).

Question 39

What is waveform modeling used for?

Answer 39

To match observed signals to source properties — mass, spin, distance.

Question 40

Can gravitational waves be redshifted?

Answer 40

Yes — their frequency is redshifted by cosmological expansion.