(ed.). Gravitational waves (IOP, 2001)(422s).

Gravitational and electromagnetic waves compared and contrasted 413.5 Gravitational and electromagnetic waves compared andcontrastedTo conclude this lecture it is useful to discuss the most important differences andsimilarities between gravitational waves and electromagnetic ones. We do this inthe form of a table.Table 3.1.ElectromagnetismTwo signs of charges—large bodiesusually neutral—waves usually emittedby single particles, often incoherently—waves carry ‘local’ information.A genuine physical force, acting differentlyon different bodies. Detected bymeasuring accelerations.Maxwell’s equations are linear. Physicalfield is F µν (E and B). Gauge fieldis vector potential A.Source is charge-current density J µ .Charge creates electric field, currentmagnetic field.Moderately strong force on the atomicscale: e2 /4πɛ 0Gm 2 = 10 39 .pWave generation for A µ : ∂ β ∂ β A µ =4πɛ 0 J µ in a convenient gauge (Lorentzgauge).Propagate at the speed of light, amplitudefalls as 1/r.Conservation of charge ⇒ radiation bylow-velocity charges is dominated bydipole component.General relativityOne sign of mass—gravityaccumulates—waves emitted morestrongly by larger body—waves carry‘global’ information.Equivalence principle: gravity affectsall bodies in the same way. Representedas a spacetime curvature rather than aforce. Detected only by tidal forces—differential accelerations.Einstein’s equations are nonlinear.Physical field is Riemann curvature tensorR µναβ . Gauge fields are metric g µνand connection Ɣµν α . Gauge transformationsare coordinate transformations.Source is stress-energy tensor T µν .Mass creates a Newtonian-like field,momentum as gravito-magnetic effects.Stress creates field too.Weaker than ‘weak’ interaction.Wave generation for h µν = g µν − η µν :∂ β ∂ β (h µν − 1 2 η µνh α α) = 8πT µν in aconvenient gauge.Propagate at the speed of light, amplitudefalls as 1/r.Conservation of mass and momentum⇒ radiation by low-velocity masses isdominated by quadrupole component.