# Field of Moving masses

## Main Question or Discussion Point

A moving charge that starts or stops generates a spherical wave-front of EM wave, can the same analogy be drawn for a moving mass?

Reference: Electricity & Magnetism by EM Purcell

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mfb
Mentor
It will emit gravitational waves, yes, mass is the "charge" of gravity. Usually that is completely negligible.

• Supantho Raxit
So, by drawing analogy with EM, I can easily find the eqn of field of a moving mass, the power radiated or other quantities ???
And, as this is highly negligible, is that the reason why it took so long to detect it?

mfb
Mentor
So, by drawing analogy with EM, I can easily find the eqn of field of a moving mass, the power radiated or other quantities ???
It is a bit more complicated for gravity, but yes, in principle it is possible.
And, as this is highly negligible, is that the reason why it took so long to detect it?
Right. You need really massive objects accelerating really fast to produce notable gravitational waves.

pervect
Staff Emeritus
So, by drawing analogy with EM, I can easily find the eqn of field of a moving mass, the power radiated or other quantities ???
And, as this is highly negligible, is that the reason why it took so long to detect it?
The analogy isn't quite perfect - gravitational radiation is given by a quadrupole formula, EM radiation by a dipole formula. This is related to the issue that you just can't have a moving mass stop for no reason, the conservation of momentum is built into the Einstein field equations, and a mass stopping with no cause is therefore not a solution of Einstein's field equations. So you need to reformulate your test problem in a way that conserves momentum in order to actually solve the equations and get out a number for gravitational radiation.

See for instance the wiki https://en.wikipedia.org/wiki/Gravitational_wave
More technically, the third time derivative of the quadrupole moment ... of an isolated system's stress–energy tensor must be non-zero in order for it to emit gravitational radiation. This is analogous to the changing dipole moment of charge or current that is necessary for the emission of electromagnetic radiation.
I snipped some confusing parts of the wiki article that relate to higher order moments. A slightly better statement of what I snipped is is from http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf

It follows that gravitational radiation is of quadrupolar or higher nature and is directly linked to the quadrupole moment of the mass distribution.

• mfb and Supantho Raxit