1. Jun 2, 2010

### Passionflower

Consider the Schwarzschild solution where millions of test particles move towards the event horizon.

Will the particles falling in radiate? If so, how can they radiate as they do not have any proper acceleration?

2. Jun 2, 2010

### bcrowell

Staff Emeritus
If the infalling cloud is spherically symmetric, then there is no radiation: http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity)

In the case of a single infalling particle, the radiated power is proportional to the mass of the test particle raised to some power p, where p>1. (I believe p=2 for a small mass infalling toward a large mass.) The whole idea of a test particle is that we're taking the limit where its mass is small, and therefore if the radiated power is proportional to $m^p$, it becomes negligible, in the sense that the square of an infinitesimal number dx is negligible compared to the original number dx. If radiation by a test particle wasn't negligible in this sense, then there would be no way to define geodesics using test particles.

If a mass m infalls toward another mass, yes, you will get gravitational radiation. If m is infinitesimally small (the case of a test particle), then there is no radiation. If m is not infinitesimally small, then it radiates, but it also doesn't follow a geodesic, so it's not true that it experiences zero proper acceleration.

3. Jun 2, 2010

### Passionflower

Agreed, assuming you speak of gravitational radiation here.

4. Jun 2, 2010

### bcrowell

Staff Emeritus