View Full Version : Relativistic Gravity

2004-Dec-12, 04:40 PM
Hi, given that as the relative speed of an object increases the more massive it becomes and hence presumably the greater the gravitational attraction. Why could not the "missing matter" anomaly simply be due to high relative speeds within the universe?

2004-Dec-12, 08:52 PM
The source term for the gravitational field in GR is the energy-momentum tensor T^mn. In it are mass, momentum, energy densities, stress, pressure, etc. The form of the energy momentum tensor is going to look different to different observers.

The energy density is defined as T^oo. But a general coordinate transform Tmn to T^' mn yields (a^m[sub]o a^n[sub]o T^oo,) which is not T^oo. Thus what looks like energy density to one observer looks like a combination of momentum density and energy flux density to others.

Typically the invariant trace of the energy momentum tensor T^mn is regarded as the rest mass of an object. However you should note that this isn't the complete source for gravitation. When deciding which "energies" contribute as gravitating sources, a good test is to consider whether a general coordinate transform can "remove" the energy. This rules out kinetic energies as gravitating sources - they will disappear in rest frame transforms, similar to your example.

2004-Dec-12, 10:22 PM
The relative velocities are not so high.