# Mass energy equivalence

by Katamari
Tags: energy, equivalence, mass
 P: 9 I understand energy mass equivalence, but when mass is changed to energy what happens to it's gravitational field?
 Sci Advisor P: 3,697 Nothing. Stays the same. Whatever form the 'energy' takes: kinetic energy of the decay products, photons, etc, all those things are sources of gravity also. At least initially until things fly apart, the gravitational field will be the same.
 Mentor P: 16,271 Mass is not the source of the gravitational field. The source of the gravitational field is the stress energy tensor: http://en.wikipedia.org/wiki/Stress%...3energy_tensor The mass only gravitates in the first place because it has a lot of energy.
PF Gold
P: 4,047

## Mass energy equivalence

I think the radiation would have to be kept in a perfectly reflecting box, or the gravitational field would change for a nearby observer. If the matter and antimatter are in the box, then anihilate, the field produced by the box and contents would not change. Pedantic is my middle name.
Emeritus
PF Gold
P: 5,415
 Quote by Katamari I understand energy mass equivalence, but when mass is changed to energy what happens to it's gravitational field?
Even in Newtonian gravity, without conversion of mass to energy, the gravitational field of a system can change when the system evolves over time. For example, the gravitational field of the earth-moon system changes as they orbit around their common center of mass. However, those changes fall off quickly with distance, so an observer who is far away compared to the size of the system observes a constant field, equal to the field that would have been produced by a single particle with the same total mass.

In GR, there is no uniquely defined measure of mass-energy that is conserved in all spacetimes. As DaleSpam pointed out, it's the stress-energy tensor that is really fundamental in GR, not mass-energy. However, there are scalar measures of mass-energy such as ADM and Bondi mass that are conserved in specific types of spacetimes, such as asymptotically flat spacetimes. The distant, static field of a system in an asympotically flat spacetime is determined by its ADM or Bondi mass in exactly the way you would think. ADM and Bondi "mass" include both mass and energy (because otherwise they wouldn't be conserved).

So the short answer to your question is yes if you're talking about the distant, static field, in an asymptotically flat spacetime, and no otherwise -- which is not that different from the Newtonian answer.

-Ben

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