Gravitational field caused by a charged particle

[ngkamsengpeter]

I am new to General Relativity, so this question might sound silly. I know that the source of gravitational field is the stress-energy tensor. What I wonder is how do I find the spacetime metric, g_mn caused by a stationary charged particle? What is the stress-energy tensor of a stationary charged particle? Is it just the T₀₀ component exist?

Besides that, consider two particles in which the gravitational field caused by each particle will affect each other, how do I analyzed the motion of these two particles?

 

[Dickfore]

Please define "stationary" particle.

 

[ngkamsengpeter]

Please define "stationary" particle.

Sorry if it confusing. What I mean is a static, not moving particle.

 

[Dickfore]

Sorry if it confusing. What I mean is a static, not moving particle.

If you took a course in Relativity, the first thing you should have learned is that motion is relative. So, define what you mean by non-moving particle.

 

[TrickyDicky]

You seem to be looking for some electrovacuum solution, look up "Reissner–Nordström metric" in wikipedia, that is a non null solution for a charged mass.

 

[TrickyDicky]

What I mention above is not exactly the same as a metric for a static particle, as Dickfore said there is no meaningful way of saying that an isolated particle is in motion (with constant velocity) or not under the relativity paradigm, so the metric I mentioned is rather a static electrovacuum solution for a charged body, and here "static" has a different, more technical meaning than "static" as in "not moving".

 

[quantumfoam]

Hello ngkamsengpeter! Perhaps you may be provided some insight on the thread labelled Charge Particles and Gravity

 

[quantumfoam]

I am new to general relativity too and I had asked a similar question.