Gravitational field caused by a charged particle

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Discussion Overview

The discussion revolves around the gravitational field generated by a stationary charged particle within the framework of General Relativity. Participants explore the relationship between the stress-energy tensor and the spacetime metric, particularly focusing on the implications of defining a "stationary" particle and the interaction between multiple particles.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions how to determine the spacetime metric, gmn, caused by a stationary charged particle and inquires about the form of the stress-energy tensor for such a particle.
  • Another participant requests clarification on the definition of a "stationary" particle, prompting further discussion on the relativity of motion.
  • A subsequent reply emphasizes the need for a precise definition of "stationary," suggesting that the term "static" may have a more technical meaning in this context.
  • One participant suggests looking into the Reissner–Nordström metric as a potential solution for the gravitational field of a charged mass.
  • There is a distinction made between the metric for a static particle and the concept of motion in relativity, indicating that the terminology may lead to confusion.
  • Several participants express their own novice status in General Relativity, indicating a shared learning experience.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of "stationary" or the implications of motion in relativity. Multiple competing views regarding the nature of the metric and the stress-energy tensor remain present.

Contextual Notes

The discussion highlights the ambiguity in defining "stationary" and "static" within the context of General Relativity, as well as the potential for confusion regarding the stress-energy tensor components for charged particles. There is also an acknowledgment of the complexity involved in analyzing the motion of multiple interacting particles.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of General Relativity, particularly those exploring the intersection of electromagnetism and gravitational theory.

ngkamsengpeter
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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, gmn 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?
 
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Please define "stationary" particle.
 
Dickfore said:
Please define "stationary" particle.
Sorry if it confusing. What I mean is a static, not moving particle.
 
ngkamsengpeter said:
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.
 
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.
 
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".
 
Hello ngkamsengpeter! Perhaps you may be provided some insight on the thread labelled Charge Particles and Gravity:smile:
 
I am new to general relativity too and I had asked a similar question.:smile:
 

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