Comments about "Mass in general relativity" in Wikipedia
This document contains comments about the document "Mass in general relativity" in Wikipedia
 The text in italics is copied from that url
 Immediate followed by some comments
In the last paragraph I explain my own opinion.
Contents
Introduction
The article starts with the following sentence.

The concept of mass in general relativity (GR) is more complex than the concept of mass in special relativity

The concept of mass in SR is also complex, because how is it calculated?

In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions that are applicable under different circumstances.

In SR you also have similar problems, because what exactly is a restmass and why does mass change as a function of speed?










1. Review of mass in special relativity

In special relativity, the invariant mass or rest mass (hereafter simply "mass") of an isolated system can be defined in terms of the energy and momentum of the system by the relativistic energy–momentum equation:
 m = sqrt{E^2  (p*c)^2} / c^2


Why do they use the word "system"?
A system, IMO, assumes more than one object. But how can they be all at rest?
How is the Energy (and momemtum) calculated? This are serious problems in our understanding.








2 Defining mass in general relativity: concepts and obstacles












3. The relativistic energymomentum equation












3.1 Komar mass in stationary spacetimes








3.2 ADM and Bondi masses in asymptotically flat spacetimes








3.3 The Newtonian limit for nearly flat spacetimes








4. History








5. Questions, answers, and simple examples of mass in general relativity








6. See also
Following is a list with "Comments in Wikipedia" about related subjects
Reflection 1 "Gravitation by MTW" 1973
In Paragraph $19.2 the "Measurement of the Mass and angular Momentum" is dicussed.
At page 450 we read:

The values of a sytem's mass and angular momentum can be measured by probing the imprint they leave in its external gravitational field

IMO it is impossible in practice to directly measure the gravitational field. The only thing you can measure are how different objects influence each other.

Of all the tools one might use to probe, the simplest is a tset particle in a gravitationally bound orbit,

That means we in practice are studying the Sun and one small planet.

To determine the source's mass M one need only apply Kepler's third law. (perhaps better called "Keplers 123 law")

That means in a more general sense we use Newton's Law.
The same subject is also discussed at the pages 450,457 and 636ff. See Subject index under: Massenergy
In paragraph $19.3 the "Mass and Angular Momentum of fully relativistic sources" is discussed
At page 452 we read:

Two types of nonlinearities turn out far from the source: (1) non linearities in the static Newtonian part of the metric, which generate metric corrections etc etc
therby putting the metric in the form ds^2 = function of (M,r,dt^2,Sk,delta jk dxjdxk) (19.13)



At page 453 we read:

The mass of the sun is measured in practice by studying the orbits of the planets in its external gravitational field, a procedure equivalent to reading the Mass M of the line element (19.13) rather than evaluating the volume integral "integral T00 d3x"

Equation (19.13) is a rather complex equation. See above.
Next we read:

one defines the "total massenergy" M of the sun or any other body to be the constant that appears in the line element (19.13) for its distant external spacetime geometry.

The question is how is this done in reality if more stars are involved.
In paragraph $20.4 "Why the energy of the gravitational filed cannot be localized" the discussion is about the Earthmoon system and a neutron star.
In paragraph $20.5 "Conservation laws for total 4Momemtum and Angular Momemtum" the discussion is about our Galaxy or Solar system.
At page 474 we read:

this force is to be calculated as half the difference between the retarded field and the advanced field caused by that particle. This difference is singularity free

Interesting.

Reflection 2
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Created: 1 November 2016
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