Gravitational field of photons

[espen180]

Note the modern usage does not use the symbols $m_0$ for rest mass and m for relativistic mass. The unqualified symbol "m" and the unqualified term "mass" simply mean rest mass and generally in modern GR, there is not considerd to be any other kind of mass.

From my understanding, it's not meaningful to distinguish between mass and energy in GR. In SR it is neccesary because it determines acceleration, but in GR mass really plays no role. Only energy is important.

The only one of these terms that I hadn't heard of is "momentum energy". Taylor and Wheeler just call this momentum (i.e. 3-momentum). I see Blandford & Thorne call the vector 4-momentum, $\vec{p}$. They call its time component "energy $\varepsilon$". This energy minus its length (i.e. mass) they call "energy $E$" (well, at least they were thoughtful enough to give them different symbols, if not different names...), and its spatial components they call "momentum $\textbf{p}$". They call the first row of components of a matrix representing the stress-energy tensor "energy flux". Presumbly the other rows are "momentum flux".

I think this comes from E²=(pc)²+(mc²)².

 

[yuiop]

From my understanding, it's not meaningful to distinguish between mass and energy in GR. In SR it is neccesary because it determines acceleration, but in GR mass really plays no role. Only energy is important.

Rest mass has significance in relativity because any particle with rest mass is excluded from traveling at the speed of light and any particle with zero rest mass can only move at the speed of light. A baryon and a photon behave differently due to the presence or absence of rest mass even if they have identical total energy. The importance of the absense or presence of rest mass in active gravitational terms, especially in the case of a photon, has yet to be determined in this thread.

 

[Jonathan Scott]

I think that if you take two masses moving slowly along parallel paths with a gravitational attraction between them and Lorentz transform the system to a frame from which they are moving very rapidly, then adjust the rest masses so that the total energy is the same as it was to start with, you can show that when you take the limit of velocity c (where the rest masses are zero and there is only kinetic energy) the relative acceleration reaches zero.

There is a subtle difference between energy and mass in general relativity when you consider the effective mass in a non-isotropic coordinate system. As the coordinate speed of light varies with direction in that case, the coordinate mass is no longer a scalar but has different values depending on the direction in which the speed of light is measured.