The Mass of the Gravitational Field

Abstract

<jats:title>Abstract</jats:title> <jats:p>By mass–energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of mass: the role in conservation of mass, the inertial role, and the role as source for gravitation. The difficult case of general relativity is compared to the more straightforward cases of Newtonian gravity and electromagnetism by way of gravitoelectromagnetism, an intermediate theory of gravity that resembles electromagnetism. 1Introduction2The Mass of the Electromagnetic Field2.1The conservational role2.2The inertial role2.3The gravitational role3The Mass of the Gravitational Field in Newtonian Gravity3.1The conservational role3.2The inertial role3.3The gravitational role4The Mass of the Gravitational Field in Gravitoelectromagnetism4.1The conservational role4.2The inertial role4.3The gravitational role5The Mass of the Gravitational Field in General Relativity5.1The conservational role5.2The inertial role5.3The gravitational role6ConclusionAppendix</jats:p>

Is electromagnetic field momentum due to the flow of field energy?

“…(2) and eq. (19) show that such an event also has (V A /c) = 1 and hence (V B /c) = 1 which is an unphysical value for a Lorentz boost velocity. The case E = B 0 and 0 = E • B therefore must be approached as a limit.…”

“…(2) proves that 0 ≤ V A ≤ c. As (V A /c) increases from 0 to 1, eq. (19) shows that (V B /c) increases monotonically from 0 to 1, with V B ≤ V A at every point. It follows that 0 ≤ V B ≤ c also.…”

“…Geppert [7] makes the same identification. More recently, Sebens [18,19] relies on these and other sources to identify V A as the EM mass flow velocity. Sebens also considers earlier, pre-Einstein studies by Poincare.…”

Dark Matter = Modified Gravity? Scrutinising the spacetime-matter distinction through the modified gravity/ dark matter lens

“…This in turn means that the part of spacetime structure that is surveyed by rods, clocks, test particles and light rays needs to be either (effectively) pseudo-Riemannian or Weylian. 49 Of 47 For more precise definitions, see [93,94]. 48 Arguably there is one additional relevant criterion: one needs independent reasons to believe that the dimensionality of the manifold matches the dimensionality of physical spacetime.…”

“…Without this additional constraint, the 5-dimensional metric of a Kaluza-Klein theory would satisfy all the criteria in the main text, even though it is arguably the 4-dimensional metric that one obtains from projecting the 5-dimensioal metric into four dimensions that corresponds to physical space [76]. 49 See [95] for a proof to that effect.…”