I Gravitoelectromagnetism: Why Equation Differs in Sources

  • I
  • Thread starter Thread starter olgerm
  • Start date Start date
  • Tags Tags
    Sources
olgerm
Gold Member
Messages
532
Reaction score
35
In article "A note on the gravitoelectromagnetic analogy" by Matteo Luca Ruggiero (https://arxiv.org/pdf/2111.09008v1.pdf) equation number 18 is ##\nabla \dot\ E=4 \pi G \rho##
, but corresponding equation in the wikipediapage(https://en.wikipedia.org/wiki/Gravitoelectromagnetism#Equations) is ##\nabla \dot\ E_g=-4 \pi G \rho_g##
. ##E## notes same thing in the article as ##E_g## on the wikipedia page. ##\rho## note same thing in the article as ##\rho_g## on the Wikipedia page. Why is this equation different in these sources? To me seems that Wikipedia equation is correct, because from it follows that direction of gravitational field is directed to (not away from) bodies(with positive mass).
 
Physics news on Phys.org
Possibly useful: https://en.wikipedia.org/wiki/Gravitoelectromagnetism#Scaling_of_fields

The literature does not adopt a consistent scaling for the gravitoelectric and gravitomagnetic fields, making comparison tricky.
For example, to obtain agreement with Mashhoon's writings, all instances of Bg in the GEM equations must be multiplied by −1/2c and Eg by −1. These factors variously modify the analogues of the equations for the Lorentz force. There is no scaling choice that allows all the GEM and EM equations to be perfectly analogous. The discrepancy in the factors arises because the source of the gravitational field is the second order stress–energy tensor, as opposed to the source of the electromagnetic field being the first order four-current tensor.
This difference becomes clearer when one compares non-invariance of relativistic mass to electric charge invariance. This can be traced back to the spin-2 character of the gravitational field, in contrast to the electromagnetism being a spin-1 field. (See Relativistic wave equations for more on "spin-1" and "spin-2" fields).
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
Back
Top