Linearized gravity / Linearized Einstein Field Equations / GEM

[JustinLevy]

Are the phrases "Linearized gravity", "Linearized Einstein Field Equations", "GEM (gravitoelectrodynamics)", all referring to mathematically equivalent approximations of Einstein's full non-linear field equations?

If not, could someone tell me what order (in some rough sense) these would be listed in order of "approximating away" more terms from the full equations?

And is there any experimental data yet that let's us verify "strong field" GR as opposed to just weak field tests (ie. distinguish between the linear approximations and the full non-linear field equations)?

 

[Chris Hillman]

Suggest some arxiv eprints

I deprecate using the term "linearized gravity", since gtr is not the only theory of gravitation, not even the only classical relativistic field theory of gravitation, not even the only currently viable classical relativistic field theory of gravitation. However, the "linearized EFE" plays the same role in "linearized gtr" that the EFE plays in gtr proper.

There are several things one might mean by "gravitomagnetism"; see for example this review paper, which discusses two theories, one using the Bel decomposition of the Riemann tensor which always valid (in particular, works for strong-field gtr), and the other the GEM formalism which is indeed basically a reformulation of weak-field gtr (vacuum fields).

As for observational tests of strong-field gtr, see for example http://arxiv.org/abs/gr-qc/0402007

 

[Entropia]

Linearized gravity, Linearized Einstein Field Equations, and GEM (Gravitoelectrodynamics) are all terms used to describe different approximations of Einstein's full non-linear field equations. These approximations are used to simplify the complex equations and make them more manageable to solve.

The linearized gravity approximation is used when studying weak gravitational fields. It assumes that the gravitational field is small and the metric tensor can be linearized, making the equations easier to solve. This approximation is useful for calculations involving objects with small masses, such as planets and stars.

The Linearized Einstein Field Equations are a set of equations that describe the behavior of gravitational fields in the linear approximation. They are derived from the full non-linear field equations and are used to study weak gravitational fields. These equations are commonly used in astrophysics and cosmology to model the behavior of the universe on large scales.

GEM (Gravitoelectrodynamics) is a theory that describes the interaction between gravitational and electromagnetic fields in the linear approximation. It is based on the analogy between gravity and electromagnetism and is often used to study the behavior of gravity in the presence of strong electromagnetic fields.

In terms of "approximating away" more terms from the full equations, GEM would be the first approximation, followed by the Linearized Einstein Field Equations, and then the Linearized gravity approximation. This is because GEM only considers the interaction between gravitational and electromagnetic fields, while the Linearized Einstein Field Equations still take into account the effects of matter and energy on the gravitational field.

Currently, there is no experimental data that allows us to directly verify the full non-linear field equations. However, there have been numerous tests and observations that support the predictions of general relativity in both weak and strong gravitational fields. For example, the bending of light around massive objects, the gravitational redshift, and the precession of Mercury's orbit are all well-supported by observations and can only be explained by the full non-linear field equations. Therefore, while we cannot directly verify the full equations, the evidence from these tests and observations strongly suggests that they are correct.