Differences in Newtonian and Relativistic predictions of gravity

[espen180]

In what situations do Newton's law of universal gravity fail to predict correctly how matter moves? The examples I know of are frame dragging (around rotating BH), shifting of light paths, shifting orbits of planets.

But does Newton's law really predict the magnitude of gravity accuratly? How does the predicted Newtonian value compare to the predicted relativistic value in different situations?

Also, given the symmetry between the electromagnetic and gravitomagnetic forces, how come there isn't a spacetime-equivalent theory for electromagnetism? Am I wrong in my assuption of said symmetry?

I hope to get some answeres on my questions. Any help/feedback is appreciated.

 

[Matterwave]

Anywhere the gravitational fields are very very strong, GR will give different results than Newtonian gravity. Newtonian gravity is retrieved in GR in the weak field limit.

Since GR no longer has a notion of "force" of gravity, and instead replaces it with a curvature of spacetime, there is no way to say the "magnitude" of gravity is different between the two or not, only that they give different orbits or results.

 

[Entropia]

There are several key differences between Newtonian and Relativistic predictions of gravity. One of the main differences is in the concept of spacetime. In Newtonian gravity, space and time are considered separate entities and gravity is described as a force acting between objects. However, in Relativity, space and time are combined into a single entity known as spacetime, and gravity is described as the curvature of spacetime caused by the presence of mass and energy.

One of the main situations where Newton's law of universal gravity fails to predict correctly is in extreme gravitational fields, such as around rotating black holes. In these situations, the curvature of spacetime becomes significant and cannot be accurately described by Newtonian gravity. This can lead to phenomena such as frame dragging, where the rotation of a black hole causes the spacetime around it to twist, affecting the motion of nearby objects.

Another example is the shifting of light paths, known as gravitational lensing. In Relativity, the curvature of spacetime can cause light to bend as it passes near massive objects, which can result in the appearance of distorted or multiple images of the same object. This has been observed in the bending of light from distant galaxies by massive galaxy clusters.

In terms of the magnitude of gravity, Relativity predicts a slightly different value compared to Newtonian gravity. This difference is very small in most situations, but becomes more significant in extreme gravitational fields. For example, the predicted value of the precession of Mercury's orbit is more accurate when calculated using Relativity compared to Newtonian gravity.

As for the symmetry between electromagnetism and gravitomagnetism, it is true that there are similarities between the two forces. Both involve the interaction between objects through the exchange of particles (gravitons for gravity and photons for electromagnetism). However, there are also significant differences, such as the fact that electromagnetism can be both attractive and repulsive, while gravity is always attractive. Additionally, the equations that describe these forces are different and cannot be easily unified into a single theory.

In summary, while Newton's law of universal gravity is a useful and accurate theory in most situations, it fails to accurately predict the behavior of gravity in extreme situations where the effects of spacetime curvature become significant. Relativity provides a more comprehensive and accurate description of gravity, taking into account the fundamental relationship between mass, energy, and spacetime.