In a natural, "static" coordinate system the speed of gravity can be superluminal

What is the speed of changes in the gravity field? Usually people assume that it is the local speed of a photon. That is, the local speed of light.

The speed of a photon, as seen by a faraway observer, can be very slow if it travels in a low gravitational potential.

Is it true that changes in the gravity field can only propagate at the local speed of light?

Here we assume a "static", cartesian, initial coordinate system and study how quickly a spherical shell reacts, relative to that coordinate system, to changes in an external gravity field.

If we would define spatial coordinates through using physical, tense rubber strings in space, then the speed of gravity seems to be less than the local speed of light.

A spherical shell under a changing gravity field

Let us have a strong spherical shell which is close to being inside its Schwarzschild radius. Measured by a faraway observer, photons move very slowly close to the sphere.

Let us assume that the speed of gravity is only the local speed of light.

Let us put swiftly a mass M at some moderate distance from the shell. The gravity of M starts pulling on the shell.

               O                          ● <-------

     massive shell        mass M

But the surface of the shell receives the information about the changed gravity field much later. Does the shell stay static for a long time? That would be strange. That would mean that objects behave differently in the field of M - a breach of an equivalence principle.

We conclude that the surface of the shell must react to the changed gravity field faster than what is allowed by the local speed of light. It has to start moving quickly, relative to our coordinate system.

                    |

                    \

                 O  |  --->   shell movement

                    /

                    |

         rubber string

If we would use physical rubber strings to define the spatial coordinates, then the shell would push them in front of it, because the local speed of light is slow close to the shell. The movement of the shell would happen through changes in the metric making the distance between the shell and M shorter. In the rubber coordinate system there probably are no superluminal reactions.

If the shell moves along a complicated path, it may make the rubber strings entangled. The rubber coordinate system is not very practical.

Minkowski & newtonian gravity

On February 25, 2023 we wrote about the speed of gravity in our own theory of gravity, Minkowski & newtonian gravity.

We suggest that the external gravity field of the mass M "grabs" the entire system, the shell and its gravity field. It exerts a force on the entire system. The slow speed of a photon inside the system is a result of interactions within the system. That does not prevent the external field of m

M grabbing the entire system and moving it.

We may interpret the process like this: the combined gravity field of the shell and the mass M tries to get to a lower energy state. The outer field of the shell is "attached" to the field very close to the shell, and ultimately to the matter in the shell.

The field of M exerts a force on the outer field of the shell. The attachment relays the force to the inner field and to the matter in the shell.

The whole system, the inner field & the matter, starts to move under the force. This is essentially newtonian mechanics.

Superluminal communication to an observer on the shell is not possible

Can one send a signal to an observer on the shell superluminally?

Let us use a small, local change in the gravity field as the signal. It propagates at the local speed of light. It is not superluminal.

Suppose that the shell carries an electric charge but the observer is neutral. Let us pull on the shell with an electric field. What does the observer see?

Changes in the electric field lines propagate only at the local speed of light. It takes a long time for the observer to notice anything. The electric field makes the shell to move immediately, but the observer is oblivious of this.

Conclusions

In a "natural" coordinate system we must allow systems to react faster to changes in the gravity field than what is the local speed of light.

The global speed limit has to be the the speed of light in the surrounding asymptotic Minkowski space. Otherwise, we would have the time travel paradoxes.

Our observation has implications for LIGO calculations. It is not clear to us what speed of gravity they use in their computer models. If it is the local speed of gravity, it may be too slow.