Yes and this is a standard exercise in general relativity. It suffices to write down Einstein's equations, search for solutions that describe travelling waves and deduce the dispersion relation for waves about any fixed background. If the background backreacts too strongly it's the concept of a wave itself that becomes less useful.

In fact one of the interesting measurements involving neutron stars was to compare the speed of gravitational waves with that of electromagnetic waves-and it was a non-trivial control of the backgrounds that allowed the deduction that both signals arrived as was to be expected, were the speed of the two waves equal.

In fact, I was determined to provide the answer to my question when I received one from our French friend in Tours.

The answer is intelligent, but unfortunately completely wrong.

I know this is the standard answer one receives in most French universities, at the CNRS, and even in the West.

The above question is that Einstein used some of his magical thought experiments (he invented many, all fanciful and misleading) to prove this theory of general relativity, among others.

First, these thought experiments do not constitute rigorous proofs and are sometimes flawed.

Second, he should have used one of the universal laws to strengthen the credibility and make his theory of general relativity more elegant, but he did not.

Our personal answer is this: simply because the great Einstein did not understand physics to such an extent, one sometimes wonder if he ever studied physics and, if so, who taught it to him?

The true stress-strain tensor/matrix of general relativity is not Einstein's, but the one proposed by the author, where time is defined as a vector with four components: tx, ty, tz, tt.

Here, the proposed theory induces Einstein's general relativity in a single sentence. In the matrix/tensor formulation,

∇2xx ∇2xy ∇2xz ∇2xt [U]

∇2yx ∇2yy ∇2yz ∇2yt [U]

∇2zx ∇2zy ∇2zz ∇2zt [U]

∇2tx ∇2ty ∇2tz ∇2tt [U]

What is the energy density of spacetime! x

C^2

X

Cxx Cxy Cxz Czt

Cyx Cyy Cyz C yt

Czx Czy Czz C zt

Ctx Cty Ctz C tt

= I(unit matrix) . . (1)

where, ∇2zx U=Fxy and Cxy=curvature in xy.

Note that the theory of general relativity (Equation 1) is nothing other than the Lorentz transformation law in the 4D unit space xyzt expressing its conservation.

which is the modern general relativity proposed by the author.

Furthermore, Equation 1 shows that:

1- Special relativity is only a special case of general relativity.

2- Contrary to Einstein, gravity is a real force that produces curvature, not the other way around.

3- Equation 1 can be either a wave equation or a diffusion equation, depending on the choice of input elements for the main diagonal of the transition matrix B.

4- It also shows that gravitational waves exist at the speed of light C.

In my opinion:

The speed of gravitation is zero, since gravitation is an emergent phenomenon.

Ismail Abbas M. Abbas can you elaborate on "Contrary to Einstein, gravity is a real force that produces curvature, not the other way around."

According to Einstein's theory of general relativity, gravitational waves, which are ripples in spacetime caused by accelerating masses, propagate at the speed of light in a vacuum. This was confirmed by the detection of gravitational waves from merging black holes and neutron stars by experiments like LIGO and Virgo.

The answer to

“Is it true that the speed of gravity is equal to the speed of light?”

- is Yes. Gravity is fundamentally nothing else than some fundamental Nature force, as that Weak, Electric, and Nuclear/Strong Forces are. At that, as that it is rigorously shown in the Shevchenko-Tokarevsky’s initial Planck scale models of these Force4s, more see https://www.researchgate.net/publication/395113364_Planck_scale_informational_physical_model_and_fundamental_problems_in_physics , section 6 “Mediation of the fundamental forces in complex systems”,

- the at least Gravity, Electric, and Nuclear/Strong, Forces mediators propagate [don’t move, since fundamentally aren’t particles] in the 3DXYZspace of Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, [4+4+1]4D spacetime with metrics (cτ,X,Y,Z, g,w,e,s,ct).only with the speed of light.

Intensive flaws of the mediators are observed on macro “classical” scale as the Forces fields.

At that nothing happens with the spacetime when anything in Matter exists and happens, it is nothing else than some “empty container” that fundamentally cannot be impacted by anything in Matter, and impact on anything in Matter.

More see the link; SS posts in

https://www.researchgate.net/post/If_you_were_to_look_for_a_new_theory_of_gravity_to_replace_general_relativity_what_criteria_would_that_theory_have_to_meet#view=68c42257d90aaf79fd097a05/50/51, pages 51, 52, and

https://www.researchgate.net/post/It_tries_to_answer_the_most_fundamental_question_where_do_space-time_and_matter_come_from

-are relevant in this case also.

Cheers