Dear Ben,
Thanks.
I apologize for the long absence in the forum.
My explanations are follows:
1. On page 7, you say, "Now our space-time can be regarded as a bimetric, and this fact has a deep physical meaning: It can be thought as a pseudo-Euclidean E in the IRFs and as a Riemannian V in the PRFs." Are you speaking only about gravity in this context?
No. If in an IRF some force field is given, the space-time metric in PRFs of this field is determined by the Lagrangian governing the motion of particles under the influence of this field according to eq.(1).
Sometimes, this metric has a simple form. For example, if the reference body is formed by non-interacting charges in a constant electromagnetic field, it is a Finsler metric, in the case of an ideal isentropic fluid - is a Riemannian metric wich is conformal to the Minkowski space, and in the case of gravity - is a Riemannian metric.
2. By "pseudo-Euclidean," do you always mean Minkowski space, or are you using the more general meaning?
I mean Minkowski metric, according to special relativity.
3. Do the new equations predict only supermassive objects without event horizon, or do they predict both objects with event horizons and objects without?
The new equations predict only supermassive objects without event horizon.
This result does not contradict the observations. Furthermore, it is the properties of gravity near the event horizon can explain the features of the Hubble diagram at high redshifts up to z=8.
But the problem is that the observation of supermassive objects, and the Hubble diagram can be explained without such a radical change in the theory.To prove the validity of these equations, and these ideas, we need to find facts that are difficult to explain in the orthodox theory.
Sincerely,
Leonid