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Any Lorentz transformation is simply a hyperbolic rotation (+boost) of your coordinate system - you are merely labelling the same physical events in your spacetime in a different way. You are always free to do this, since it has no physical consequences in the classical world - the energy-momentum tensor is the conserved Noether current associated with time translation invariance, so you can choose to do this either in the future direction, or into the past, the difference just being a sign convention. The actual dynamics of the system are the exact same, so no laws of physics change form. So of course you can describe classical anti-particles as propagating backwards in time (relative to their positive-energy counterparts), but that just means you’ve chosen a different sign convention in your description of the system. And again, all Lorentz transformations (antichronous and orthochronous) are diffeomorphisms, so applying them to a given metric does not change anything about the geometry of that spacetime. Sure. However, this isn’t the only thing it does - it also changes the spatial components of the 4-vector such that its overall norm remains conserved. This is why 4-vectors (more generally: objects that are representations of the Lorentz group) are covariant under all Lorentz transformations, and laws formulated with them retain their form. There is no change in particle trajectories, such a spacetime has the exact same geodesic structure, only future-directed time-like unit vectors are now sign-inverted, so all processes “run backwards”, and all energies are negative wrt to the ordinary case. All curvature tensors and their invariants remain unaffected, so this is the same geometry described simply in a sign-inverted way. To make a long story short, the point is just this - if you start off with a positive energy-momentum tensor and run through the maths, you don’t end up with a negative-energy region beyond the horizon during a collapse process - at least not in any solution that I’m aware of, since M is a global property of the entire spacetime.

I stay with the quote of Steve Hawking: "I have noticed that even those who assert that everything is predestined and that we can change nothing about it still look in both ways before they cross the road." But we don't have total free will, our decisions are always conditioned by some things, environmental or personal ones, physical or psychological. We should talk about a conditioned free will. So it is something in the middle between total free will and determinism.

Doubtfully. The theory of relativity deals with the relation between space and time, while your geometry is only spatial.

I sincerly hope this is not another preaching attempt, so I will take your question as genuine. You might find reading Marcus Du Sautoy's book interesting in answer to your question Other books of interest might be the wooden books series,particarly sacred deometry by Mirand Lundy and Symmetry by David Wade https://woodenbooks.com/index.php

Yes I am, I'm accusing you of not understanding the topic you started, and not understanding the argument's I've presented; or!!! you're trolling... 🤔 I have an understanding of how AI works (are you sure yo do???), it's the same level of intelligence/consciousness as an anthill/colony; you're conflating what it means to be a human (an evolutionary process of design) now, with what it might be like for an AI (after a similar evolutionary process)... 🙄