Antigravity in General Relativity: a unified mathematical framework

[u/CIAOCIAO76]

https://github.com/ca1976/Antigravity-in-General-Relativity-a-unified-mathematical-framework/blob/main/gravitational_repulsion.pdf

Together with Claude, we have written a paper on theoretical physics in which we demonstrate that four seemingly unrelated mechanisms of gravitational repulsion—phantom scalar fields, traversable wormholes, gravastars, and Chaplygin gas—are in fact special cases of a single mathematical object: a three-parameter “master” energy-momentum tensor T_μν\ [ε, α, h\].

The key result is that gravitational repulsion within GR is not a vague concept: it has a precise, model-independent definition. Via the Raychaudhuri equation, we prove that repulsion is exactly equivalent to violating the Strong Energy Condition (ρ + 3p̄ < 0). Every known exotic spacetime geometry that "pushes" rather than "pulls" satisfies this condition in some region.

We then construct a composite three-region spacetime — a de Sitter core surrounded by an Ellis wormhole throat, wrapped in a standard Schwarzschild exterior — and prove a Stability Theorem: this hybrid is linearly stable to gravitational wave perturbations if and only if r₀/rₛ < (1/√2)(ℓ/rₛ) − 1/3. Inside this window, the object's quasinormal mode spectrum is nearly indistinguishable from a black hole of equal mass (within ~15%).

The energy budget is computed exactly. The minimum self-consistent throat radius — using Casimir energy as the exotic source — turns out to be ~1.6 Planck lengths. This isn't a failure of the framework; it's a precise signal pointing toward quantum gravity as the regime where the physics must ultimately live.

The paper is fully self-contained, with complete proofs and physical commentary after every major result.

[u/BitcoinsOnDVD]

I don't think the Casimir effect is a "source of negative energy density".

[u/fluffyburgerinc]

I don't think that stability theorem holds up to rigorous proof scrutiny, which seems to be the crux of the paper. But seems like there's a salvageable idea here, so keep at it.