Common Relativity (CR) arises from the need to overcome three structural limits of General Relativity (GR), limits that do not derive from conceptual errors in Einstein's theory, but from the lack, at the time, of complete knowledge of ultradense matter physics, topological structures of matter, and the hierarchical organization of the Cosmos.
Beyond the limits of GR
GR is a local theory, extremely elegant and powerful, that describes how matter curves spacetime. But, like any physical theory, it works within a defined domain: that of densities and curvatures below the critical thresholds imposed by quantum mechanics.
Once these thresholds are crossed, in regions inside gravitational collapses and in the primordial conditions of bubble-universes, GR loses descriptive validity and generates mathematical objects with no physical interpretation: singularities.
The fact that such divergences emerge does not indicate that "nature diverges," but that the local theory has been forced beyond its domain of validity.
The ten axioms of Common Relativity
Axiom I: Existence of cosmic time t0
There exists a global scalar temporal field, t0, that orders the evolution of physical states of the Cosmos. The temporal hierarchy is:
τ ⊂ t ⊂ t0
Axiom II: Universality of physical laws
Throughout the Cosmos, the same fundamental constants (c, G, ℏ, α, me, etc.) and the same physical laws apply. Bubble-universes differ only in initial conditions, not in laws.
Axiom III: Ontological reality of matter beyond the horizon
Matter that crosses an event horizon remains physically real. The horizon is a limit of optical observability, not of physical existence.
Axiom IV: Uniqueness of the compact object
There exists only one type of gravitationally collapsed body: the fermionic neutron star, visible below TOV and obscured beyond TOV. "Black holes" do not exist as distinct entities.
Axiom V: Existence of the aggregation constant ξ
There exists a universal mass constant, ξ, representing the maximum limit of baryonic aggregation before triggering the gravitational phase transition.
ξ ≈ 3 × 1054 kg
Axiom VI: The bounce as physical transition
Beyond the ξ threshold, the system undergoes a deterministic bounce that generates a new expanding causal domain: a bubble-universe.
Axiom VII: Global conservation of information
Quantum information is not destroyed in collapses. The identity of matter is preserved and transferred to the daughter domain.
Axiom VIII: Global thermodynamic coherence
Cosmic time t0 increases with the total entropy of the Cosmos, providing a natural origin for the arrow of time.
Axiom IX: Topological emergence of matter
Elementary particles are not point-like entities but topological configurations (solitons) of the fundamental geometric field.
Axiom X: Coherence metric as informational structure
Beyond the local geometric metric, there exists an informational metric that describes the coherence of field configuration.
The temporal hierarchy
CR introduces a three-level temporal structure:
- τ (proper time): the most local level, defined by an observer's trajectory along their world line
- t (cosmological time): the time of each bubble-universe, describing the evolution of the scale factor
- t0 (absolute cosmic time): a global scalar field that orders the evolution of the entire hierarchical structure of the Cosmos
This hierarchy does not violate local relativity of simultaneity: it extends it, providing a complete description of physical evolution across all scales.
The aggregation constant ξ
The constant ξ can be obtained through six distinct theoretical paths, all convergent:
- Extended TOV derivation
- Finite internal curvature
- Degenerate Fermi gas (Pauli)
- Cosmological aggregation
- Vacuum energy and ξ-Λ relation
- Aggregation hierarchy
The constant ξ plays in CR the same role that c, ℏ, kB, and G play in their respective theories:
- c limits velocities
- ℏ limits action
- kB limits entropic density
- G regulates gravitational force
- ξ limits gravitational aggregation
Connection between ξ and Λ
CR does not treat the cosmological constant Λ as a simple free parameter. It derives from bounce dynamics:
ρΛ = c5 / (ℏG2ξ)
This equation implies that:
- Λ is the energetic memory of the previous bounce
- Universes with different ξ possess different vacuum density
- Λ is not an arbitrary addition: it is a determined physical variable
Summary
Common Relativity is not a local modification of gravity: it is a reformulation of the ontological and topological foundations of reality.
It unifies:
- The dynamics of gravitational collapses
- The emergence of matter
- The structure of the Standard Model
- The behavior of black holes (obscured neutron stars)
- The origin of bubble-universes
- The connection between ξ and Λ
A Cosmos in which nothing is annihilated, nothing is created from nothing, and every domain derives from a real physical history.