Thin dust shell
Two parametrizations, by world time and proper time, are related under the physical constraint connecting the shell radius and time variables.
MATHEMATICAL PHYSICS
Theory of Parameter Constraints
A general framework for identifying and resolving constraints among parameters that represent physical properties of a system and its environment.
The problem
Physical theories specify relations among dynamical variables, but those relations are governed by parameters. When combinations of parameters contain hidden dependence, varying them as if they were independent can produce a physically inconsistent picture.
Classification of parameters
An independent parameter represents a distinct physical characteristic. A fully dependent parameter is expressible through independent ones and should be eliminated from final formulas. A partially dependent parameter combines dependent contributions with genuinely new physical content and must be cleaned until that new independent content is isolated.
Constraint-cleaning procedure
For a composite parameter such as P(p₁,p₂,p₃;q), dependencies on p₁, p₂ and p₃ are removed successively until the independent characteristic q remains. Conserved quantities that characterize the system become parameters, and admissible variations must respect the resulting constraints.
Relativistic-gravity applications
The current development applies the method to relativistic collapse and compact stars: a thin dust shell, a dust star described on hypersurfaces of world time, charged stars, slowly rotating stars, and combined charge–rotation systems.
Purpose
The aim is not to claim novelty for every individual constraint technique, but to formulate a unified mathematical-physics framework for systems with dependent parameters, systematize existing partial methods, and prevent parameter-induced errors in physical models.
APPLICATIONS TO RELATIVISTIC GRAVITY
Unified sequence of examples
Dust star
The Oppenheimer–Snyder construction is examined on hypersurfaces of world time, where the matching to the exterior Schwarzschild solution fixes the admissible parameter relations.
Charged star
Charge contributions are separated from the mass parameter so that physically independent characteristics are varied independently.
Rotating star
Rotation contributions are treated analogously, with dependent combinations eliminated before interpreting gravitational effects.
Charge + rotation
The combined case requires staged elimination of dependencies so that charge and angular momentum are not counted twice through composite mass parameters.
Constraint-respecting variation
Once conserved quantities become parameters, variations must remain on the allowed parameter subspace rather than move through physically forbidden combinations.
Working principle: a parameter may be used as independent only after the physical characteristic it represents has been separated from contributions already encoded in other parameters.