Theory

Physical picture

A collapsing star is one extended physical system. To describe its state at a given moment, one must determine where all of its layers are simultaneously. In the Frozar formulation this is done in a reference frame at rest with the source, using a single world time that labels its hypersurfaces of simultaneity.

Every layer has local physical processes — particle motion, atomic oscillations, radiation, chemical and nuclear reactions. Their local rate is expressed by the proper time of that layer. Proper times at different radii need not run at the same rate relative to world time.

World time has a different role. It is defined throughout the reference frame and tells which events at different places belong to the same global state. In an asymptotically flat system, far from the source where the field becomes negligible, its rate is synchronized with the proper time of a distant observer at rest.

Therefore the proper times of different layers cannot be chosen independently when one wants the state of one star at one moment. They must all be related to the same world time.

Physical picture

The customary phrase “gravitational time dilation” or “slowing of time” is convenient, but it can obscure what is physically happening. In the Frozar framework, this terminological conflation is treated as one of the methodological sources of confusion in gravitational collapse.

The physical effect is not that an independent entity called “time” itself changes its rate. What is observed is a synchronous slowing of all local physical processes in a gravitational field relative to the chosen world time. The closer to the source and the stronger the field, the greater this slowing.

Every possible clock is only one example of such a local process. Atomic transitions, oscillations, motion of matter, radiation processes, chemical and nuclear reactions all slow by the same local relativistic factor.

A more precise expression is therefore: slowing of local proper times relative to the world time of the hypersurfaces of simultaneity.

Physical picture

The clearest first model is a spherical thin shell made of pressureless matter. Far from its gravitational radius the shell contracts comparatively rapidly. As it enters a stronger gravitational field, all of its local processes slow increasingly relative to world time, and so does the contraction itself.

On a world-time diagram the radial motion becomes progressively slower. The shell approaches its limiting radius ever more closely, while crossing it is pushed to ever later world-time moments. This simple model already contains the basic mechanism of frozarization.

Physical picture

A real star consists of many nested layers. For each layer, the relevant gravitational scale is determined by the mass enclosed inside that layer, not only by the total mass of the star.

Therefore different layers enter the strong-slowing regime under different local conditions. Frozarization is not confined to the visible surface: it is a layer-by-layer process involving the whole stellar structure.

The resulting object is therefore not an empty region bounded by a single frozen surface, but an ultra-compact material configuration whose internal layers are themselves strongly slowed relative to world time.

Physical picture

A central benchmark is the exact Oppenheimer–Snyder solution for the spherical collapse of a homogeneous dust star. It describes pressureless matter without adding a mechanism that could halt the contraction.

In comoving coordinates the motion of matter is naturally expressed through local proper time. But this local description alone does not yet answer the global question: where are all layers of the star at the same moment in the source-rest frame?

To obtain that picture, the proper time of every layer must be related to the common world time. Only then can the positions of all layers be plotted on one hypersurface of simultaneity.

Physical picture

As collapse proceeds, proper times of the stellar layers run increasingly slowly relative to world time. Their radial evolution in world time slows at the same time.

Each layer approaches the limiting radius determined by the mass inside it. For an external description, further change becomes ever slower. The star evolves into a frozar: a relativistically collapsed material object whose internal evolution is extremely slowed relative to world time.

“Frozen” does not mean that local physics ceases in the layer’s own proper time. It means that the layer’s proper time advances asymptotically slowly relative to the global world time.

Physical picture

The decisive question is not merely what one freely falling observer experiences. It is the structure of the whole star on one global hypersurface of simultaneity.

In the Frozar picture all material layers remain parts of the same global configuration. The gravitational radius is essential, but it is interpreted as an asymptotic limit of the world-time evolution of the corresponding layer.

This separates two logically different questions: whether a coordinate or analytic continuation of a metric can be written beyond a surface, and whether that surface is physically formed by collapsing matter at a finite world time. Frozar theory addresses the second question.

Physical picture

As a star approaches the frozar state, radiation from its deep gravitational field is increasingly redshifted and the observed evolution becomes slower. The object becomes extremely compact and dark, while retaining a material internal structure in the global description.

Observable differences must therefore be sought in processes sensitive to that near-limiting structure: accretion, mergers, gravitational waves, interactions with neutron stars, and the behavior of supermassive compact objects in galactic nuclei.

Each such test requires a separate quantitative model; the purpose of the theory is to identify which physical quantities must be calculated and compared with observations.