Frozars: What Happens to a Star at the Final Stage of Gravitational Collapse

Two Times of One Collapse

The concept of time combines two properties of physical reality: the rate at which processes proceed and the simultaneous existence of different parts of an extended system. Proper time characterizes the local rate of processes associated with a given object. World time makes it possible to describe different parts of the star at one and the same moment.

As long as the field is relatively weak, the difference is small. But as the surface approaches the gravitational radius, proper clocks run ever more slowly relative to world time. Radiation becomes increasingly redshifted, intervals between successive signals grow, and the further evolution of matter practically stops.

This is not an ordinary mechanical stop. Locally, matter may remain hot and highly dynamical; particles continue to move and interact. What freezes is not matter itself, but its evolution on the scale of world time.

The Star Does Not Disappear Beyond a Horizon

In Newtonian gravity, time is absolute and independent of the strength of gravity. Collapse was therefore naturally pictured as the whole star falling into a dark region and its matter eventually concentrating at a central singularity. This is how the image of a black hole arose.

In general relativity the situation is different. Consider concentric layers of a collapsing star. As contraction proceeds, their proper times slow more and more. In a global frame described by world time, the inner layers begin to freeze before the outer ones, while the surface is the last to approach the limiting state.

Matter does not disappear from the world picture of spacetime. It remains in those layers where further evolution has practically stopped. A frozar can therefore be viewed as a gravitational archive of the history of collapse: the deeper a layer lies, the earlier its evolution effectively ceased relative to the external world.

Why “Freezing” Does Not Mean Cold

The expression “frozen star” does not mean a cold or mechanically motionless object. During collapse matter is compressed and heated, and electrons, nucleons and, at sufficiently high densities, quarks may be in relativistic regimes.

Freezing refers to the rate of proper time relative to world time. Thus matter may remain extremely hot and dynamic locally while its global evolution is practically frozen.

Two Causes of Time Slowing

At the final stages of collapse, the proper time of matter slows for two reasons. The first is gravitational: the stronger the field, the slower local processes proceed relative to world time. The second is kinematic: the closer a local velocity is to the speed of light, the stronger the relativistic slowing of proper time.

In a collapsing star, radial infall velocities, thermal particle velocities, and tangential rotational velocities can all be large at the same time. Limiting freezing is therefore strengthened by the combined action of gravitational and kinematic factors.

Rotation and Charge: Why the Total Mass Cannot Be Held Fixed

When one passes to a rotating or charged star, another basic problem appears in the traditional black-hole interpretation. The total mass of the object was kept fixed while the rotational energy or the energy of the electric field was increased.

But energy has mass. If a star acquires additional rotational energy or creates a stronger electric field, its total energy rises and so does its total mass. In frozar theory, the total mass is the mass of the neutral nonrotating matter plus the mass-equivalents of rotational and electric-field energies.

Objects with different charges and angular momenta should therefore be compared at the same initial mass of matter, not at an artificially fixed total mass.

Why Rotation Strengthens Gravity

Rotation does create a centrifugal effect that opposes contraction. But its energy simultaneously increases the total mass of the star and thereby strengthens gravity.

If angular momentum is increased while the total mass is held fixed, one obtains the paradoxical impression that rotation weakens gravitational effects until they disappear and even leads to formal antigravitational regimes. The reason is simple: rotational energy is added to the system but is not allowed to increase its mass.

In frozar theory, increasing rotational energy increases the total mass and strengthens gravity. The centrifugal effect remains, and there is also additional kinematic time dilation caused by large tangential velocities. Rotation therefore does not remove gravitational freezing.

Why Charge Also Strengthens Gravity

A stronger electric field contains more positive energy. Increasing the charge therefore increases the total energy and mass of the system.

If the charge is increased while the total mass is artificially kept unchanged, one obtains the false conclusion that charge weakens gravity. Physically, such a procedure means that some other part of the system’s energy must simultaneously decrease, so one is no longer comparing the same star.

In frozar theory, increasing charge means increasing electric-field energy and total mass. Electric repulsion remains, but it is not accompanied by an artificial reduction of the source of gravity. The general principle is simple: any positive energy added to an isolated system increases its total mass.

What Remains Visible

If the frozar surface is practically frozen, why can a supercompact object be bright? Because most of the observed radiation is produced not by the surface itself but by the surrounding gas and plasma.

An accretion flow or disk heats up, interacts with magnetic fields and radiates intensely. The closer the emitting region lies to the frozar surface, the stronger the redshift, the slower the observed processes, and the smaller the fraction of photons able to escape. The surface itself may therefore be nearly invisible while the surrounding plasma remains extremely bright.

The Frozar Shadow: “Hair” and Even a “Hairstyle”

Modern images of supercompact objects show a dark central region—the shadow—surrounded by a bright ring of plasma. But the shadow alone does not determine the internal nature of the central object; it arises primarily from strong bending of light trajectories.

Here one of the main differences between the black-hole and frozar pictures appears. In the traditional theory there is the well-known statement that a black hole “has no hair.” After collapse, the external object is characterized only by a few global parameters—mass, charge and angular momentum—while details of the matter distribution disappear from the external description.

A frozar is different. Its real frozen matter structure remains. Figuratively speaking, a frozar has not only “hair” but even a “hairstyle.”

A Superfrozar Is Inhomogeneous from Birth

A supermassive frozar in a galactic center need not form in a single spherical collapse. When galaxies merge, their central superfrozars can also approach one another and stick together.

Sticking does not erase the structures of the progenitors. As they approach, the facing regions enter an ever stronger common gravitational field, their proper times slow, and further rearrangement gradually freezes. The new object retains the inhomogeneities of its components.

After several such events, a large superfrozar becomes a gravitational conglomerate that preserves a memory of successive stickings of many smaller objects.

Accretion Creates Mascons

Later accretion adds another source of inhomogeneity. Infalling matter does not disappear beyond a horizon. It reaches particular regions of the frozen surface, becomes radially flattened before it can spread uniformly, and freezes there.

This produces local excesses of mass—mascons, by analogy with the mass concentrations known on the Moon. A real superfrozar therefore has at least two sources of inhomogeneity: large-scale structure inherited from earlier stickings and smaller mascons created by subsequent accretion.

An Inhomogeneous Shadow and a More Turbulent Disk

At large distances the field is determined mainly by the total mass, but close to the object local inhomogeneities become important. They should slightly alter photon trajectories, so the boundary of a real superfrozar shadow need not be perfectly smooth.

The inhomogeneous field also affects plasma. Passing above more massive surface regions, the plasma receives additional local accelerations; compressions, vortices and extra turbulence arise. The accretion flow around a superfrozar should therefore be more complex than around an ideally smooth central object with the same averaged parameters.

Locally heated regions appear as bright spots. Such brightness inhomogeneities are already visible in published images of M87* and Sagittarius A*. By themselves they do not prove the existence of mascons, because magnetic fields, plasma turbulence and relativistic motion can also produce them. Frozar theory adds another possible source: inhomogeneity of the gravitational field of the central object itself.

From a Photograph to a “Movie”

Long series of observations are therefore more important than isolated images. A random plasma inhomogeneity appears, moves and disappears relatively quickly. A mascon or a large structural inhomogeneity of a superfrozar changes extremely slowly because of gravitational freezing.

One should therefore look not merely for bright spots but for persistent regions of enhanced activity. Even stronger evidence would be a correlation between local deviations of the shadow boundary and plasma behavior in the same directions. A “movie” of the neighborhood of a superfrozar may thus be far more informative than a single picture.

Sticking Instead of Falling Through

If the surfaces of two frozars are already strongly gravitationally frozen, their common field becomes still stronger as they approach. Proper times in the closest surface regions slow further, and the contact process develops ever more slowly relative to the external world.

Gravitational sticking occurs. At the early stage the system changes rapidly and emits gravitational waves, losing part of its energy and angular momentum. As a new supercompact object forms, further rearrangement slows more and more.

The result is not the disappearance of matter into an empty region but a new, more massive and still more inhomogeneous frozar.

What Gravitational Waves Can Show

The early stages of approach of supercompact objects may look similar because they are governed mainly by the external field. The most interesting part is therefore the final stage of the gravitational-wave signal.

Here the essential question is whether the material structure disappears or is preserved during sticking and subsequent freezing. As detector sensitivity improves, one can search for weak late-time features connected with the structure of the sticking objects and the formation of a common frozar.

Must Every Superdense Star Become a Frozar Immediately?

No. An intermediate state may exist between a stable neutron star and a limiting frozen frozar, especially for masses only slightly above the maximum stable neutron-star mass.

For example, a neutron star in a binary system may gradually accrete matter. Once the stability limit is exceeded, further contraction begins and the density may become high enough for matter itself to enter a new phase.

Quark Matter and the Gloozar

At enormous densities a hadron–quark phase transition may occur. Instead of matter composed of separate protons and neutrons, an ultradense quark medium can appear.

If its pressure is able to resist further contraction for some time, a quasistable supercompact star is formed—a gloozar.

A gloozar has not yet reached limiting gravitational freezing. Its radius may be close to the photon radius, where light bending is already extremely strong, while proper processes inside the star can still proceed comparatively rapidly.

Why a Gloozar Should Be Extremely Hot

During contraction, gravitational energy is converted into internal energy. In a sufficiently compact gloozar, electrons—and, in a quark phase, quarks—can be relativistic, with local velocities amounting to a substantial fraction of the speed of light.

An enormous reservoir of relativistic motion is therefore stored in a comparatively small volume. A gloozar becomes a reservoir of relativistic energy.

Relativistic Explosion

If the quasistable state of a gloozar is disrupted, a substantial part of this energy can be released within a short proper-time interval. This is not an ordinary thermonuclear explosion: the energy is already stored in the ultradense relativistic medium.

If the structure of quark matter changes rapidly, or if the energy of relativistic particles is converted into radiation and motion of outer layers, the ejected matter itself can become relativistic. This produces a relativistic explosion.

Such a scenario is most likely in a relatively narrow mass range just above the stability limit of neutron stars: at lower mass the star remains stable, whereas at substantially larger mass the intermediate quasistable stage may be too short.

How to Test the Frozar Picture

Frozar theory leads to several independent observational consequences. One should search for persistent irregularities of shadow boundaries and long-lived structures of bright regions in accretion flows; study the late stages of gravitational-wave signals; and search for intermediate superdense objects slightly above the neutron-star stability limit and for powerful short transients that may be relativistic explosions of gloozars.

The most valuable evidence would be a convergence of several signatures. For example, if persistent shadow irregularities correlate with repeatedly active plasma regions, two independent observational channels would point to the same source—the inhomogeneous field of the central object.

These Are Not Two Theoretically Equal Models

The issue is sometimes presented as if black holes and frozars were two theoretically equal models and future observations would eventually decide between them. But both pictures claim to describe the same process within the same general theory of relativity, with the same equations and physical principles.

The first question is therefore theoretical: which picture actually follows from those principles? In frozar theory the answer is obtained by describing the whole extended star in one global frame and considering all of its layers at the same moment of world time.

Gravitational slowing of proper times cannot be discarded precisely when it becomes limiting. The inner layers freeze before the outer ones, the surface approaches the gravitational radius asymptotically, and a horizon that would have to be crossed in finite world time does not form. In this way general relativity yields a frozar.

Where the Black-Hole Picture Goes Wrong

The problem is not in the equations of general relativity but in their physical interpretation. Gravitational time slowing is accepted in the external field, but the global evolution of matter is then continued as if that slowing no longer prevented further collapse.

Two incompatible logics are combined: outside, one uses relativistic spacetime with gravitational slowing of proper times; inside, the fate of matter is effectively treated by the pre-relativistic scheme of continuing the fall through the gravitational boundary.

The black-hole concept is therefore, in the frozar framework, not an equal alternative within general relativity but an erroneous physical interpretation of relativistic collapse. A similar inconsistency appeared in treatments of charge and rotation when their energies were increased while the total mass was artificially held fixed.

What Observations Then Test

Observations remain essential, but their role changes. They do not choose between two logically equal versions of the same theory; they test concrete physical consequences of a consistent application of general relativity.

If frozars form, their material structure should persist; superfrozars should be inhomogeneous because of previous stickings and later accretion; mascons should influence shadows and accretion flows; mergers should preserve structural memory; and gloozars and relativistic explosions may occur in the intermediate mass region.

From a Black Hole to a Frozen Star

The frozar picture does not require a new theory of gravity. It begins with the consistent application of one of the central effects of general relativity—the gravitational slowing of proper time.

As a result, inner layers freeze before outer ones, the surface approaches the gravitational radius ever more slowly, and matter does not disappear from the physically existing world. Rotation and charge do not remove this result because their energies contribute to the total mass. Mergers lead to sticking and preserve inhomogeneous structure. Slightly above the neutron-star stability limit, hot gloozars may exist and may produce relativistic explosions.

This gives a unified picture of relativistic compact objects derived from the physical principles of general relativity.

Error and Science

The history of physics shows that even a great theory does not protect us from erroneous interpretations of its equations. The long lifetime of an idea does not turn it into a physical principle. What matters is whether it follows from the original principles of the theory and from consistent logic.

Revising the black-hole concept therefore does not mean rejecting general relativity. On the contrary, it means applying its physical principles consistently precisely where relativistic effects become limiting.

A thought associated with P. L. Kapitsa is appropriate here: an error is not yet pseudoscience; pseudoscience begins with the refusal to recognize an error.

The theoretical task is to apply general relativity consistently. The observational task of the next stage is to search for and measure the specific properties of the objects that follow from that application.

If general relativity is applied consistently, the final result of relativistic collapse is not a black hole but a frozar.