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The time barrier that prevents formation of black holes

As a mass is compacted to have a smaller and smaller radius, the escape velocity at the surface of the resulting sphere increases. If the sphere could be compacted to a critical radius (called the Schwarzschild radius) so that the escape velocity at the surface of the sphere is equal to the speed of light, nothing could escape from the gravity field. The result would be the formation of a black hole. However, the dilation of time that occurs with increasing gravity erects an impenetrable barrier at the Schwarzschild radius that is able to prevent any mass from compacting sufficiently to form a black hole.

Time dilation

Einstein’s theory of general relativity predicts that gravity affects distance, light and time. When a distant observer watches how light is impacted by gravity, it appears that gravity decreases the frequency of light and the wavelength of light. If the frequency of the light is used as a clock to measure the passage of time, then gravity can be understood to slow down the clock that measures the passage of time.  This phenomena, referred to as time dilation, results in different perspectives on how fast things occur dependent upon the observer's location in a gravity field.  Something that appears to occur quite slowly when measured by the clock of an observer in a relatively weak gravity field, will appear to occur much faster when measured by the clock of an observer in a stronger gravity field. 

How time is affected at the surface of a very compacted mass

Because of the effects of gravity, very large masses, such as a planet or a sun, tend to have the shape of a sphere. As a large mass is compacted the force of gravity at the surface of the resulting sphere increases. The increase in the force of gravity at the surface decreases the frequency of light and thus the clock that measures the passage of time. As a result what takes place in a very short time as measured by a clock near the surface of such a compacted mass, can take place in a much longer time when measured by the clock of a distant observer. The interesting effects that this can produce may be understood by considering Bob’s adventure as he approaches a very compact mass. Betty, from a large distance away, will use a camera to produce a video recording of Bob’s adventure.  As Bob draws near to the surface of the compacted mass, Bob will perceive  things happen in a very short time that will be perceived by Betty as taking a very long time.  Betty, therefore, will use the fast forward playback feature of the camera in order to understand how events appear to Bob.

Bob’s Adventure

Let’s say Betty and Bob are exploring the universe and spy in the distance a mass compacted so much that the escape velocity at the surface of the mass is just at the speed of light. They are curious and want to learn more. Bob volunteers to travel down to the surface, take a look and report back. Bob starts down. What happens to Bob? Betty records it on her video camera.

Figure 1, not to scale, represents how Betty sees Bob’s journey. As Bob gets close to the surface of the mass, his progress seems to slow down. Finally just before he arrives, he is going so slow that, to Betty, he appears to stop moving.  The reason for this is that Bob's progress is measured by Bob's clock.  However, from Betty's perspective, Bob's clock  keeps moving slower and slower as Bob approaches the surface.  As the clock at Bob's location slows, Bob's progress is slowed until he appears to Betty to be standing still. This slowing of the passage of time and the accompanying effect of length contraction (another relativistic effect caused by gravity) prevents Bob from ever reaching the surface.

Betty is patient, so she decides to keep recording.  As she watches, radiation from space overtakes and impacts Bob.  Betty's camera is very sensitive so the portion of radiation that impacts Bob and reflects back to Betty brings with it a progress report on Bob's location and condition.  As it turns out, everything in the universe eventually disintegrates into radiation*.  After a very long time Betty notices that Bob also is disintegrating into radiation. It may take a very long time (things like protons are pretty stable) for Bob to completely disintegrate, but eventually all of Bob has been emitted as radiation and Bob is gone. Thus, in Betty’s time frame, as recorded, Bob ended his journey suspended in space, slowly disintegrating with some of the resulting radiation rising back into space and toward Betty.

To understand how Bob perceived the  journey, Betty plays back the video of Bob’s journey in increasingly faster motion as Bob approaches the surface of the mass. Because of the force of gravity, Bob will perceive himself to be going very fast near the surface, so Betty speeds up the video accordingly. The fast forward version of the video shows Bob hurtling towards the surface and then in a very brief instant of time Bob went from being whole to being gone. In Bob’s perception, he instantly disintegrated before reaching the surface. Figure 2 shows Bob’s complete journey.  All the radiation that in Betty's perception overtook Bob over the course of the long time he was near the surface of the mass, in Bob's perspective arrived almost instanteously, making things uncomfortably warm for him and hastening his demise.

What Bob’s demise teaches about Cosmology

What happened to Bob is the fate of everything in a very strong gravity field where the escape velocity is close to the speed of light.  The disintegration that from the time frame of a weaker gravity field takes a long time, happens instantaneously in a gravity field where the escape velocity is close to the speed of light.

This is why a star can never collapse into a black hole. Once a collapsing star has compacted so that the escape velocity at the surface of the collapsing star approaches the speed of light, the disintegration of the matter at the surface of the collapsing star that appears to take a very long time when observed from a distance will happen instantly.  This instant disintegration will  reduce the mass of the collapsing star and the gravity at its surface.  Because of the reduced gravity, the star can compact further until the escape velocity at the surface of the collapsing star again approaches the speed of light.  The  process repeats until enough of the mass of the collapsing star has disintegrated so that it no longer collapses.

The disintegration that happens instantaneously in the time frame at the surface of the collapsing star takes much longer in the time frame of a distant observer. To a distant observer, the collapsing star in its early stages of collapse can appear to be a dark mass compacted to a radius slightly larger than the critical radius for a black hole, and thus indistinguishable from a black hole.  As more of the collapsing star disintegrates so that the critical radius retreats into the collapsing mass--lessening the effects of time dilation--bursts of radiation from the collapsing star will be seen, explaining the sudden appearance of quasars.

For a more thorough treatment of this subject, see the two journal articles: Five fallacies used to link black holes to Einstein’s relativistic space-time and How black holes violate the conservation of energy.

*Even protons have a half life (estimated to be on the order of 1032 years) and black holes, if they existed, would emit radiation (called Hawking radiation) and eventually disintegrate.

Copyrighted Article--by Doug Weller--used with permission

Next: Hawking Radiation and black hole evaporation