Part 5 - The Relativity of Death: What do we know about Black Holes?

The ideas expressed in the previous parts of this essay were based on theology and notions such as the Soul, Creation, Information Worlds. But for nonbelievers these arguments do not work or do not hold, they can simply say they do not believe in the notions of G-d, Creation and Soul.

In the article below I will attempt to put forward certain arguments in support of the idea of the Relativity of Death based on physical facts and in particular on the physics of Black Holes.                 

The sources used in this chapter are At Home in the Universe by John A. Wheeler, From Strange Simplicity to Complex Familiarity by Manfred Eigen, Information Theory by James V. Stone, the article Singularities and Black Holes by Erik Curiel, The Stanford Encyclopedia of Philosophy, Black Holes and Entropy, Phys Rev D7, by J.D. Bekenstein.

A Black Hole is a region of spacetime the gravity of which is so strong that nothing, not even light, can escape from it. They form as a result of the gravitational collapse of a body onto itself. The critical stage of the gravitational collapse occurs when the body collapses to its so-called Schwarzschild radius, which is proportional to the mass of the body. For a standard (uncharged, non-rotating) Black Hole, the event horizon lies at the Schwarzschild radius.

The event horizon of a Black Hole is the surface formed by the points of no return. It is the boundary of the collection of all events in the spacetime at which a light signal can still escape to the external universe. Everything on and inside the event horizon is the Black Hole itself. According to John A. Wheeler, the event horizon of a Black Hole marks ‘The Gates of Time’.

Black Holes are purely gravitational entities which contain no matter whatsoever. They are vacuum solutions to Einstein’s field equations. This fact raises a lot of questions about what happens to matter which crosses the event horizon, and what is there beyond the event horizon.

According to the General Theory of Relativity, at the center of a Black Hole there is a singularity, which signifies the breakdown not just of all the matter, but of the geometry of spacetime itself. This presents enormous difficulties. We cannot tell where the singularity is, as it has no location in the spacetime.

The existence of singularities was proved by Penrose, Geroch and Hawking. Their theorems indicate that our universe began with an initial singularity, the Big Bang, approximately 14 billion years ago. They also indicate the existence of singularities in Black Holes. According to current cosmological theories, the two most likely scenarios of the end of the universe are either a global collapse into a Big Crunch singularity or the destruction of everything in a Big Rip singularity. As John A. Wheeler put it, ‘the singularity in the center of Black Hole is not topologically distinct from the final cosmological singularity but part and parcel of it. One has a choice whether to rocket into the nearest Black Hole and counter the singularity in the near future or wait some billions of years down the road to encounter the final singularity.’

The precise definition of singularity does not exist. Currently, there are a number of approaches attempting to describe singularities.

The first one is ‘Path Incompleteness’. A path in spacetime is a continuous chain of events through space and time. In the physics of Black Holes, the paths represent the possible trajectories of particles and observers. If a path is incomplete, it means that after a finite amount of time a particle or observer would ‘run out of the world’ and vanish.

The necessary condition of the existence of a singularity is the maximality of spacetime, which means that our spacetime is not a part of some other, bigger spacetime.

The second one is the ‘Missing Points’. In this model, a singularity is described as the missing points of spacetime.

The third one is ‘Curvature Pathology’, where the idea is that the curvature of spacetime blows up as one approaches the singularity of the Black Hole or the Big Bang singularity.   

The physical manifestation of the spacetime curvature is the tidal force which is generated by the difference in the intensity of the gravitational field in neighboring points of spacetime. When you stand, your head is farther from the center of the Earth than your feet, so it feels a smaller downward pull. This is practically negligible, but in regions of extreme curvature of spacetime, the tidal force can grow without bounds.

The fate of an observer approaching the point of extreme curvature could be different. They could be torn apart by the extremely strong tidal force, or, using acceleration and deceleration in a certain way, they could approach very near to the point of extreme curvature, but their final fate remains the same.  

It is important to know that the three ways of describing singularities mentioned above are incomplete. There is no universally accepted definition of a singularity. There is no understanding of ‘where’ they exist and whether the notion of existence be attributed to them at all, taking into account the Aristotelean ‘to exist is to exist in spacetime’.

The views of the scientific community regarding the existence of singularities are as follows.

First, singular behavior means the breakdown of the General Theory of Relativity.

Second, non-maximal spacetime cannot exist. This idea is based on the Principle of Sufficient Reason formulated by Gottfried Leibniz: if whatever creative force responsible for spacetime could have continued to create more of it, what possible reason could there have been for it to have stopped at any particular point? Third, the extreme state of spacetime should be described by the theory of Quantum Gravity.

Elephants and Crocodiles

According to ‘No – Hair’ theorems, Black Holes are entirely characterized by just three numbers representing its mass, angular momentum and electric charge. The information about the structure of the matter which has fallen into a Black Hole is washed away. That means that we cannot distinguish between the Black Hole made of one million elephants and a Black Hole made of one million crocodiles, provided that the masses of the elephants and crocodiles are the same.

The Entropy of Black Holes

In the early 1970s, Jacob Bekenstein put forward the idea that a Black Hole has a finite entropy. His rationale was that the collapse of material into a Black Hole leads to the decrease of the entropy of the part of the universe outside the event horizon. This, in turn, violates the Second Law of Thermodynamics, which asserts that the entropy of a closed system can never decrease.

The collapse of matter into a Black Hole increases its mass and its size. Bekenstein suggested that the area of the event horizon is the measure of the entropy of a Black Hole. Later, Hawking proved that the surface area of the event horizon can never decrease. As a result, Bekenstein proposed the Generalized Second Law of Thermodynamics, which says that the sum of the area of a Black Hole’s event horizon and the entropy of external systems can never decrease.

What is the meaning of Bekenstein entropy?

In thermodynamics, according to the Boltzmann’s definition, entropy is proportional to the number of microstates representing the same externally observable macrostate. According to the information theory, entropy represents the degree of our uncertainty.

As Manfred Eigen put it, ‘entropy is not information, rather it is an amount of lost, or missing information. The Black Hole is to be seen as an ultimate state of matter – like a book that has been dissolved into each individual letter. In a similar way, all its information about structure has become lost – except that of its total mass, charge and angular momentum.’

There are different approaches aimed at interpreting Bekenstein’s entropy based on the String Theory and Quantum Gravity.

It is important to note that the entropy expressed in a single number is a compression of complexity and does not tell us anything about the complex, chaotic dynamics of a system.

Besides, we should take into account that there are a number of proposed mechanisms of the violation of the Generalized Second Law. That could be the result of the controversial status of the Second Law of Thermodynamics, which has never been proven. Many physicists and philosophers consider that the ordinary Second Law does not hold universally.

Black Hole Information Loss Paradox

In 1974, Hawking showed that a Black Hole generates heat at a temperature inversely proportional to its mass. The temperature of Hawking’s radiation is extremely low for a Black Hole with a big mass. The existence of Hawking’s radiation means that Black Holes may slowly evaporate. However, the process of evaporation of a Black Hole with a stellar mass would be extremely long.

The possibility of the evaporation of Black Holes created a big conundrum in physics. The Hawking radiation is random and does not carry with it any information about the structure of matter that has fallen into the Black Hole, which flies in the face of the laws of quantum physics. According to the quantum theory, the evolution of a quantum system is unitary, which guarantees the preservation of information.

The evaporation of a Black Hole means that information is lost irretrievably. This problem was called the Black Hole Information Loss Paradox.

There are different approaches to resolving this paradox:

1. Information loss is valid and the principle of unitarity is violated, which is not surprising since in the process of measuring the quantum system unitarity is destroyed.
2. The information is not lost but stored in a remnant of the Black Hole.
3. Hawking’s radiation is non-random.
4. The correlations are not lost, but only appear to be lost depending on the state of the observer. This is so-called Complementarity Principle.
5. The information is preserved in a certain kind of entanglement between the particles outside and inside event horizon (firewall).

The ‘Complementarity Principle’, put forward by Leonard Susskind in 1993, is worth thorough consideration.

According to the General Theory of Relativity, time slows down with the increase in the force of gravity. Here is a classic example: picture someone falling into a Black Hole and, in the process of falling, flashing a light signal to an external observer. For the external observer, the times between the arrival of successive light signals grow larger without limit as the falling person approaches the event horizon. So, for them, the falling person will never cross the event horizon will seem to be eternally ‘frozen’ just above it. At the same time, for the infalling person, nothing extraordinary is happening and they do not even notice the crossing of the event horizon.

Based on that, Susskind proposed that information stays at the event horizon and is returns in the form of radiation, and at the same time crosses event horizon and disappears. Since the radiation is extremely hot, the external observer should conclude that the infalling person gets burned up before they cross the event horizon. But that is in a contradiction with the fact (mentioned above) that the infalling person will cross the event horizon without even knowing that.

In order to resolve the obvious contradiction, Susskind put forward the idea that the account of the infalling person should be considered to be complementary to the account of the external observer, by analogy with the complementarity of the position and momentum in the description of quantum particles. Susskind based his arguments on the fact that the infalling person cannot communicate to the external world that they have survived their passage through the event horizon.

Conclusion

Out of all the theories used for the description of Black Holes, only the General Theory of Relativity has been experimentally proven. The String Theory, Loop Quantum Gravity Theory, Bekenstein Entropy and Hawking Radiation have never been experimentally verified.

By tacit agreement, all of them assume that our universe is a closed system, which is absolutely implausible.

Almost all the related calculations were made for a certain idealized type of a Black Hole.

In his essay The Great Black Hole Paradox (New Scientist magazine), the physicist Paul Davies noted that ‘attempts to provide an answer [to the paradox] so far have either appealed to idealized special cases or descended into speculative mathematical backwaters with only a tenuous link to reality’. He also said that ‘calculations tend to assume that the Black Hole and its products form an isolated system, which is obviously unrealistic’.