White Holes – Theoretical Foundations and Evolution

 

Many of us are familiar with black holes. We know that when a star with a mass more than three times that of our Sun dies, it keeps collapsing under its own gravitational pull and eventually turns into a black hole. Professor Jamal Nazrul Islam defined a black hole in his famous book Black Hole in the following way:

“If the mass of a star exceeds three times the mass of the Sun, the Fermi pressure of neutrons and other outward pressures can no longer withstand the inward pull of gravity. As a result, the star begins to collapse and ultimately reaches an extremely dense state within a very small volume. According to Einstein’s theory of gravitation, when the matter of a star is confined within a certain small volume, it becomes cut off from the outside world, because no light ray, electromagnetic wave, or material particle can escape from the star. Gravity pulls everything inward. This state of the star is called a black hole” [1].

Numerous scientists have studied and continue to study the mystery of black holes. However, among those who popularized this mystery, the name that comes first is Stephen Hawking. In his popular books, he humorously described in simple language how one could throw a television set, a diamond ring, or even one’s worst enemies into a black hole forever [2].

Nothing—not even light—can escape from a black hole. Therefore, there is no way to observe what is happening inside it. The last boundary that can be observed at the entrance of a black hole is called the event horizon. In 1974, Stephen Hawking discovered that some radiation is emitted from the event horizon of a black hole, which later became known as Hawking radiation. But just beyond the event horizon lies the point of no return. After that, there is no way for anything to come back. Beyond the event horizon there is only the dark abyss of the black hole.

But could the opposite also happen? Is there something that is the reverse of a black hole—something from which only emission occurs and into which nothing can enter? Theoretical physicists have been discussing such a surprising possibility for several years. Opposite to the black hole, it has been named the white hole. One of the main reasons for calling it a black hole is that even light cannot escape from it; everything is pitch dark. The name white hole may therefore seem to be chosen as the opposite of black hole. However, the surprising fact is this: the term “white hole” was used even before “black hole.” We will come to that history a little later.

Among those who are advancing the theoretical possibility of white holes, the Italian physicist Carlo Rovelli is currently at the forefront. His popular book Buchi Bianchi, written in Italian in a way accessible to general readers, was published in English translation as White Holes in 2023 [3]. (The renowned translator and science writer Abul Basar has translated the book into Bengali.) In this book, Carlo Rovelli explains in simple language how white holes could exist as the opposite of black holes. Everything falls into a black hole; nothing can enter a white hole. Nothing can escape from a black hole; everything emerges from a white hole. The direction of the flow of time in a white hole is opposite to that in a black hole. This is precisely where the reality of white holes becomes questionable. Carlo Rovelli explains how the laws of physics can, in principle, support this reverse flow of time.

In films and dramas, we often see present events shown in reverse order, moving backward into the past. In science fiction, we also see time travel—where changing an event in the past alters the future. We watch such stories and sigh: if only this were possible in reality! In reality, it is not possible, because time cannot be reversed. A recorded event can be played backward on a camera, allowing us to watch it from end to beginning, but we cannot make what has already happened “unhappen.” This is our great frustration. The fact that the arrow of time points only forward is something we all understand intuitively, without any scientific explanation. But this seemingly simple idea of time was radically transformed in 1905 by a junior clerk at the German Patent Office—Albert Einstein.

From Einstein’s Special Theory of Relativity, we learn that there is no such thing as “absolute time.” Time is relative; it changes with the motion of the observer. From this emerged the concept of spacetime. Ten years after the Special Theory of Relativity, when Einstein published his General Theory of Relativity, the physics of the entire universe changed. Newton’s centuries-old laws of motion and gravitation became obsolete overnight. The universe had to be recalculated anew. Time was no longer just time; it became inseparably linked with space. Calculations of gravity and cosmic motion began to be based on spacetime.

The central equation of Einstein’s General Theory of Relativity is the Einstein field equation, which can be written succinctly as:

Here, G_μν is the Einstein tensor, representing the curvature of spacetime due to gravity. Λ is the cosmological constant, which denotes the energy density of empty space. g_μν is the metric tensor, describing the geometry of spacetime curvature. T_μν is the energy–momentum tensor, representing the distribution of matter and energy in spacetime. G is the gravitational constant, and c is the speed of light in vacuum. The core idea of the General Theory of Relativity is that the curvature of spacetime is proportional to the total energy and momentum of matter. The greater the energy and momentum of matter, the greater the curvature of spacetime.

From Einstein’s theory emerged the theory of black holes. Not only black holes, but white holes also arise from the General Theory of Relativity. White holes are often described as the neglected twin sister of black holes—whose possibility scientists long ignored.

Only a few weeks after Einstein published his field equations at the end of 1915, in early 1916 a German soldier and lieutenant, Karl Schwarzschild, found an exact solution to those equations. For a non-rotating spherical body, he calculated the dimensions of spacetime and showed that as spacetime curvature increases, the radius of the event horizon decreases. If the radius of the event horizon shrinks beyond a certain limit, nothing can escape from it. This radius is known as the Schwarzschild radius.

We can derive the Schwarzschild radius in a simple way using the escape velocity equation. If an object attempts to escape the gravitational pull of a planet with mass M and radius r, the minimum required velocity (vₑ) is:

According to Einstein’s Special Theory of Relativity, no object can exceed the speed of light. If we set the escape velocity equal to the speed of light, vₑ = c, then the equation becomes:

From this, we obtain:

r = 2GM / c²

This is the Schwarzschild radius.

Einstein himself found it hard to accept that stars in the universe could collapse to such an extent that even light could no longer escape. He rejected the physical reality of this consequence of his own theory, appealing to common sense. At that time, the term “black hole” had not yet been coined.

When Einstein realized that his field equations implied the existence of singularities in the universe, he began searching for alternative explanations. In 1935, together with his colleague Nathan Rosen, he published a new theory showing that before spacetime reaches a singularity, it might connect to another spacetime through an extremely narrow bridge. Their paper, titled “The Particle Problem in the General Theory of Relativity,” was published in Physical Review in 1935 [4]. This concept later became famous as the Einstein–Rosen bridge. Essentially, it connects two spacetimes—but how?

Einstein formulated the theory in such a way that although no singularity forms, the bridge collapses mathematically as soon as anyone attempts to pass from one spacetime to another. Two years after Einstein’s death, in 1957, the American physicist John Wheeler, while discussing such possibilities inside collapsed stars (the term “black hole” was not yet in use), compared the connection of two spacetimes by a bridge to a worm-eaten tunnel inside an apple. Thus, the term “wormhole” was born, which we may translate into Bengali as shweto-gahbar or shweto-bibar. However, such holes do not allow travel from the present to the past.

The instability of wormholes and their proximity to singularities make their observation impossible. Nevertheless, the Einstein–Rosen bridge stimulated interest in exploring what other possibilities might exist. In 1960, the American mathematical physicist Martin David Kruskal and the Austrian mathematician George Szekeres independently discovered a new coordinate system that allows two spacetimes to be connected beyond the event horizon. This is essentially another form of the Einstein–Rosen bridge, in which two separate universes are connected by a bridge. In this construction, it was found that on one side everything falls in and nothing comes out, while on the other side everything comes out but nothing can fall in. Clearly, the direction of time changes along the bridge.

In 1960, the British physicist Roger Penrose began drawing diagrams representing various possible causal structures of spacetime, now known as Penrose diagrams. He showed that from the Schwarzschild radius, two types of event horizons are possible: one that traps signals from the future, allowing nothing to escape (corresponding to real time), and another that allows nothing to enter but let’s everything emerge. This latter case appears unreal—how can something spew everything out without ever taking anything in?

The Soviet physicist Igor Novikov also spent many years studying all possible implications of Einstein’s field equations. Using the Kruskal–Szekeres coordinate system, he found that a wormhole mathematically connects two worlds moving in opposite directions. From one direction everything falls in; from the other direction everything emerges. The world from which everything emerges, he named a white hole. This was in 1964. At that time, the term “black hole” had still not been established; it was introduced later, in 1967, by John Wheeler.

Although the name white hole came earlier, white holes have not received the same level of attention as black holes. There are several reasons for this. The main issue is time. While mathematically time can run backward, accepting this possibility seems unnatural.

The fate of the universe is essentially the fate of time; therefore, the history of the universe is the history of time. In his famous book A Brief History of Time, Stephen Hawking discussed the direction of time in detail. In the real world, time has several arrows: the thermodynamic arrow, the cosmological arrow, and the psychological arrow. Among these, only psychological time can move freely between past and present—we can recall the past from the present. But we cannot see the future.

The relationship between time and thermodynamics is extremely strong and straightforward. Entropy increases with time. As time progresses, entropy inevitably increases; it is impossible to reduce it. In a white hole, time flows from the present toward the past. If this were real, entropy would have to decrease—but that is impossible. This is why the reality of white holes is questioned.

The cosmological arrow of time also points forward—the universe is expanding. If white holes were globally real, then under the pull of backward-flowing time the universe should contract, eventually collapsing in on itself. But within the framework of established physics, this is impossible.

Naturally, no white hole has ever been observed, nor does anyone seriously expect to observe one. However, theoretically, conditions similar to a white hole may arise inside a black hole itself. Physicist Carlo Rovelli firmly believes in the theory of white holes. He believes that white-hole-like conditions can indeed arise in the universe.

Let us consider Hawking radiation. If a black hole were to evaporate completely through Hawking radiation at some point in time, what would happen then? What would become of the energy and information contained within it? According to General Relativity, no information can escape from a black hole. On the other hand, according to quantum mechanics, information can never be destroyed. So, what happens in that case? Carlo Rovelli, along with several other scientists, proposes that just as a black hole is formed through the death of a star, the death of a black hole may give rise to a white hole. A connection between a black hole and a white hole could exist through a wormhole, allowing all the information stored in the black hole to emerge from the white hole.

This idea is undoubtedly fascinating. But without a well-defined and widely accepted scientific theory behind it, why should we accept it?

Carlo Rovelli and many other scientists are currently working to establish the theory of loop quantum gravity. If this theory is successfully established, the path toward white holes may become significantly clearer. According to General Relativity, gravity depends on the curvature of spacetime, and gravitational interaction is treated as a continuous classical force. However, inside a black hole, when spacetime is compressed to extremely small scales, spacetime itself becomes discontinuous. In such conditions, quantum physics appears to be more relevant than classical physics. The primary goal of loop quantum gravity is to establish a consistent relationship between General Relativity and quantum mechanics.

To achieve this, spacetime must be represented as discrete, extremely small quantum units governed by the laws of quantum mechanics. The Planck length (~10⁻³⁵ meters) is the smallest physically meaningful length. A “loop” represents a quantum state of the gravitational field. These loops form spin networks, which describe spacetime at the quantum level. In loop quantum gravity, spacetime does not require a pre-existing background; since spacetime is not continuous, it can emerge from quantum states themselves. The unification of space and time occurs through spin networks or spin foams. Spin foam represents the quantum dynamics of spacetime. For a reliable description of spacetime at the Planck scale, John Wheeler introduced the concept of “quantum foam.” Spin foam is mathematically analogous to quantum foam.

If loop quantum gravity is validated, the one-way fate of black holes—the singularity—may be avoided, and the argument for the transformation of a black hole into a white hole would become physically plausible. However, mathematical consistency alone does not guarantee that white holes will be observed. For that, we may have to wait many more years.

References

[1] Jamal Nazrul Islam, Krishnobibor (Black Hole), Bangla Academy, Dhaka, 1985, p. 32.
[2] Stephen Hawking, Black Holes: The BBC Reith Lectures, Bantam Books, London, 2016, p. 17. (Bengali translation by Abul Basar.)
[3] Carlo Rovelli, White Holes (translated from Italian into English by Simon Carnell), Riverhead Books, New York, 2023. (Bengali translation by Abul Basar.)
[4] Albert Einstein and Nathan Rosen, Physical Review, 1935, Vol. 48, No. 1, pp. 73–77.