Could Black Holes Break the Third Law of Thermodynamics? A New Quantum Argument Says Nature May Stop Them

Black holes are among the most extreme objects in the universe. They have such strong gravity that nothing can escape once it crosses the event horizon. But some black holes can become even more extreme when they carry a very large electric charge.

A recent theoretical discussion by Hod and Piran explores an important question: Can nature actually create an extremely charged black hole, or does physics prevent it from happening?

The question is connected to one of the important ideas in black-hole thermodynamics, known as the third law of thermodynamics. Earlier studies suggested that forming an extremal black hole could create a problem for this law. Now, quantum physics may offer a possible solution.

What Is an Extremal Black Hole?

A Reissner–Nordström black hole is a theoretical black hole that has mass and electric charge but does not rotate.

Normally, a black hole has to have enough mass compared with its electric charge. If the charge becomes extremely large compared with the mass, the black hole approaches a special limit called an extremal state.

An extremal Reissner–Nordström (eRN) black hole is therefore a black hole at this extreme limit.

It is important because the extremal state represents a boundary in the physics of charged black holes. According to the usual understanding of black-hole thermodynamics, reaching this exact state through a physical process should not happen in a finite amount of time.

This idea is related to the third law of black-hole thermodynamics.

The Problem Raised by Earlier Research

Researchers Kehle and Unger recently showed that a self-gravitating charged classical scalar field could collapse and form an extremal Reissner–Nordström black hole in a finite amount of time.

In simple terms, their work suggested that a system made from charged matter could collapse under gravity and reach the extreme black-hole state without requiring an infinite amount of time.

That result is interesting because it appears to challenge the traditional understanding of the third law.

If an extremal black hole can really form in finite time, an important question follows:

What prevents nature from reaching this extreme state?

One possible answer comes from another study by Reall.

Reall's Classical Limit

Reall showed that there is a restriction on the mass-to-charge ratio of the field involved in the collapse.

The important condition is

m/e ≥ 1

Here, m represents the mass of the charged particles or field, while e represents their electric charge.

According to Reall's result, when this ratio is at least one, classical physics prevents the dynamical formation of an extremal Reissner–Nordström black hole.

This provided a possible way to protect the third law.

However, Hod and Piran argue that this classical limit may not be the complete story.

They suggest that quantum physics can provide another important protection mechanism.

The Quantum Vacuum Is Not Completely Empty

One of the strange ideas in quantum physics is that empty space is not truly empty.

Even a vacuum can contain temporary quantum fluctuations. Under extremely strong electric fields, these effects can become much more important.

A sufficiently powerful electric field can cause the vacuum to produce pairs of charged particles.

This phenomenon is known as vacuum pair production and is closely related to the Schwinger effect.

For a highly charged black hole, this could become extremely important because the region around the black hole can contain a very strong electric field.

If the field becomes strong enough, it can start producing charged particles from the vacuum.

The Black Hole Can Discharge Itself

This quantum process could help prevent a charged black hole from reaching the extremal state.

Imagine a charged black hole getting closer and closer to its maximum allowed charge.

As its charge becomes very large, its electric field also becomes extremely strong.

Eventually, according to the quantum argument proposed by Hod and Piran, the electric field can become strong enough to create pairs of charged particles.

These particles can carry electric charge away from the system.

As a result, the black hole can lose some of its charge.

This is called discharge.

The important point is that the process works against the formation of an extremal black hole. Instead of allowing the charge to continue increasing until the extreme limit is reached, quantum effects can remove charge from the system.

In this way, quantum physics may provide a natural mechanism that protects the third law.

The Proposed Quantum Condition

Hod and Piran point out that vacuum polarization should occur when

(eQ/ℏ)² > (mQ/ℏ)² + 1/4

Here, Q represents the charge of the system, e is the particle's electric charge, m is its mass, and ℏ is the reduced Planck constant.

The equation describes a regime in which the electric field becomes strong enough for quantum pair production to become important.

When this condition is satisfied, charged particles can be produced from the vacuum and help discharge the black hole.

This means that the quantum effects themselves can stop the system from reaching the dangerous extreme state.

Hod and Piran's Stronger Proposal

The researchers therefore suggest that Reall's original classical limit may not be the sharpest possible boundary.

They propose that classical physics should prevent the formation of an extremal Reissner–Nordström black hole when

m/e ≥ √[1 − (ℏ/2eQ)²]

This expression includes a quantum correction through ℏ.

The idea is especially interesting because there are two different regions to consider.

In one region, quantum vacuum polarization becomes strong enough to create charged particles. These particles discharge the black hole and protect the third law.

In another region, the quantum effect is not strong enough to provide this protection. Hod and Piran therefore suggest that classical physics itself should prevent the extremal black hole from forming there.

Why This Idea Is Important

This research brings together three major areas of modern physics.

The first is general relativity, which explains gravity and the formation of black holes.

The second is black-hole thermodynamics, which describes black holes using ideas similar to temperature, entropy and the laws of thermodynamics.

The third is quantum physics, which explains what happens at very small scales and predicts unusual effects such as vacuum pair production.

Usually, these theories are studied in different situations. But black holes provide an environment where they all become important at the same time.

The extreme electric fields near charged black holes could therefore provide a natural laboratory for understanding how gravity and quantum physics interact.

A Possible Safety Mechanism in Nature

The main idea proposed by Hod and Piran can be understood quite simply.

A charged system tries to collapse under gravity and move toward an extremal black-hole state.

If the system enters a regime where quantum effects become strong, the electric field can produce charged particle pairs. These particles can remove charge from the black hole.

The black hole therefore cannot simply continue increasing its charge without limit.

If quantum effects are not strong enough, the proposed classical bound may prevent the system from reaching extremality in the first place.

In this picture, classical physics and quantum physics work together to prevent the formation of an extremal black hole through ordinary gravitational collapse.

What Happens Next?

The proposal by Hod and Piran is a conjecture, not a final experimental result or a completely proven law.

More theoretical work will be needed to determine whether the proposed stronger bound is correct and whether it fully resolves the apparent conflict between gravitational collapse and the third law.

Nevertheless, the idea highlights an important lesson in modern physics: a mathematical possibility allowed by one theory may be restricted when additional physical effects are included.

For charged black holes, the extremely strong electric field may trigger quantum processes that fundamentally change what happens during collapse.

The study therefore raises a fascinating possibility: perhaps nature has built-in mechanisms that prevent black holes from reaching their most extreme state in a finite time.

If future research confirms this picture, it could provide a deeper understanding of how general relativity, quantum mechanics and black-hole thermodynamics work together under the most extreme conditions known in physics.

Reference: Shahar Hod, Tsvi Piran, "The third law of black hole thermodynamics and the mass-to-charge ratio of scalar fields", Arxiv, 2026. https://arxiv.org/abs/2609.30170