A black hole is a region of spacetime where gravity is so intense that nothing, not even light, can escape its pull. This boundary, called the event horizon, is the only measurable dimension of a black hole, making its size a central question in astrophysics. The pursuit of the smallest possible black hole pushes the limits of general relativity and quantum mechanics, leading to a theoretical minimum size far beyond those formed by stellar collapse.
The Relationship Between Mass and Size
The size of a black hole is determined solely by its mass, not by the physical volume of the matter that collapsed to form it. This size is defined by the Schwarzschild radius, which represents the distance from the central singularity to the event horizon for a non-rotating black hole. The Schwarzschild radius is directly proportional to the black hole’s mass.
This linear relationship means that doubling the mass doubles the radius of the event horizon. For instance, if the Sun were compressed into a black hole, its event horizon would be about 3 kilometers across. The Earth, with its much smaller mass, would have an event horizon of only about 9 millimeters if compressed enough. This illustrates that any object can theoretically become a black hole if it is compressed into a space smaller than its Schwarzschild radius.
Primordial Black Holes: The Smallest Candidates
Black holes formed from the collapse of massive stars are limited to a minimum mass of a few times the mass of the Sun because stellar processes must overcome internal pressure to trigger a collapse. However, general relativity allows for black holes of any mass, provided the matter is sufficiently dense.
The smallest candidates are a hypothetical class called Primordial Black Holes (PBHs). These are thought to have formed not from star collapse, but from extreme pressure fluctuations in the first moments after the Big Bang. Since they did not require stellar evolution, PBHs could have formed with a vast range of masses.
Theoretically, PBHs could range from the mass of an asteroid down to a microscopic particle. For instance, a PBH with the mass of a large mountain would have an event horizon the size of a single proton. Their formation mechanism bypasses the mass minimum required for stellar collapse, though their existence is not confirmed.
The Limit of Stability Through Evaporation
The stability and lifespan of a black hole are governed by Hawking radiation. Black holes slowly leak energy and mass over time due to quantum effects near the event horizon, causing them to evaporate. The rate of this evaporation is inversely proportional to the black hole’s mass.
This inverse relationship means that smaller black holes evaporate much faster than larger ones. A solar-mass black hole would take trillions of years to evaporate completely. In contrast, a PBH with the mass of a small mountain would survive for only about a second before radiating away.
Since the universe is approximately 13.8 billion years old, any black hole smaller than about \(10^{15}\) kilograms (roughly the mass of a large asteroid) would have already evaporated completely. This evaporation process sets a practical limit on the smallest black hole that could exist today, defining the boundary of stability for existing black holes.
The Absolute Theoretical Minimum
The concept of the black hole breaks down at the absolute smallest scale, where quantum mechanics and gravity collide. This ultimate limit is defined by the Planck scale, derived from fundamental constants of nature. The theoretical minimum mass for a black hole is the Planck Mass, which is approximately 22 micrograms.
A black hole with the Planck Mass would have an event horizon equal to the Planck Length, about \(1.6 \times 10^{-35}\) meters. This size is unimaginably tiny, far smaller than any subatomic particle. At this scale, classical general relativity fails, and quantum gravity effects entirely dominate.
Any mass smaller than the Planck Mass cannot form a stable, classical black hole because it would immediately evaporate in the Planck Time, which is \(10^{-43}\) seconds. The Planck Mass and Planck Length represent the theoretical floor for the size of a black hole, marking a boundary where the object becomes an unstable quantum gravitational entity.