The question of a black hole’s density is complex because the term “density” applies in two distinct and contradictory ways. A black hole’s mass is not distributed uniformly, which prevents a single density measurement. This cosmic object’s density is therefore measured by two different values: the average density within its boundary, or event horizon, and the theoretical density at its core, known as the singularity. This dual nature means the density of a black hole can be both astronomically high and surprisingly low, depending on which measurement is being discussed.
Defining Average Density by the Event Horizon
Scientists calculate the “average” density of a black hole by considering its mass and the volume defined by the event horizon. The event horizon is the boundary where the escape velocity exceeds the speed of light, meaning nothing, not even light, can escape once it crosses this point. The radius of this boundary, known as the Schwarzschild radius, is directly proportional to the black hole’s mass.
To determine the average density, the black hole’s total mass is divided by the volume of the sphere enclosed by the event horizon. This value is often cited in popular science because it provides a macroscopic, measurable number for comparison. However, this calculated density is technically misleading because the mass is not evenly spread out within this volume; it is concentrated at the very center.
The average density simply represents how much mass is contained within the boundary we can observe. It serves as the baseline measurement that establishes the overall size-to-mass ratio of the black hole.
The Unexpected Relationship Between Mass and Density
A counter-intuitive finding emerges when comparing black holes of different sizes: larger black holes are actually less dense on average than smaller ones. The radius of the event horizon increases in direct proportion to the black hole’s mass.
The volume of a sphere, which defines the space inside the event horizon, increases by the cube of its radius. Since density is mass divided by volume, the total mass is spread out over a volume that increases much more quickly than the mass itself. This relationship means that as the mass increases, the average density decreases rapidly.
For a stellar-mass black hole, created by the collapse of a single large star, the average density is enormous, about \(2 \times 10^{19} \text{ kg/m}^3\) for one with the mass of the Sun. In contrast, a supermassive black hole (SMBH) at the center of a galaxy, with a mass millions or billions of times that of the Sun, can have a surprisingly low average density. The average density of a billion-solar-mass black hole is roughly \(1 \text{ kg/m}^3\), which is comparable to the density of water.
The Singularity: Where Density Becomes Infinite
Shifting from the macroscopic average density to the theoretical core reveals the second, more extreme density measurement. The singularity is the point where all the mass is believed to be concentrated. Classical physics, specifically Einstein’s theory of General Relativity, predicts that immense gravitational forces compress the matter into a point of zero volume.
Since the volume at the singularity is zero, the resulting calculation yields infinite density. This mathematical breakdown signals the limits of our current understanding of physics. The infinite density is not considered a true physical description, but rather an artifact of General Relativity failing under such extreme conditions.
Physicists believe a complete theory of quantum gravity, which unites General Relativity with quantum mechanics, would replace the concept of infinite density with a finite, but still incredibly high, value. Until such a theory is confirmed, the singularity remains a theoretical point of infinite density, fundamentally distinct from the finite average density measured at the event horizon.
How Black Hole Density Compares to Ordinary Matter
The two types of black holes—stellar-mass and supermassive—demonstrate a dramatic range of average densities when compared to everyday matter. For comparison, the density of water is \(1,000 \text{ kg/m}^3\).
A stellar-mass black hole, with a mass a few times that of the Sun, has an average density around \(2 \times 10^{18} \text{ kg/m}^3\), far exceeding any substance on Earth. This density is also greater than that of a neutron star, which is the next densest object in the universe, with a typical density of \(10^{17} \text{ kg/m}^3\).
In stark contrast, the largest supermassive black holes have an average density that can be less than that of water. For instance, the black hole at the center of the M87 galaxy has an average density of only about \(1 \text{ kg/m}^3\). This difference highlights that the boundary of a black hole is not a measure of how tightly packed the matter is, but rather the space required to contain a certain mass before the escape velocity surpasses the speed of light.