The idea of Mount Everest collapsing into an object so dense that nothing can escape its gravity is a thought experiment grounded entirely in the laws of physics and the extreme limits of gravitational compression. Any object in the universe, regardless of its size or material, possesses the theoretical potential to become a black hole. The only requirement is that its entire mass must be squeezed down into an unimaginably tiny volume. This transformation is not dependent on the object being massive like a star; it is solely determined by achieving an extreme state of compression.
The Fundamental Rule of Black Hole Formation
The physics governing this transformation is rooted in the concept of escape velocity, the speed an object needs to completely break free from a gravitational pull. If the Earth were compressed into a smaller sphere without losing any mass, its gravitational pull at the surface would become dramatically stronger, requiring a faster escape velocity.
This compression drastically increases the concentration of mass, intensifying the gravitational field. Eventually, a theoretical boundary is reached where the required escape velocity equals the absolute speed limit of the universe: the speed of light. Since nothing can travel faster than light, once an object is compressed to this point, not even light can escape its gravitational grip. The object has become a black hole.
The specific radius at which this gravitational threshold is crossed is known as the Schwarzschild radius, named after Karl Schwarzschild who first calculated it in 1916. This radius defines the boundary of the black hole, called the event horizon, which is the point of no return. The size of the Schwarzschild radius depends exclusively on the mass of the object being compressed; the greater the mass, the larger the resulting event horizon.
The formula for calculating this radius requires only the object’s mass, the speed of light, and the gravitational constant. Because these constants are fixed values, the only variable determining the size of the black hole is the amount of matter originally present. This means that a black hole formed from a mountain and one formed from a star are governed by the exact same physical rule, differing only in the numerical value of their mass input.
Estimating the Mass of Mount Everest
Before calculating the black hole size, the mass of Mount Everest must be quantified, a task that presents a significant geological challenge. Determining the mass of this complex mountain structure requires estimating both its volume and the average density of its rock composition. The mountain is a layered structure composed of different rock types, including limestone, shale, and granite.
Geological estimates often define the mountain’s mass as the material above a certain base level, leading to a wide range of figures. A commonly accepted estimate for the mass of the Mount Everest structure, including the entire massif, is approximately \(1.6 \times 10^{14}\) kilograms, or 160 trillion kilograms. This value provides the necessary input variable for the gravitational calculation, as the precise composition and volume are less important than the total quantity of matter it contains.
The Pinpoint Size of the Compressed Mountain
Applying the estimated mass of \(1.6 \times 10^{14}\) kilograms to the Schwarzschild radius equation yields the answer to how small Mount Everest would need to shrink. The resulting event horizon would have a radius of approximately \(2.376 \times 10^{-13}\) meters. This distance, which represents the outer boundary of the black hole, is a dimension almost impossible to visualize.
To grasp this scale, the radius of a hydrogen atom is about \(5 \times 10^{-11}\) meters. The calculated radius of the Everest black hole is roughly 200 times smaller than a single hydrogen atom. It is far smaller than a strand of DNA or the smallest known bacterium.
This size places the compressed mountain into the realm of subatomic particle physics. A proton has a radius of about \(8.4 \times 10^{-16}\) meters. The Everest black hole, with a radius of \(2.376 \times 10^{-13}\) meters, is hundreds of times larger than an individual proton, but it is vastly smaller than the nucleus of even a light element like helium.
The compression required to achieve this size is extreme, demanding that the mountain’s matter reach an astronomical density. The rock of Mount Everest, with a density of about 2,700 kilograms per cubic meter, would have to be squeezed past the density of a neutron star. This state, known as nuclear density, is approximately \(4 \times 10^{17}\) kilograms per cubic meter, but the Everest black hole would require a density far exceeding this to fit within its minuscule Schwarzschild radius.
The final object would not be a solid sphere of rock, but a true black hole, with all the mountain’s mass concentrated into a singularity at its center. This singularity is a point of infinite density, surrounded by the event horizon of \(2.376 \times 10^{-13}\) meters. The result is a microscopic black hole whose size is a fraction of a single atom.