Schwarzschild Radius Calculator

Yes. Every object with mass has a Schwarzschild radius, calculated as Rs = 2GM/c². However, for ordinary matter, this radius is far below the actual size of the object. It represents a hypothetical limit: if you compressed all of Earth into a sphere less than 8.87 mm in radius, it would become a black hole.

Theoretically yes, if compressed to below their Schwarzschild radius. For a 70 kg person, this is about 1x10-25 m — about 10 orders of magnitude smaller than a proton. In practice, no known physical process could create such compression outside of the extreme environments near already-existing black holes.

From Rs = 2GM/c², increasing mass M proportionally increases Rs. Doubling the mass doubles the Schwarzschild radius. This contrasts with the density needed for collapse: since density goes as M/Rs^3 = M/(2GM/c^2)^3 = c^6/(8G^3 M^2), more massive objects require LOWER density to become black holes.

A Schwarzschild black hole is non-rotating — a perfectly spherical solution to Einstein's equations with only a single parameter (mass). A Kerr black hole is rotating and has two parameters (mass and angular momentum). Real astrophysical black holes are expected to be Kerr black holes since they form from rotating stellar cores. Kerr black holes have two horizons and an ergosphere — a region outside the event horizon where rotation of spacetime cannot be avoided.

No. The event horizon is a mathematical boundary — a surface of no return — not a physical surface. An observer falling through the event horizon would not feel anything special locally at the moment of crossing. The event horizon is defined globally: it is the boundary from within which no signal can ever escape to infinity. Its location can only be determined in retrospect, given the entire future evolution of the spacetime.

Neutron stars are the densest known stable objects, with masses of 1.4-2.5 solar masses and radii of only 10-12 km. For a 1.4 solar mass neutron star, the Schwarzschild radius is about 4.1 km — roughly one-third the actual radius. Neutron stars are close to but still outside their Schwarzschild radii. Adding mass pushes them toward the limit, and above about 2-3 solar masses, nothing known can halt collapse to a black hole.

Inside the Schwarzschild radius, the time and space coordinates of general relativity interchange roles — the singularity at r=0 is in the future, not in space, so all trajectories (causal paths through spacetime) inevitably reach the singularity. There is no known mechanism to escape or halt this progression. General relativity predicts a singularity at r=0 (infinite density), but quantum gravity is expected to modify this at Planck scales.

Gravitational waves carry energy but in ordinary astrophysical settings their amplitude is far too small to cause significant compression. Near the merger of two compact objects (neutron stars or black holes), the gravitational wave amplitudes are enormous and the dynamics are governed by full numerical general relativity, with material inevitably crossing the Schwarzschild radius during the final plunge.

The photon sphere is a spherical region at radius 1.5 Rs = 3GM/c^2 around a Schwarzschild black hole where gravity is strong enough that photons orbit in circles. It is unstable — photons slightly inside will spiral in, and slightly outside will spiral out. The photon sphere plays a role in the appearance of black hole shadows observed by the Event Horizon Telescope.