The Tolman–Oppenheimer–Volkoff (TOV) equation is a key result from general relativity that describes the internal structure of neutron stars—incredibly dense, compact remnants of massive stars. It is the relativistic version of the hydrostatic equilibrium equation used for ordinary stars, but adapted to account for the strong gravitational fields in neutron stars.
The TOV equation balances three competing forces:
- Gravity, which pulls matter inward.
- Pressure gradients, which push outward.
- Relativistic corrections, which become important in extremely dense conditions.
By solving the TOV equation with different equations of state (models describing how matter behaves at high densities), scientists can predict:
- The mass-radius relationship of neutron stars
- The maximum stable mass (leading to the Oppenheimer–Volkoff limit)
- How pressure, density, and gravity vary from the center to the surface
The TOV equation is fundamental for understanding the physics of ultra-dense matter, the fate of massive stars, and the behavior of matter under conditions that can’t be replicated in any laboratory on Earth.