An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.

In 2002, physicists Gary Gibbons and Christoph Schiller suggested that there is a universal force ceiling in nature — about 10⁴⁴ newtons, the so-called Planck force c⁴/G. No interaction can exceed this: neither the pressure at the center of a neutron star nor the shockwave of a supernova. However, a rigorous proof for realistic objects without singularities was lacking. A recent work by Shahar Hod has for the first time derived exact bounds directly from the field equations.

Hod introduced a dimensionless force function F = 4πr²p(r) — the product of pressure and sphere area. From the field equations and conservation law, he derived inequalities limiting its maximum. For ordinary matter with the dominant energy condition (energy density not less than any pressure), F does not exceed 2. In isotropic media, for example in white dwarfs, where pressure is the same in all directions, the limit is stricter — maximum 1. If the sum of energy and three pressures is non-positive — the most common case — the ceiling drops to 0,5. In other words, the maximum force is half of c⁴/G, about 0,5×10⁴⁴ N.

These numbers are strict consequences of nonlinear equations. They act as a set of gravitational building codes: if in a numerical model of collapse or in observations of Accretion disks and gamma-ray bursts the force exceeds the bounds, we are dealing with new physics. Just as a crack in the foundation forces a redesign, exceeding the force ceiling would compel physicists to rewrite the theory of gravity. In the future, this can be tested in data from gravitational waves from compact object mergers.