Einstein field equations define Schwarzschild and Kerr black holes

Equivalence principle links gravity to acceleration

The equivalence principle states that the effects of gravity and acceleration cannot be distinguished locally. Objects in a gravitational field behave similarly to objects within an accelerating enclosure, such as a rocket accelerating at 9.8 meters per second squared.

Light cones and the world-lines of freely falling particles allow researchers to reconstruct the semi-Riemannian metric of spacetime.

Schwarzschild and Droste derive first exact solutions

The Schwarzschild metric was the first exact solution of the Einstein field equations other than the trivial flat space solution. In 1916, Johannes Droste independently produced the same solution using a simpler, more direct derivation.

A mass compressed inside its Schwarzschild radius, defined as r_s = 2GM/c², forms a black hole.

Kerr-Schild double copy maps black hole solutions

Researchers use the Kerr-Schild double copy to map static, spherically symmetric black hole solutions of general relativity to purely electric solutions of Maxwell's theory in flat spacetime, according to the American Physical Society.

For these configurations, the thermodynamic Smarr formula is structurally identical to the single-copy Gauss's law.

Einstein publishes general theory of relativity

Albert Einstein began proposing the theories of special and general relativity in 1905, according to the Department of Energy. Though known for E = mc² and other work, his theory of gravitation remains his most enduring yet least understood discovery.

Einstein published his general theory of relativity in May 1916. This work describes gravity as a geometric property of 4D spacetime, where curvature relates to energy, momentum, and stress. The theory describes gravity as the curvature of spacetime, as noted in 1915 reports.

Wheeler summarizes spacetime curvature mechanics

Einstein unified space and time into a single fabric called spacetime, where the curvature directs how matter and energy move, according to Big Think.

Einstein conceived of gravity as a warped spacetime fabric, with individual particles moving through that curved space as predicted by his theory. Physicist John Archibald Wheeler summarized this mechanics by stating, "Space-time tells matter how to move; matter tells space-time how to curve".

General relativity predicts gravitational phenomena

General relativity predicts phenomena including gravitational time dilation, gravitational lensing, gravitational redshift, the Shapiro time delay, singularities, and black holes. The theory provides the basis for cosmological models of an expanding universe, leading to the discovery of the Big Bang and cosmic microwave background radiation. The LIGO physics collaboration and other observatories have directly observed gravitational waves.

Quantum gravity remains an unsolved problem

Reconciling general relativity with quantum physics remains an unsolved problem, as there is no self-consistent theory of quantum gravity. Gravity is fundamentally different from all other forces. It is the only inherently non-quantum force that people can intuitively wrap their heads around.

Newtonian gravity versus Einsteinian spacetime

Before Einstein, Newtonian physics held that every mass instantaneously attracts every other mass, dependent on their masses, the gravitational constant, and the inverse square of the distance between them. In Einstein’s picture, gravity must propagate at a limited speed called the speed of gravity. This speed of gravity is identical to the speed of light.

Unlike conventional waves, gravitational waves require no medium to travel through. The Einstein tensor is symmetric, meaning a relationship exists between every component that couples one direction to another, such as the 'tx' component being equivalent to the 'xt' component.

Special relativity explains the relationship between space, time, mass, and energy, while general relativity describes how gravity fits into that framework. This framework relies on the principle that energy equals mass times the speed of light squared, where mass is the amount of material an object contains.