A black hole with maximum possible spin, where its surface gravity is zero and entropy is maximal.An extremal black hole is a black hole that spins at the maximum possible rate allowed by general relativity. At this limit, the event horizon's surface gravity becomes zero, meaning that a hypothetical observer hovering just outside the horizon would feel no gravitational pull. The entropy of an extremal black hole is maximal for its mass, and its temperature, as predicted by quantum field theory, drops to absolute zero. These properties make extremal black holes a fascinating theoretical laboratory for studying the intersection of gravity, quantum mechanics, and thermodynamics.
The Kerr solution was discovered by Roy Kerr in 1963. The concept of extremal black holes and their thermodynamic properties was developed in the 1970s by Stephen Hawking, Jacob Bekenstein, and others, as part of the formulation of black hole thermodynamics.
In general relativity, a rotating black hole is described by the Kerr solution, characterized by its mass and angular momentum. The angular momentum has an upper bound: for a given mass, the spin parameter must be less than or equal to 1 (in geometric units). When the spin parameter equals 1, the black hole is extremal. At this point, the inner and outer event horizons merge, and the geometry near the horizon becomes special — the gravitational field is so strong that the usual notion of time dilation breaks down in a particular way. The surface gravity, which is proportional to the temperature of the black hole, vanishes, so the black hole stops radiating Hawking radiation and becomes 'cold'.
Extremal black holes are primarily of theoretical interest, but they are used as testbeds for quantum gravity theories, such as string theory, where they help explain the microscopic origin of black hole entropy.
In 2019, the Event Horizon Telescope image of the supermassive black hole M87* showed a shadow consistent with a near-extremal spin, though the exact value remains uncertain.
