Black Holes Keep Growing Forever Inside

The interior growth of black holes, which continues long after thermal equilibrium, is identified as the growth of quantum computational complexity.

• Black holes reach thermal equilibrium extremely fast, but their interiors continue to grow for an exponentially long time.

• This prolonged interior growth is linked to quantum computational complexity, a measure of operations needed to achieve a quantum state.

• The concept of quantum complexity, previously niche, is now central to understanding black hole evolution.

Black holes quickly reach thermal equilibrium, typically within milliseconds, where their horizon area stabilizes, representing the black hole's entropy. However, the volume of the black hole's interior continues to grow exponentially for a vastly longer period. This persistent growth of the interior is proposed to be the manifestation of quantum computational complexity, a concept describing the minimum number of quantum gates required to achieve a specific quantum state, which was previously little-known among theoretical physicists.

Black Hole Equilibrium

• 00:00:33 A black hole rapidly achieves thermal equilibrium, typically in less than a millisecond for a solar mass black hole, as its horizon area settles down after initial expansion. This stabilization of the horizon area is associated with the black hole's entropy, representing a quick settling process.

Interior Growth Mystery

• 00:01:44 While the black hole's exterior reaches equilibrium quickly, its interior volume continues to grow exponentially for an immensely long time, a phenomenon observed from Einstein's equations. The puzzle lies in identifying what physical or information-theoretic quantity within the black hole's interior is responsible for this prolonged growth.

Complexity as Explanation

• 00:02:25 Quantum computational complexity is the only known quantity that continues to grow long after a system reaches thermal equilibrium. This concept, originating from computer science, describes the minimum number of simple operations (gates) needed to transform a simple state into a target quantum state. The idea was put forward that this long-term growth of the black hole's interior corresponds to the growth of its quantum computational complexity.

Complexity Definition & Impact

• 00:04:20 Complexity in quantum mechanics defines the minimum number of operations, or 'gates' (like those acting on pairs of qubits in a quantum computer), required to transform an initial simple state into a desired target state. This complexity can increase for an exponentially long time in quantum systems, unlike in classical physics where it saturates quickly, and this proposed connection to black hole interiors has become a widely accepted concept among physicists.