Abstract
We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity with a negative cosmological constant in any dimension. Wormholes in the Euclidean path integral for gravity cause these states to have small, but nonzero, quantum mechanical overlaps that have a universal form. The overlaps have a dramatic consequence: The microstates span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy. The semiclassical microstates we construct contain Einstein-Rosen bridges of arbitrary size behind their horizons. Our results imply that all these bridges can be interpreted as quantum superpositions of wormholes of size at most exponential in the entropy.
- Received 5 April 2023
- Revised 19 October 2023
- Accepted 18 December 2023
DOI:https://doi.org/10.1103/PhysRevX.14.011024
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In the 1970s, physicists Bekenstein and Hawking used general relativity and quantum mechanics in curved spacetime to propose that black holes behave as thermodynamic objects. They found that black holes carry an entropy described by a remarkable formula that applies for any mass, charge, angular momentum, or spacetime dimension. Here, we use new results at the interface of quantum information theory and quantum gravity to address an outstanding challenge: how to explain the microscopic origin of this formula.
In quantum mechanics, entropy measures the logarithm of the dimension of the space of microstates consistent with the macroscopic description of a system. We show that, in any theory of gravity that reduces to general relativity with matter at low energies, there are infinite families of states that have geometries identical to the black hole outside the horizon but different structures inside. We show that these states overlap quantum mechanically because of gravitational wormholes. The overlaps have a dramatic consequence: The microstates span a space whose dimension equals the exponential of the Bekenstein-Hawking entropy formula.
This explanation of black-hole entropy does not require new forms of matter and involves a novel description of all black-hole microstates as quantum superpositions of objects having geometric semiclassical descriptions. Our results also imply a macroscopic manifestation of quantum mechanics in cosmic settings: We show that one can understand long Einstein-Rosen bridges between universes as quantum superpositions of short bridges.
