hole complementarity, arguing instead that no space-like surface contains duplicated quantum information. Recent developments Significant progress was made in 2019, when starting with work by Penington and Almheiri, Engelhardt, Marolf and Maxfield, researchers were able to compute the von Neumann entropy of the radiation emitted by black holes in specific models of quantum gravity. These calculations showed that, in these models, the entropy of this radiation first rises and then falls back to zero. As explained above, one way to frame the information paradox is that Hawking's calculation appears to show that the von Neumann entropy of Hawking radiation increases throughout the lifetime of the black hole. However, if the black hole formed from a pure state with zero entropy, unitarity implies that the entropy of the Hawking radiation must decrease back to zero once the black hole evaporates completely. Therefore, the results above provide a resolution to the information paradox, at least in the specific models of gravity considered in these models. These calculations compute the entropy by first analytically continuing the spacetime to a Euclidean spacetime and then using the replica trick. The path integral that computes the entropy receives contributions from novel Euclidean configurations called "replica wormholes". (These wormholes exist in a Wick rotated spacetime and should not be conflated with wormholes in the original spacetime.) The inclusion of these wormhole geometries in the computation prevents the entropy from increasing indefinitely. These calculations also imply that for sufficiently old black holes, one can perform operations on the Hawking radiation that affect the black hole interior. This result has implications for the related firewall paradox, and provides evidence for the physical picture suggested by the ER=EPR proposal, black hole complementarity and the Papadodimas–Raju proposal. It has been noted that the models used to perform the Page curve computations above have consistently involved theories where the graviton itself has a mass, unlike the real world where the graviton is massless. These models have also involved a "nongravitational bath", which can be thought of as an artificial interface where gravity ceases to act. It has also been argued that a key technique used in the Page-curve computations, called the "island proposal", would be inconsistent in standard theories of gravity with a Gauss law. This would suggest that the Page curve computations are inapplicable to realistic black holes and only work in special toy models of gravity. The validity or otherwise