Contrasting the fuzzball and wormhole paradigms for black holes

Abstract

We examine an interesting set of recent proposals describing a 'wormhole paradigm' for black holes. These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon. We prove the 'effective small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside. This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation. We try to illustrate various proposals for nonlocality by making simple bit models to encode the nonlocal effects. In each case, we find either nonunitarity of evolution in the black hole interior or a nonlocal Hamiltonian interaction between the hole and infinity; such an interaction is not present for burning coal. We examine recent arguments about the Page curve and observe that the quantity that is argued to follow the Page curve of a normal body is not the entanglement entropy but a different quantity. It has been suggested that this replacement of the quantity to be computed arises from the possibility of topology change in gravity which can generate replica wormholes. We examine the role of topology change in quantum gravity but do not find any source of connections between different replica copies in the path integral for the Rényi entropy. We also contrast the wormhole paradigm with the fuzzball paradigm, where the fuzzball does radiate like a piece of coal. Just as in the case of a piece of coal, the fuzzball does not have low-energy semiclassical dynamics at its surface at energies E ∼ T (effective dynamics at energies E ≫ T is possible under the conjecture of fuzzball complementarity, but these E ≫ T modes have no relevance to the Page curve or the information paradox).

Redefining entanglement entropy -- can it solve the information paradox?

“…Resolutions to protect unitarity can be created using bit models but they must target the right issues of the paradox. Recent Islands resolutions which aim to tackle the paradox either lead to non-localities or violate the small corrections theorem as observed in Ref [7,8]. The issue of the Page curve of a black hole is the inconsistency between the von Neumann entropy of a burning piece of coal and the von Neumann entropy of a black hole.…”

“…2. If the qubit model, which consists of a horizon, aims to resolve the paradox, it must show how the effective pair creation at the horizon takes place without violating the effective small corrections theorem [7].…”

AdS/CFT beyond inter-representational dualities

“…In [14], holography of information is criticized on the ground that it brushes aside horizon locality constraints too easily. Since one expects an illusion of falling into a black hole, there must be an explicit demonstration on why approximate locality seems to be respected and when approximate locality breaks down.…”

“…Since one expects an illusion of falling into a black hole, there must be an explicit demonstration on why approximate locality seems to be respected and when approximate locality breaks down. And indeed, the point in [14] and [9] is that the small corrections theorem in [21] can be extended to eliminate both holography of information and the islands proposal. Now it does seem that for holography of information, if black hole interior geometry is assumed not to really exist (and only its illusory reconstruction in the exterior exists), then we would naturally expect that corrections from the semiclassical picture are not small, and the small corrections theorem is not really applicable.…”

“…While the points made in [17] regarding the AdS/CFT correspondence are mainly addressed, this paper is intended to be a conceptual review (avoiding unnecessary math as much as possible) of recent developments in holographic gravity as well -holography of information [18,12,27,26,23] and the islands proposal [15,2,5,7,4], as well as critiques of these views [21,29,14,9]. These developments and criticisms suggest that there are conceptual disagreements regarding what AdS/CFT is supposed to mean, despite a relative lack of discussions about them.…”