Black hole information, unitarity, and nonlocality

The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arise from ultra-Planckian modes in Hawking’s derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-Planckian physics. This indicates that a reliable argument for information loss has not been constructed, and that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information.

Figure 1

The Kruskal diagram for the Schwarzschild geometry, together with two kinds of time slices. An explicit construction of the first kind (solid line) is given by 14: it consists of a segment of the hyperbola of constant $r=r_c$ for $U>V$, attached to the matching horizontal slice in the region $U<V$. The second kind (dashed) consists of a horizontal segment for $U<V$, which terminates at the singularity. Action of the Schwarzschild time translation $t\to t+\alpha$ on either of these slices generates a family of slices foliating the region outside the black hole, as well as the region at weak curvature inside the black hole.

Figure 2

The intrinsic geometry of a member of the family of slices of Fig. 1 that avoids the strong curvature region.

Figure 3

The intrinsic geometry of a member of the family of slices of Fig. 1 that intersects the singularity.

Figure 4

A representation of the situation described in the text, on a slice avoiding the singularity. Both a Hawking mode and its inside counterpart are represented, in the process of separation from the horizon. A mode that entered the black hole at an earlier time is boosted relative to these modes by an amount exponential in this time difference, whereas its distance along the slice is linear in the time.