Spacetime topology change and black hole information

doi:10.1016/j.physletb.2006.11.016

Physics Letters B

Volume 644, Issue 1, 4 January 2007, Pages 67-71

https://doi.org/10.1016/j.physletb.2006.11.016 Get rights and content

Abstract

Topology change—the creation of a disconnected baby universe—due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can be unitary and consistent with conventional quantum mechanics. We discuss the issue of cluster decomposition, showing that any violations thereof are likely to be unobservably small. Topology change is similar to the black hole remnant scenario and only requires assumptions about the behavior of quantum gravity in Planckian regimes. It does not require non-locality or any modification of low-energy physics.

Section snippets

Introduction: Black hole information loss

What is the ultimate fate of something that falls into a black hole? Is it crushed out of existence at a singularity, or does it end up “somewhere else”? The answer to this question is central to the black hole information loss paradox [1]. We will examine the possibility that black hole formation leads to spacetime topology change, and that matter that falls through the horizon ultimately reaches some topologically disconnected component of the universe, referred to here as a baby universe.

Topology change

Below we describe the specific assumptions of our scenario, which concern the dynamics quantum gravity (QG), but do not modify physics at large distances or low energies.

Gravitational collapse leads to a region of Planckian densities and curvature, where QG effects (fluctuations of the metric) are large. The size of this QG-dominated region increases with the size of the black hole, and it likely resolves the singular collapse endpoint found in classical relativity. It seems plausible, and we

Evolution from pure to mixed states

Objection I, given above, relates to the evolution of pure to mixed states. Here we explain that this is only a problem if the initial and final surfaces are both complete Cauchy surfaces.

In quantum field theory, any subset of a Cauchy surface is generically described by a mixed state, even if the entire Cauchy surface is in a pure state. It is therefore not surprising if the Hawking radiation which remains after black hole evaporation is in a mixed state, since all of it crosses the incomplete

Cluster decomposition

Topology change by black holes can lead to violation of cluster decomposition, which is objection II above. This point was emphasized in [9], and led Polchinski and Strominger [12] to propose a third quantization scenario for baby universes, with consequent loss of predictability similar to that due to spacetime wormholes. Here, we note that the violations of cluster decomposition are likely to be unobservably small, even in hypothetical gedanken experiments. (Although, as stressed by Susskind

Relation to remnants

There are obvious parallels between our topology change scenario and that of remnants [3]. The potentially enormous amount of information stored in a remnant instead disappears into a baby universe. In the remnant case one imagines that the throat of the distorted spacetime region connecting the black hole horizon to the classical singularity is somehow stabilized, rather than pinching off.

The main problem with remnant scenarios is that there must be a distinct, long-lived, roughly Planck mass

Conclusions

We discussed a solution of the black hole information paradox which depends entirely on details of Planckian physics—no modifications of low-energy physics, such as non-locality, are required.

The main assumptions are that the interior evolution of large black holes produces topology change, and that the associated quantum gravitational dynamics are strongly coupled. Thus, small perturbations to the initial state of a black hole lead to different internal state vectors describing the resulting

Acknowledgements

The author thanks T. Jacobson, B. Murray, J. Preskill and A. Strominger for useful comments, and S. Giddings in particular for clarification of the third quantization approach. T. Jacobson provided a number of useful references to earlier work. This research supported by the Department of Energy under DE-FG02-96ER40969.

References (21)

S.W. Hawking
Commun. Math. Phys.
(1975)
S.W. Hawking
Phys. Rev. D
(1976)
A. Strominger
T. Banks
S.B. Giddings
T. Jacobson
L. Susskind et al.
The Holographic Universe
(2005)
S.B. Giddings et al.
Phys. Rev. D
(2004)
S.B. GiddingsS.B. GiddingsS.B. Giddings
T. Banks et al.
Nucl. Phys. B
(1984)
L. Susskind
F. Dyson, IAS preprint, 1976,...

There are more references available in the full text version of this article.

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