STM-D-1028Paper1997Published and peer-reviewed

Topological Censorship and Chronology Protection

John L. Friedman

Abstract and summary · read the original at the source · none found

In one page

Einstein’s equations are far more permissive than the universe looks. Every three-dimensional shape you can imagine turns up somewhere in the solutions — handles, tunnels, loops in time — and yet the sky overhead is plain: no wormhole mouths, no closed timelike curves, no visible topology at all. John L. Friedman’s conference review asks why, and gathers the results that were then converging on an answer. Topological censorship, the theorem he proved with Kristin Schleich and Donald Witt, says that in a spacetime that is well behaved and whose matter obeys the null energy condition, any topological structure pinches off faster than light can cross it — so no observer can send a signal through it and come back with news. Chronology protection is the companion question for time loops. Together they mark out exactly where the door is: the theorems assume an energy condition, and it is the vacuum that is known to break it.

Why it matters hereChapter 4 is built on wormholes and engineered metrics, and this is the review that states, in one place, what classical general relativity will and will not permit — which is precisely why the negative-energy literature matters, since the energy condition is the hypothesis the theorem needs. Chapter 13 takes the wider point: the ordinariness of the sky is itself a physical result to be explained, not an assumption.

What it claims

01The chapter’s own framing, in its two-sentence abstract: closed timelike curves and structures with non-Euclidean topology are both present in the space of solutions to the vacuum Einstein equations, yet neither appears common in the macroscopic universe — and the then-recent results on topological censorship and chronology protection are attempts to explain why the macroscopic topology and causal structure of spacetime are ordinary.Abstract, both sentences
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02The permissiveness is not a loophole in the theory but a fact about it. All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources — so general relativity kinematically allows any spatial topology whatever, and the question of why we do not see one is dynamical.Friedman, Schleich and Witt, Physical Review Letters 71, pages 1486 to 1489, 1993, opening sentence of the abstract
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03Topological censorship is the theorem the chapter is named for, and it is stated sharply: in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal geodesic running from past null infinity to future null infinity is homotopic to a topologically trivial curve between the same two points. The physical reading the authors give is that general relativity does not allow an observer to probe the topology of spacetime, because any topological structure collapses too quickly to let light traverse it.Friedman, Schleich and Witt, Physical Review Letters 71, 1486, 1993, main theorem; erratum at volume 75, page 1872, 1995
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04The hypothesis is where the engineering lives. The theorem forbids traversal only for matter obeying the null energy condition, so a wormhole that could actually be crossed requires a source that violates it — which is the same requirement Morris, Thorne and Yurtsever had already reached from the other direction, and the reason the Casimir vacuum, the one laboratory system known to sit below the ambient vacuum level, became the candidate material.The theorem’s stated hypothesis; compare Morris, Thorne and Yurtsever, Physical Review Letters 61, page 1446, 1988, held on this site
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05The programme the chapter belongs to is stated plainly in the author’s later review of the same title, written with Atsushi Higuchi: over two decades, substantial effort has gone into understanding the way physics enforces the ordinary topology and causal structure we observe, from subnuclear to cosmological scales — covering topological censorship, the topology of event horizons, chronology protection in classical and semiclassical gravity, and the related progress in establishing quantum energy inequalities. Those inequalities, which bound how much negative energy quantum field theory permits and for how long, are the live measurement underneath the whole subject.Friedman and Higuchi, Topological censorship and chronology protection, Annalen der Physik 15, pages 109 to 128, abstract
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Abstract

Despite the presence of closed timelike curves and of structures with noneuclidean topology in the space of solutions to the vacuum Einstein equations, neither appears common in the macroscopic universe. Several recent results on topological censorship and chronology protection seek to explain why the macroscopic topology and causal structure of spacetime are ordinary.

J. L. Friedman, University of Wisconsin-Milwaukee. In Gravitation and Cosmology, Proceedings of the ICGC-95 Conference, Pune, edited by Sanjeev Dhurandhar and Thanu Padmanabhan, Astrophysics and Space Science Library, Springer Netherlands, 1997, chapter 11, pages 157 to 167. The abstract as deposited by the publisher.

(Abstract only — see the rights note above for what was read and what was not. The eleven pages are at the source.)

Where this sits on the site. The paper that opened the modern wormhole literature, and that supplies the energy-condition violation this theorem’s hypothesis rules out, is Morris, Thorne and Yurtsever’s Wormholes, Time Machines, and the Weak Energy Condition. Matt Visser’s book-length stock-take of the whole subject is at /library/stm-1e6a0b75bc, and the scalar-field and energy-condition analysis that cites topological censorship directly is at /library/stm-ba1630c1e9. On causality and warp drives: Allen Everett’s Warp drive and causality, and the Everett and Roman book Time Travel and Warp Drives. The quantum energy inequalities that bound the negative energy available are at /library/stm-09a7d97555 and /library/stm-5e822858ce, with the energy conditions themselves at /library/stm-1bcd336342. The chronology-protection question as it reaches warp-drive engineering appears again at /library/stm-f8f8dbc7c0 and /library/stm-e1ecd12292.

The way in

https://doi.org/10.1007/978-94-011-5812-1_11WHICH BOOK THIS IS. The batch record described the volume as Black Holes and Relativistic Stars; the Crossref record for the containing DOI, 10.1007/978-94-011-5812-1, and the CoLab record for this chapter agree on a different book, and it is the one used here: Gravitation and Cosmology, Proceedings of the ICGC-95 Conference held at the Inter-University Centre for Astronomy and Astrophysics, Pune, India, 13 to 19 December 1995, edited by Sanjeev Dhurandhar and Thanu Padmanabhan, Astrophysics and Space Science Library, Springer Netherlands, 1997, print ISBN 9789401064552 and electronic ISBN 9789401158121. This is chapter 11, pages 157 to 167. The discrepancy is recorded rather than silently corrected. AUTHOR. The chapter prints J. L. Friedman; the given name is expanded from the author’s own eprints, which INSPIRE-HEP records as John L. Friedman of the University of Wisconsin-Milwaukee. LICENCE. Springer registers no licence for this chapter in Crossref, and OpenAlex and Unpaywall both report it closed with no repository copy, so nothing beyond its own abstract is reproduced here. WHAT WAS READ, AND WHAT WAS NOT. The eleven pages themselves could not be read. Springer answers automated requests to both the chapter page and its content PDF with a client challenge rather than the article; the author posted no eprint of this conference contribution, which an author search of the whole arXiv gravitation and cosmology archive confirms; Semantic Scholar holds no record of the DOI; and the Internet Archive was offline on 2026-09-08. The abstract below is the one Springer deposited, retrieved from the CoLab record for this DOI. The first claim on this page is located to that abstract. The remaining claims describe the two results the chapter’s title names, and each is located to the author’s own published paper on that result rather than to this chapter: Topological censorship, John L. Friedman, Kristin Schleich and Donald M. Witt, Physical Review Letters volume 71, pages 1486 to 1489, 1993, with erratum at volume 75, page 1872, 1995; and the later review of the same title as this chapter, John L. Friedman and Atsushi Higuchi, Topological censorship and chronology protection, Annalen der Physik volume 15, pages 109 to 128, eprint arXiv 0801.0735. Both were read in the form of their published abstracts as carried by INSPIRE-HEP. When the eleven pages can be read, this sheet should be rewritten from them. RELATED PAGES: see the cross-links at the foot of this page.

How to cite it

John L. Friedman (1997) Topological Censorship and Chronology Protection. doi:10.1007/978-94-011-5812-1_11

Where it sits in the curriculum

The metric, warp drives and wormholes The unified picture