5.3 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Cosmic censorship hypothesis | 2/2 | https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis | reference | science, encyclopedia | 2026-05-05T09:59:16.959067+00:00 | kb-cron |
There are technical difficulties with properly formalizing the notion of a singularity. It is not difficult to construct spacetimes which have naked singularities, but which are not "physically reasonable"; the canonical example of such a spacetime is perhaps the "superextremal"
M
<
|
Q
|
{\displaystyle M<|Q|}
Reissner–Nordström solution, which contains a singularity at
r
=
0
{\displaystyle r=0}
that is not surrounded by a horizon. A formal statement needs some set of hypotheses which exclude these situations. Caustics may occur in simple models of gravitational collapse, and can appear to lead to singularities. These have more to do with the simplified models of bulk matter used, and in any case have nothing to do with general relativity, and need to be excluded. Computer models of gravitational collapse have shown that naked singularities can arise, but these models rely on very special circumstances (such as spherical symmetry). These special circumstances need to be excluded by some hypotheses. In 1991, John Preskill and Kip Thorne bet against Stephen Hawking that the hypothesis was false. Hawking conceded the bet in 1997, due to the discovery of the special situations just mentioned, which he characterized as "technicalities". Hawking later reformulated the bet to exclude those technicalities. The revised bet is still open (although Hawking died in 2018), the prize being "clothing to cover the winner's nakedness".
== Counter-example == An exact solution to the scalar-Einstein equations
R
a
b
=
2
ϕ
a
ϕ
b
{\displaystyle R_{ab}=2\phi _{a}\phi _{b}}
which forms a counterexample to many formulations of the cosmic censorship hypothesis was found by Mark D. Roberts in 1985:
d
s
2
=
−
(
1
+
2
σ
)
d
v
2
+
2
d
v
d
r
+
r
(
r
−
2
σ
v
)
(
d
θ
2
+
sin
2
θ
d
ϕ
2
)
,
φ
=
1
2
ln
(
1
−
2
σ
v
r
)
,
{\displaystyle ds^{2}=-(1+2\sigma )\,dv^{2}+2\,dv\,dr+r(r-2\sigma v)\left(d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}\right),\quad \varphi ={\frac {1}{2}}\ln \left(1-{\frac {2\sigma v}{r}}\right),}
where
σ
{\displaystyle \sigma }
is a constant.
== See also ==
Black hole information paradox Chronology protection conjecture Firewall (physics) Fuzzball (string theory) Thorne–Hawking–Preskill bet
== References ==
== Further reading == Earman, John (1995). Bangs, crunches, whimpers, and shrieks: singularities and acausalities in relativistic spacetimes (PDF). New York: Oxford University Press. See especially chapter 2. ISBN 978-0-19-509591-3. Wald, Robert M. (1998). "The Question of Cosmic Censorship". In Wald, Robert M. (ed.). Black holes and relativistic stars. Chicago: University of Chicago Press. ISBN 978-0-226-87034-2. Penrose, Roger (1979). "Singularities and time-asymmetry". In Hawking, Stephen; Israel, W. (eds.). General relativity: an Einstein centenary survey. Cambridge [Eng.] ; New York: Cambridge University Press. See especially section 12.3.2, pp. 617–629. ISBN 978-0-521-22285-3. Shapiro, Stuart L.; Teukolsky, Saul A. (25 February 1991). "Formation of naked singularities: The violation of cosmic censorship" (PDF). Physical Review Letters. 66 (8). American Physical Society (APS): 994–997. Bibcode:1991PhRvL..66..994S. doi:10.1103/PhysRevLett.66.994. ISSN 0031-9007. PMID 10043968. S2CID 7830407. Archived (PDF) from the original on 2019-12-05. Wald, Robert M. (1984). General relativity (PDF). Chicago: University of Chicago Press. pp. 299–308. ISBN 978-0-226-87032-8.
== External links == The old bet (conceded in 1997) The new bet