Cosmic censorship hypothesis: Difference between revisions

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If you compare registry products there are a amount of elements to look out for. Because of the sheer amount of for registry products available found on the Internet at when it might be very simple to be scammed. Something frequently overlooked is that some of these products can the reality is end up damaging a PC. And the registry they say they have cleaned may just lead to more difficulties with the computer than the ones you started with.<br><br>Firstly, you need to employ a Antivirus or safety tool plus run a scan on a computer. It can be done that a computer is infected with virus or malware that slows down a computer. If there is nothing found in the scanning report, it might be the RAM which cause the problem.<br><br>The error is basically a outcome of problem with Windows Installer package. The Windows Installer is a tool chosen to install, uninstall and repair the most programs on the computer. Let us discuss a limited points which helped a great deal of folks whom facing the synonymous issue.<br><br>Your computer was quite quick when you first purchased it. Because the registry was extremely clean plus without errors. After time, your computer begins to run slow plus freezes up now and then. Because there are mistakes accumulating inside it plus several info is rewritten or completely deleted by your incorrect uninstall of programs, improper operations, malware or other details. That is the reason why your computer performance decreases slowly and become especially unstable.<br><br>If you are interested in the number one [http://bestregistrycleanerfix.com/regzooka zookaware] program, be sure to look for 1 which defragments the registry. It should also scan for assorted items, such as invalid paths and invalid shortcuts and programs. It should also detect invalid fonts, check for device driver difficulties and repair files. Also, make sure which it has a scheduler. That technique, you are able to set it to scan the system at certain instances on certain days. It sounds like a lot, yet it is very absolutely vital.<br><br>Why this problem happens frequently? What are the causes of it? In truth, there are 3 major causes which will lead to the PC freezing issue. To resolve the issue, we should take 3 procedures in the following paragraphs.<br><br>Another problem with all the damaged version is that it takes too much time to scan the system plus while it really is scanning, you cannot use the computer otherwise. Moreover, there is not any technical support to these damaged versions meaning in the event you get stuck somewhere, you can't ask for aid. They even never have any customer service aid lines wherein you may call or send to solve a issues.<br><br>A registry cleaner is a program that cleans the registry. The Windows registry usually gets flooded with junk data, information which has not been removed from uninstalled programs, erroneous file organization and other computer-misplaced entries. These neat little system software tools are quite common nowadays plus you will find many superior ones found on the Internet. The superior ones provide you choice to maintain, clean, update, backup, and scan the System Registry. When it finds supposedly unwelcome elements inside it, the registry cleaner lists them plus recommends the consumer to delete or repair these orphaned entries plus corrupt keys.
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{{expert-subject|Science|date=November 2008}}
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The weak and the strong '''cosmic censorship hypotheses''' are two mathematical conjectures about the structure of [[gravitational singularity|singularities]] arising in [[general relativity]].
 
Singularities that arise in the [[Solutions of the Einstein field equations|solutions]] of [[Einstein's field equation|Einstein's equations]] are typically hidden within [[event horizon]]s, and therefore cannot be seen from the rest of [[spacetime]]. Singularities that are not so hidden are called ''[[naked singularity|naked]]''. The '''weak cosmic censorship hypothesis''' was conceived by [[Roger Penrose]] in 1969 and posits that no naked singularities, other than the [[Big Bang]] singularity, exist in the [[universe]].
 
==Basics==
Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, [[causality]] may break down, and [[physics]] may lose its predictive power. The issue cannot be avoided, since according to the [[Penrose-Hawking singularity theorems]], singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe is [[determinism|deterministic]] {{Citation needed|date=February 2013}} &mdash;it is possible to predict the entire evolution of the universe (possibly excluding some finite regions of space hidden inside event horizons of singularities), knowing only its condition at a certain moment of time (more precisely, everywhere on a [[spacelike]] three-dimensional hypersurface, called the [[Cauchy surface]]). Failure of the cosmic censorship hypothesis leads to the failure of determinism, because it is yet impossible to predict the behavior of spacetime in the causal future of a singularity. Cosmic censorship is not merely a problem of formal interest; some form of it is assumed whenever [[black hole]] event horizons are mentioned.
 
The hypothesis was first formulated by [[Roger Penrose]] in 1969, and it is not stated in a completely formal way. In a sense it is more of a research program proposal: part of the research is to find a proper formal statement that is physically reasonable and that can be proved to be true or false (and that is sufficiently general to be interesting).<ref>[http://www.theory.caltech.edu/people/preskill/nyt_bet_story.html A Bet on a Cosmic Scale, And a Concession, Sort Of (New York Times, February 12, 1997)]</ref> Because the statement is not a strictly formal one, there is sufficient lattitude for (at least) two independent formulations, a weak form, and a strong form.
 
== Weak and strong cosmic censorship hypothesis ==
 
The weak and the strong cosmic censorship hypothesis are two conjectures concerned with the global geometry of spacetimes.
* The '''weak cosmic censorship hypothesis''' asserts there can be no singularity visible from [[future null infinity]]. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a [[black hole]].
Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.
 
* The '''strong cosmic censorship hypothesis''' asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory. In other words, the classical fate of all observers should be predictable from the initial data. Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular [[Lorentzian manifold]].
 
The two conjectures are mathematically independent, as there exist spacetimes for which the weak cosmic censorship is valid but the strong cosmic censorship is violated and, conversely, there exist spacetimes for which the weak cosmic censorship is violated but the strong cosmic censorship is valid.
 
==Example==
The [[Kerr Metric]], corresponding to a black hole of mass <math>M</math> and angular momentum <math>J</math>, can be used to derive the [[effective potential]] for particle [[orbits]] restricted to the equator (as defined by rotation). This potential looks like:<ref name="hartle_gravity">James B Hartle, ''Gravity'' in chapter 15: Rotating Black Holes. (2003. ISBN 0-8053-8662-9)</ref>
:<math> V_{\rm{eff}}(r,e,l)=-\frac{M}{r}+\frac{l^2-a^2(e^2-1)}{2r^2}-\frac{M(l-ae^2)}{r^3},~~~
a\equiv \frac{J}{M} </math>
where <math>r</math> is the coordinate radius, <math>e</math> and <math>l</math> are the test-particle's conserved energy and angular momentum respectively (constructed from the [[killing vectors]]).
 
To preserve ''cosmic censorship'', the black hole is restricted to the case of <math>a < 1</math>. For there to exist an [[event horizon]] around the singularity, the requirement: <math>a < 1</math> must be satisfied:.<ref name="hartle_gravity" />  This amounts to the [[angular momentum]] of the black hole being constrained to below a critical value, outside of which the horizon would disappear. 
 
The following thought experiment is reproduced from Hartle's ''Gravity'':
 
Imagine specifically trying to violate the censorship conjecture. This could be done by somehow imparting an angular momentum upon the black hole, making it exceed the critical value (assume it starts infinitesimally below it). This could be done by sending a particle of angular momentum <math>l = 2Me</math>.  Because this particle has angular momentum, it can only be captured by the black hole if the maximum potential of the black hole is less than <math>(e^2-1)/2</math>.
 
Solving the above effective potential equation for the maximum under the given conditions results in a maximum potential of exactly <math>(e^2-1)/2</math>!  Testing other values shows that no particle with enough angular momentum to violate the censorship conjecture would be able to enter the black hole, '''because''' they have too much angular momentum to fall in.
 
==Problems with the concept==
There are a number of difficulties in formalizing the hypothesis:
 
* 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" <math>M<|Q|</math> [[Reissner-Nordstrom]] solution, which contains a singularity at <math>r=0</math> that is not surrounded by a horizon. A formal statement needs some set of hypotheses which exclude these situations.
* [[Caustic (mathematics)|Caustic]]s 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 hypothesis.
 
In 1991, [[John Preskill]] and [[Kip Thorne]] [[scientific wager|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, the prize being "clothing to cover the winner's nakedness".[http://www.theory.caltech.edu/people/preskill/new_naked_bet.html]
 
== Counter-example ==
 
An exact solution to the scalar-Einstein equations <math>R_{ab}=2\phi_a\phi_b</math> which forms a counter example to many formulations of the
cosmic censorship hypothesis was found by Mark D. Roberts in 1985:
:<math>ds^2=-(1+2\sigma)dv^2+2dv\,dr+r(r-2\sigma v)\left(d\theta^2 + \sin^2 \theta \,d\phi^2\right),\quad
\phi = \frac{1}{2} \ln\left(1 - \frac{2\sigma v}{r}\right),</math>
where <math>\sigma</math> is a constant.
 
==See also==
*[[Black hole information paradox]]
*[[Chronology protection conjecture]]
 
==References==
{{reflist}}
 
==Bibliography==
*Earman, John: ''Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes'' (1995), see especially chapter 2 (ISBN 0-19-509591-X)
*Roberts,  Mark D. : ''Scalar Field Counter-Examples to the Cosmic Censorship Hypothesis. Gen.Rel.Grav.21(1989)907-939.
*Penrose, Roger: "The Question of Cosmic Censorship", Chapter 5 in ''Black Holes and Relativistic Stars'', Robert Wald (editor), (1994) (ISBN 0-226-87034-0)
*Penrose, Roger: "Singularities and time-asymmetry", Chapter 12 in ''General Relativity: An Einstein Centenary Survey'' (Hawking and Israel, editors), (1979), see especially section 12.3.2, pp.&nbsp;617–629 (ISBN 0-521-22285-0)
*Shapiro, S. L., and Teukolsky, S. A.: "Formation of Naked Singularities: The Violation of Cosmic Censorship", Physical Review Letters '''66''', 994-997 (1991)
*Wald, Robert, ''General Relativity'', 299-308 (1984) (ISBN 0-226-87033-2)
 
==External links==
*[http://www.theory.caltech.edu/people/preskill/old_naked_bet.html The old bet] (conceded in 1997)
*[http://www.theory.caltech.edu/people/preskill/new_naked_bet.html The new bet]
 
{{black holes}}
 
{{DEFAULTSORT:Cosmic Censorship Hypothesis}}
[[Category:Black holes]]
[[Category:General relativity]]

Latest revision as of 21:29, 9 January 2015

If you compare registry products there are a amount of elements to look out for. Because of the sheer amount of for registry products available found on the Internet at when it might be very simple to be scammed. Something frequently overlooked is that some of these products can the reality is end up damaging a PC. And the registry they say they have cleaned may just lead to more difficulties with the computer than the ones you started with.

Firstly, you need to employ a Antivirus or safety tool plus run a scan on a computer. It can be done that a computer is infected with virus or malware that slows down a computer. If there is nothing found in the scanning report, it might be the RAM which cause the problem.

The error is basically a outcome of problem with Windows Installer package. The Windows Installer is a tool chosen to install, uninstall and repair the most programs on the computer. Let us discuss a limited points which helped a great deal of folks whom facing the synonymous issue.

Your computer was quite quick when you first purchased it. Because the registry was extremely clean plus without errors. After time, your computer begins to run slow plus freezes up now and then. Because there are mistakes accumulating inside it plus several info is rewritten or completely deleted by your incorrect uninstall of programs, improper operations, malware or other details. That is the reason why your computer performance decreases slowly and become especially unstable.

If you are interested in the number one zookaware program, be sure to look for 1 which defragments the registry. It should also scan for assorted items, such as invalid paths and invalid shortcuts and programs. It should also detect invalid fonts, check for device driver difficulties and repair files. Also, make sure which it has a scheduler. That technique, you are able to set it to scan the system at certain instances on certain days. It sounds like a lot, yet it is very absolutely vital.

Why this problem happens frequently? What are the causes of it? In truth, there are 3 major causes which will lead to the PC freezing issue. To resolve the issue, we should take 3 procedures in the following paragraphs.

Another problem with all the damaged version is that it takes too much time to scan the system plus while it really is scanning, you cannot use the computer otherwise. Moreover, there is not any technical support to these damaged versions meaning in the event you get stuck somewhere, you can't ask for aid. They even never have any customer service aid lines wherein you may call or send to solve a issues.

A registry cleaner is a program that cleans the registry. The Windows registry usually gets flooded with junk data, information which has not been removed from uninstalled programs, erroneous file organization and other computer-misplaced entries. These neat little system software tools are quite common nowadays plus you will find many superior ones found on the Internet. The superior ones provide you choice to maintain, clean, update, backup, and scan the System Registry. When it finds supposedly unwelcome elements inside it, the registry cleaner lists them plus recommends the consumer to delete or repair these orphaned entries plus corrupt keys.