Talk:Kerr metric

message: The image showing the static limit and (outer) event horizon appears twice. Moreover, in its second incarnation, the caption incorrectly refers to the outer event horizon as the static limit. I'm not bold enough to decide which copy should go. Certainly one must, and the correct caption used. Warrickball (talk) 23:09, 13 March 2008 (UTC)
thread_title:  Image Showing Static Limit and Event Horizon 

message: Does anyone else object to this section of the text, or is it just me?
"Such black holes have two event horizons where the metric appears to have a singularity. The outer horizon encloses the ergosphere and has an oblate spheroid shape, a flattened sphere similar to a discus. The inner horizon is spherical and marks the "radius of no return"; objects passing through this radius can never again communicate with the world outside that radius."
I would say it's both wrong and misleading. Firstly, the outer surface that encloses the ergosphere is the "stationary limit surface" and not an event horizon (it even says so explicitly in Hawking and Ellis). Secondly, I would say that the metric exists independently of which coordinates you use to describe it and hence whether it appears to have a singularity in a given coordinate system or not isn't really relevant. In Boyer-Lindquist coordinates the metric is not singular at the stationary limit surface/boundary of ergosphere and it is singular at the true singularity (which isn't a horizon). Thirdly, if we are going to call something the "inner horizon" then we really ought to be talking about the inner horizon as the inner Cauchy horizon. I believe that is standard usage - it is where I come from.
--Eujin16 (talk) 05:17, 6 December 2007 (UTC)
thread_title:  Objection to introduction 

message: I was exhausted yesterday, and did not realize just how tired I was.  I just cannot do any intellectual "heavy lifting" when I'm like that.  I knew that (r^2 + a^2)^2/\rho^2 was involved with g_{\phi\phi}.  I had lost track of the fact that it was involved with the coframe version and sorts itself out into a form such as is in the article.
So I was tired and irritated (due to other things) and was not able to respond to my own self-red-flag of "I know I could be wrong". --EMS | Talk 22:03, 28 July 2005 (UTC)
thread_title:  Sorry for the confusion 

message: Hi, Taxman, don't worry, I am certain the initial is indeed "P."---CH  (talk) 20:11, 5 August 2005 (UTC)
thread_title:  Roy P. Kerr 

message: I'm against merging rotating black hole with this article. They are parent subjects, not the same one. The content of these articles are enough different to support so. nihil 09:25, 25 November 2005 (UTC)
replies: text: Nihil may have a point.  The "no hair theorem" is or should be surprising, and Price's theorem is often summarized by saying that any inhomogeneties or anisotropies outside a black hole which can be radiated away, will be radiated away (which restores the Kerr exterior vacuum of a relaxed rotating black hole).  So, perhaps the article Rotating black hole can discuss these facts, while referring to Kerr vacuum for the relaxed state.---CH  (talk) 18:26, 25 November 2005 (UTC)
thread_title:  To Merge or not to Merge? 

message: I have elaborated slightly on this admittedly confusing issue.  As I have noted elsewhere, WP requires articles on relativistic moments, moments in weak field gtr (including Weyl moments and the multi-index mass/momomentum/stress moments), and an improved article on multipole moments in Newtonian gravitation.  Ultimately, the new section should be linked to this forthcoming articles and can perhaps then be shortened.---CH 22:24, 2 June 2006 (UTC)
thread_title:  Will the real monopole please stand up? 

message: On the article page it says "Open problems
The Kerr vacuum is often used as a model of a black hole, but if we hold the solution to be valid only outside some compact region (subject to certain restrictions), in principle we should be able to use it as an exterior solution to model the gravitational field around a rotating massive object other than a black hole, such as a neutron star--- or the Earth. This works out very nicely for the non-rotating case, where we can match the Schwarschild vacuum exterior to a Schwarzschild fluid interior, and indeed to more general static spherically symmetric perfect fluid solutions. However, the problem of finding a rotating perfect-fluid interior which can be matched to a Kerr exterior, or indeed to any asymptotically flat vacuum exterior solution, has proven very difficult. "
No wonder it is difficult. The Kerr solution has only 2 independent parameters: mass and angular momentum. These determine all the gravitational multipole moments. But a rotating star has a complicated structure and its multipole moments will be controlled by the rotational (angular) velocity within it (which can vary with distance from the center and with latitude or angle from the plane of symmetry), the pressure and density variations with depth and possibly more things like internal magnetic fields. So the external field or various example rotating stars is more than a 2-parameter family. Whoever wrote that stuff should probably fix it. Carrionluggage 06:20, 17 October 2006 (UTC)
thread_title:  trying to use Kerr solution for rotating stars is doomed 

message: I think this article is written OK. I checked the metric "ds^2 = ..." and it looks good to me, however, I suggest to include contravariant components of g_{ik} tensor too. greg park avenue 18:33, 4 June 2007 (UTC)
thread_title:  Contravariant components of metric tensor wanted 

message: if i'm not mistaken, there is an error in the Kerr metric. I'm no expert on Relativity, but the last summand in the line element has unit length*time, where it should have length^2 like the other summands. the last summand should probably read (2*r_s*r*alpha/rho^2)*dPhi*(c*dT), since all other uses of time-variables in the line element are scaled by c, too. sorry in advance if i'm talking bullshit, but it puzzled me.
i also find the mixed use of "a" and "alpha" in the line element misleading. am i right in assuming they should be the same?
Could someone with more knowledge on this subject please verify this? thx Catskineater 14:32, 15 August 2007 (UTC)
replies: text: Those were little things, but they did need fixing.  It is done now. --EMS | Talk 17:30, 15 August 2007 (UTC)
thread_title:  unit error in the Kerr metric 

message: I've clarified some of the material on this page and on the Kerr-Newman and rotating black hole pages. I believe it is now more accurate. Unfortunately, I've noticed in editing this that there is now some duplication (for instance, the figure on this page). If any frequent wikipedians want to clean these pages further, that would be great. 91.37.241.229 20:44, 1 November 2007 (UTC)
thread_title: 1 November 2007 changes

message: This page needs to be edited for notational consistency. In the first part in the definition of the metric, the length scales Lambda and alpha are introduced. Then in the rest of the article, the dimensionless parameter a and the parameter Delta are used without definition. Either they need to be defined, or more probably, the Kerr metric should be written using the conventional parameters Delta and a instead of with Lambda and alpha.  —Preceding unsigned comment added by 142.103.234.23 (talk) 18:40, 7 April 2008 (UTC)
thread_title:  Notational consistancy 

message: I commented out the duplicate copy of the ergosphere picture.  Caption was:
::Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the  ergosphere. The oblate spheroidal surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process)
in case someone wants to put some of it back into the other copy. Wwheaton (talk) 16:27, 29 April 2008 (UTC)
thread_title:  Duplicate figure 

message: "... Schwarzschild solution, with a=0, the inner..."
"When M < a, there are no..."
What is 'a'?  I've gone over it carefully and can't find it.
Długosz (talk) 20:36, 12 March 2009 (UTC)
thread_title:  What is 'a'? 

message: The expression "Kerr vacuum" is suddenly introduced and not explained. One can try in principle to understand an expression made of 2 or more words by thinking about the meanings of the individual words in the expression - this is quite standard because most such expressions have no definition and don't really need one. But here I think it's not sufficient. Being myself a mathematician interested in physics and astronomy (and just reading an astronomy book) I came into the WP-articles about black hole metrics to help myself understand more about these things. So I could not make any useful edits myself. After reading this disc. page, I think I begin to understand what is meant, but I'm not sure. The idea is that since the Schwarzschild / Kerr / Reissner-Nordström / Kerr-Newman solutions contain analytic functions (away from apparent / true singularities) they (I guess) discribe only the (supposed vacuum) outside of a massive object with a definite (spherical) boundary (Planet / Star / black hole), which seems confirmed by the considerations about e.g. "match(ing) the Schwarschild vacuum exterior to a Schwarzschild fluid interior" - so the "Kerr vacuum" might just be another name for the Kerr solution which insists on this fact. Of course it must be an approximation to reality because the outside of real astronomic objects isn't void till infinity ..., approx. that might be fairly good in the neighborhood of the object. (Here I'm ignoring the problems with the may-be complicated inner structure of the object and with the until now not realized merging of Generel Relativity with Quantum physics.) My argument about analyticity is based upon the fact that the boundary of said objects - with the vacuum imagined outside - is a surface where the matter density is not analytical.--UKe-CH (talk) 09:40, 5 July 2009 (UTC)
thread_title:  What is the Kerr vacuum? 

message: I have heard that the Kerr metric is used by gps.  If someone with some expertise could expand on this in the article, I think this would be a great addition.  — Preceding unsigned comment added by 24.85.82.38 (talk) 02:31, 19 September 2011 (UTC)
replies: text: I think that that is unlikely. The deviations from a Schwarzschild metric due to mass-concentrations in the Earth are probably much (many orders of magnitude) greater than the relativistic corrections needed due to the Earth's rotation. JRSpriggs (talk) 06:48, 19 September 2011 (UTC)
thread_title:  gps 

message: The article said, without citation:
:Even stranger phenomena can be observed within the innermost region of this spacetime, such as some forms of time travel. For example, the Kerr metric permits closed, time-like loops in which a band of travelers returns to the same place after moving for a finite time by their own clock; however, they return to the same place and time, as seen by an outside observer.
I strongly doubt that closed time-like loops can be "seen by an outside observer," or that a "band of travelers" or any other finite physical system could traverse such a loop, whether seen by an outside observer or not. This seems like unsubstantiated hype-flavored stuff. If someone has a really good citation, thinks that it actually advances understanding, and can write a really clear description of this essentially non-physical idea, go to it.  — Preceding unsigned comment added by 86.140.51.175 (talk) 00:37, 2 March 2013 (UTC)
replies: text: No, this is correct, the precise statement is that any pair of events inside the region r<0 (the universe "behind" the hole) can be connected by a timelike future-pointing curve. So one can return to one's past. The beef here is that in the region g_{\phi\phi}<0, moving along the \phi coordinate curve (now timelike) "fast enough" decreases the t coordinate. What would such a traveller look like to another observer in the region is a cool question, a bit of computer ray tracing should solve this. The region g_{\phi\phi}<0 is a solid torus tangent to the ring singularity on the "inside". Its cross-section is not circular but some weird distorted oval-like quartic curve — another computer plotting assignment. Finally, this solid torus is accessible by a timelike future-pointing curve from/to any event with r<0. Jan Bielawski (talk) 22:55, 13 May 2013 (UTC)
thread_title:  Removed "time travel" 

message: I am fairly certain (though I'm no expert) that the trajectories shown in one of the pictures in "Trajectory equations" are wrong. I mainly refer to the left picture but I have serious doubts about the right one too. In the left, the center mass is supposed to rotate clockwise; but, except one, all of the trajectories, when they enter the ergosphere, continue to "circle" the center mass in counterclockwise direction. This violates what I know about ergospheres. From the diagram I see a dPhi that multiplied with alpha becomes negative, causing the squared line element (as given at the beginning of the page) to be negative, hence imaginary proper time, hence space-like. The one trajectory that starts at r*sin(Phi)=0 falls straight through the ergosphere into the center, showing no frame-dragging at all, which is wrong IMHO too.
My understanding would be that as the particles fall in, frame dragging consumes all the orbital angular momentum until (at latest) at the ergosphere surface the orbital angular momentum changes sign to point into the same direction as J. This means that within the ergosphere the particle co-rotates with the center mass. Straight trajectories like the one shown for r*sin(Phi)=0 should not be possible.
Maybe some expert can comment on my observation and either confirm (meaning the picture should be removed) or explain why my understanding would be wrong?WikiPidi (talk) 09:06, 15 October 2014 (UTC)
replies: text: WikiPidi's complaint looks sound.  The radial infall is telling in both pictures.   The particle should be perturbed spinward as it falls into the BH. Cloudswrest (talk) 20:19, 15 October 2014 (UTC)
replies: text: So after four months no expert has shown up to comment. But with one supporting comment I decided to remove the pictures now.WikiPidi (talk) 16:08, 24 February 2015 (UTC)
thread_title:  Wrong trajectories diagram 

message: The original author of this article and the one on the Schwarzschild metric uses the terminology "vacuum" which is used by some experts, but a minority. More use "geometry". I am an editor of the monograph "The Kerr Spacetime: Rotating Black Holes in General Relativity", a collection of articles by 12 leading experts in the field: Kerr, Carter, Penrose, ... The relative frequency of word counts from the source files gave: "Kerr black hole" 118, "Kerr metric" 52, "Kerr geometry" 14, "Kerr vacuum" 1. I realise that this article refers to the geometry, and not just the black hole which is more frequent because of its usage in the astrophysics literature. However, "Kerr vacuum" is really used by a minority, whereas "Kerr geometry" is far more common.  — Preceding unsigned comment added by DavidLWiltshire (talk • contribs) 01:51, 15 February 2016 (UTC)
thread_title:  "Geometry" versus "vacuum" 

message: :In the section "Mathematical form" it says:
:"In the non-relativistic limit where M (or, equivalently, rs) goes to zero, the Kerr metric becomes the orthogonal metric for the oblate spheroidal coordinates"
:followed by a function depending on a.
:But if M=0, the whole solution reduces to flat Minkowski space, even if a>0.
:Then it continues with
:"which are equivalent to the cartesian coordinates"
:followed by the standard transformation Boyer-Lindquist to cartesian background coordinates(which is also valid in the fully relativistic field).
:Therefore I will move the transformation up, below the passage
:"where the coordinates r,θ,ϕ are standard spherical coordinate system".
:The history of the entry is here.
:--Yukterez (talk) 19:41, 8 July 2017 (UTC)
thread_title:  Nonrelativistic Limit, Cartesian Coordinates 

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thread_title:  External links modified 

message: I wanted to add the fact that this was discovered by Roy Kerr in the introduction, but I don't want to mess things up with my low experience. PopoDameron (talk) 12:56, 19 April 2019 (UTC)
thread_title:  Roy Kerr 

message: After Eq: 13-- the definition of {\displaystyle {\vec {a}}} ;  I have to presume something like a^{2}=g_{uv}a^{u}a^{v} and \vec{a}=a^{u}
Actually I think the article http://www.scholarpedia.org/article/Kerr-Newman_metric
is much better for "Kerr–Schild coordinates".  While a little longer is more intelligible.
Rrogers314 (talk) 15:03, 28 May 2020 (UTC)
thread_title:  Unused definition?: <math>{\displaystyle {\vec {a}}}</math> and comment on Kerr–Schild coordinates section 

message: I found an article that refers to the Kerr-NUT metric w.r.t. axial symmetry. I think a citation should probably be added or else just have the parenthetic that refers to it removed entirely, but I'm not knowledgeable enough in this field to make the contribution. I actually thought this was a vandalism change from Newman to NUT until I looked it up, as there is no context in this Wikipedia article for it and, well... "NUT". 
Article link: https://link.springer.com/article/10.1007/BF00765705
TricksterWolf (talk) 00:01, 30 July 2021 (UTC)
replies: text: I think the clause in brackets should be removed until the Kerr-NUT article is created. Bellowhead678 (talk) 14:23, 2 August 2021 (UTC)
thread_title:  Kerr-NUT Paper Citation? 

message: There is an equation for rH+ which I interpret as the radius of the outer event horizon.  That simple equation seems to be for a sphere, assuming the radius is the same in all directions (unlike the ergosphere equation, there is no parameter related to latitude angle in the rH+ equation).  Yet the imagine clearly shows the outer event horizon flattening, and I have seen in other places that the outer event horizon is described as oblong (https://www.space.com/black-holes-event-horizon-explained.html) as the parameter "a" increases.
Is the formula for rH+ wrong, is it just applicable to the equatorial radius, or is the shape a sphere within the identified coordinate system?  
If the shape is squished top to bottom and rH+ is the equator's radius, is there another equally simple formula for the pole to pole distance? 2601:648:8700:3750:E533:3A24:7957:B9EA (talk) 18:54, 29 January 2023 (UTC)
replies: text: It would help if you specified which equation you find incorrect; the equation I find which seems to follow your description is the one specific to the Schwarzschild event horizon, which means non-rotating. The Kerr solution (which includes the latitude) is for a rotating black hole. Tarl N. (discuss) 21:35, 29 January 2023 (UTC)
replies: text:  If the Boyer Lindquist r is constant then the cartesian R ain't, in the equator R=√(r²+a²) while over the poles R=r, see the article on BL coordinates where everything is explained. --Yukterez (talk) 17:57, 19 August 2023 (UTC)
thread_title:  Important Surfaces