Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.physics.relativity > #452601 > unrolled thread

event horizon.

Back to article view | Back to sci.physics.relativity

Contents

  event horizon. Simon Roberts <retenshun@gmail.com> - 2018-03-13 23:32 -0700
    Re:event horizon. Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com> - 2018-03-14 08:14 +0100
      Re: event horizon. mlwozniak@wp.pl - 2018-03-14 00:53 -0700
      Re:event horizon. Térov Balónky <iytn@yeicenlw.ik> - 2018-03-14 15:59 +0000
        Re:event horizon. "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-14 09:19 -0700
      Re:event horizon. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-14 18:18 +0100
    Re: event horizon. Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-14 22:15 -0500
      Re: event horizon. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-15 16:29 +0100
        Re: event horizon. Gary Harnagel <hitlong@yahoo.com> - 2018-03-15 09:20 -0700
        Re: event horizon. Térov Balónky <iytn@yeicenlw.ik> - 2018-03-16 14:48 +0000
        Re: event horizon. Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-19 10:36 -0500
          Re: event horizon. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-20 00:56 +0100
            Re: event horizon. Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-20 14:13 -0500
              Re: event horizon. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-20 20:56 +0100
                Re: event horizon. Steven Carlip <carlip@physics.ucdavis.edu> - 2018-03-22 09:17 -0700
                  Re: event horizon. Darryl Fletcher <lu@ewiwwe.tt> - 2018-03-22 16:37 +0000
                  Re: event horizon. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-22 18:10 +0100
                    Re: event horizon. JanPB <filmart@gmail.com> - 2018-03-23 13:13 -0700
                  Re: event horizon. Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2018-03-22 14:54 -0700
                  Re: event horizon. Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-22 23:06 -0700
              Re: event horizon. Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 22:51 -0700
                Re: event horizon. Odd Bodkin <bodkinodd@gmail.com> - 2018-03-21 11:37 +0000
                  Re: event horizon. Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-22 13:51 -0700
                Re: event horizon. JanPB <filmart@gmail.com> - 2018-03-23 13:31 -0700
                  Re: event horizon. Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-23 15:59 -0500
                  Re: event horizon. Emma Blazer <aemb@wmopswxa.as> - 2018-03-23 22:19 +0000
                    Re: event horizon. JanPB <filmart@gmail.com> - 2018-03-23 15:43 -0700
                      Re: event horizon. Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-23 22:06 -0700
                      Re: event horizon. mlwozniak@wp.pl - 2018-03-23 23:05 -0700
                      Re: event horizon. Emma Blazer <aemb@wmopswxa.as> - 2018-03-24 10:55 +0000
      Re: event horizon. JanPB <filmart@gmail.com> - 2018-03-19 20:42 -0700
        Re: event horizon. Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-23 10:37 -0500
      Re: event horizon. Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 22:44 -0700
    Re: event horizon. numbernumber1964@gmail.com - 2018-03-20 13:55 -0700
      Re: event horizon. Odd Bodkin <bodkinodd@gmail.com> - 2018-03-20 23:02 +0000
    Re: event horizon. alsor@interia.pl - 2018-03-20 16:12 -0700
    Re: event horizon. numbernumber1964@gmail.com - 2018-03-22 15:24 -0700
      Re: event horizon. Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2018-03-22 17:14 -0700
      Re: event horizon. pnalsing@gmail.com - 2018-03-22 17:32 -0700
    Re: event horizon. numbernumber1964@gmail.com - 2018-03-23 10:37 -0700
      Re: event horizon. Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2018-03-23 13:32 -0700
    Re: event horizon. numbernumber1964@gmail.com - 2018-03-23 10:38 -0700
      Re: event horizon. moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-03-24 01:36 +0000

Page 1 of 3  [1] 2 3  Next page →

#452601 — event horizon.

event horizon. 

What happens when the event horizon's radius becomes smaller than its black hole? 

Simon Roberts 

[toc] | [next] | [standalone]

#452603

Simon Roberts <retenshun@gmail.com> Wrote in message:
> event horizon. 
> 
> What happens when the event horizon's radius becomes smaller than its black hole? 
> 
> Simon Roberts 

See evaporation of black holes by the Hawking radiation. This
 radiation progressively increases with the BH mass decreasing,
 ending with a big shower of particles.

For usual BH masses, this process is extremely slow even if
 compared to the supposed universe age.



-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

[toc] | [prev] | [next] | [standalone]

#452607

On Wednesday, 14 March 2018 08:14:21 UTC+1, Libor Striz  wrote:

> See evaporation of black holes by the Hawking radiation. This
>  radiation progressively increases with the BH mass decreasing,
>  ending with a big shower of particles.

Yeah, SEE it! SEE it in your mind's eyes.

[toc] | [prev] | [next] | [standalone]

#452624

Libor Striz wrote:

> See evaporation of black holes by the Hawking radiation. This
>  radiation progressively increases with the BH mass decreasing,
>  ending with a big shower of particles. 
> For usual BH masses, this process is extremely slow even if
>  compared to the supposed universe age.

Illucid. You cant decrease mass, since mass is indestructible. Hard-wired 
into the fabric of spacetime.

[toc] | [prev] | [next] | [standalone]

#452629

Event horizon byway of centripetal Force

((1 / ((0.5pi) * 6.52485 ((kg m) / s))) * kg * (c^2)) / (13.8881435 billion light years) = 6.67407999e-11 hertz 

((1 / (0.5 * pi * 6.52485)) * kg * (c^2)) / (13.8881435 billion light years) = 6.67407999e-11 newtons 


https://1.bp.blogspot.com/-7kzNrcVf5ew/V-gKl4zkEHI/AAAAAAAAE6U/Z2tGoh1Oor0Z8dJg4Ds7_Fk-kCwKoQ-oACLcB/s1600/1.gif 

http://www.webassign.net/question_assets/tamucolphysmechl1/lab_3/images/figure3-2.png 


(1 / (0.5pi * 6.52485)) * kg = 0.0975684916 kilograms 

(0.5pi * 6.52485) * kg = 10.2492104 kilograms 

[toc] | [prev] | [next] | [standalone]

#452635

[It should be noted that, sadly, Stephen W. Hawking died this morning
 at the age of 76, which might have caused the question to be posted.]

Libor Striz wrote:

> Simon Roberts <retenshun@gmail.com> Wrote in message:
>> event horizon.
>> 
>> What happens when the event horizon's radius becomes smaller than its
>> black hole?
> 
> See evaporation of black holes by the Hawking radiation. This
>  radiation progressively increases with the BH mass decreasing,
>  ending with a big shower of particles.

You should be more specific.

The *temperature* of the radiation should be progressively increasing:

  T_H = ℏ c³∕(8π G M k_B).
 
Therefore the *luminosity*

  P = Aₛ ε σ T_H⁴ = ℏ c⁶∕(15360 π G² M²).

  Aₛ = 4 π rₛ²     Schwarzschild surface
  rₛ = 2 G M∕c²    Schwarzschild radius

  G – Newton’s gravitational constant
  M – mass of black hole
  c – speed of light in vacuum
  ε – emissivity
  σ – Stefan–Boltzmann constant

<https://en.wikipedia.org/wiki/Hawking_radiation>

> For usual BH masses, this process is extremely slow even if
>  compared to the supposed universe age.

While your answer makes sense, the question is just word salad.

A (non-rotating) black hole is *defined* as the spherical region surrounding 
a spacetime singularity, whose radius is that of the (outer) event horizon.  
So the “event horizon's radius” cannot “[become] smaller than its black 
hole”.

<https://en.wikipedia.org/wiki/Event_horizon#Event_horizon_of_a_black_hole>

Instead, evaporation is precisely the process where the black hole loses 
mass by emitting Hawking radiation, so that the radius of its event horizon 
shrinks *accordingly*, and the black hole *becomes* *smaller* as a result.

<http://jila.colorado.edu/~ajsh/bh/singularity.html#r=1>


PointedEars
-- 
Q: Who's on the case when the electricity goes out?  
A: Sherlock Ohms.

(from: WolframAlpha)

[toc] | [prev] | [next] | [standalone]

#452733

On 3/14/18 1:32 AM, Simon Roberts wrote:
> What happens when the event horizon's radius becomes smaller than its black hole?

Can't happen. The event horizon is the boundary of the black hole.

	Note, however, that "radius" is not really applicable. The
	radius of a sphere would be measured inside the sphere, but
	the causal structure of the manifold inside the horizon of
	a black hole does not permit that. Also there are black
	holes whose horizons are not spherical.

In GR, the only theory we have that describes black holes, it is not 
possible for the horizon of a black hole to shrink. Indeed there is a 
theorem that states that the total area of all horizons in the manifold 
never decreases (I omit the conditions and caveats here).

But GR is a classical (non-quantum) theory. Hawking discovered from 
general semi-classical/semi-quantum ideas that quantum radiation is 
emitted at the horizon, and causes the horizon to shrink, and eventually 
disappear. But this takes an exceedingly long time -- for a (small) 
black hole of 1 solar mass, the lifetime is very much longer than the 
age of the universe; more massive (larger) black holes take much longer 
to evaporate away.

Tom Roberts

[toc] | [prev] | [next] | [standalone]

#452784

Tom Roberts wrote:

> On 3/14/18 1:32 AM, Simon Roberts wrote:
>> What happens when the event horizon's radius becomes smaller than its
>> black hole?
> Can't happen. The event horizon is the boundary of the black hole.
> 
> Note, however, that "radius" is not really applicable. The
> radius of a sphere would be measured inside the sphere, but
> the causal structure of the manifold inside the horizon of
> a black hole does not permit that.

I don’t know about you, but I can measure the radius of a sphere from 
outside the sphere just as well.

> Also there are black holes whose horizons are not spherical.

Yes, rotating ones (Kerr or Kerr–Newman metric), which apparently applies to 
most of them (due to conservation of angular momentum).


PointedEars
-- 
Q: Where are offenders sentenced for light crimes?
A: To a prism.

(from: WolframAlpha)

[toc] | [prev] | [next] | [standalone]

#452792

On Thursday, March 15, 2018 at 9:29:49 AM UTC-6, Thomas 'PointedEars' Lahn wrote:
>
> Tom Roberts wrote:
> >
> > Note, however, that "radius" is not really applicable. The
> > radius of a sphere would be measured inside the sphere, but
> > the causal structure of the manifold inside the horizon of
> > a black hole does not permit that.
> 
> I don’t know about you, but I can measure the radius of a sphere from 
> outside the sphere just as well.

You might have a little trouble doing that if the inside were not flat,
which it's not.

[toc] | [prev] | [next] | [standalone]

#452894

Thomas 'PointedEars' Lahn wrote:

>> Note, however, that "radius" is not really applicable. The radius of a
>> sphere would be measured inside the sphere, but the causal structure of
>> the manifold inside the horizon of a black hole does not permit that.
> 
> I don’t know about you, but I can measure the radius of a sphere from
> outside the sphere just as well.

Impossible. What an idiot. The only way a distance is measured is using a 
ruler or a meterstick. The use of photons is been obsolete and deprecated 
now for years and decades. One more proof this guy is completely 
uneducated.

[toc] | [prev] | [next] | [standalone]

#453246

On 3/15/18 10:29 AM, Thomas 'PointedEars' Lahn wrote:
> Tom Roberts wrote:

>> Note, however, that "radius" is not really applicable ]to a black hole]. The
>> radius of a sphere would be measured inside the sphere, but
>> the causal structure of the manifold inside the horizon of
>> a black hole does not permit that.
> 
> I don’t know about you, but I can measure the radius of a sphere from
> outside the sphere just as well.

Sure. But in this context the MEANING of the word "radius" is a distance or line 
from the center to the surface, and that is simply not applicable to a black hole.

Tom Roberts

[toc] | [prev] | [next] | [standalone]

#453298

Tom Roberts wrote:

> On 3/15/18 10:29 AM, Thomas 'PointedEars' Lahn wrote:
>> Tom Roberts wrote:
>>> Note, however, that "radius" is not really applicable ]to a black hole].
>>> The radius of a sphere would be measured inside the sphere, but
>>> the causal structure of the manifold inside the horizon of
>>> a black hole does not permit that.
>> I don’t know about you, but I can measure the radius of a sphere from
>> outside the sphere just as well.
> 
> Sure. But in this context the MEANING of the word "radius" is a distance
> or line from the center to the surface,

Not necessarily.  It can also be easily defined as, e.g., half the diameter, 
or the circumference divided by 2π.

> and that is simply not applicable to a black hole.

Nonsense.  (Google is your friend. [psf 6.1])


PointedEars
-- 
Q: Where are offenders sentenced for light crimes?  
A: To a prism.

(from: WolframAlpha)

[toc] | [prev] | [next] | [standalone]

#453334

On 3/19/18 6:56 PM, Thomas 'PointedEars' Lahn wrote:
> Tom Roberts wrote:
>> On 3/15/18 10:29 AM, Thomas 'PointedEars' Lahn wrote:
>>> Tom Roberts wrote:
>>>> Note, however, that "radius" is not really applicable ]to a black hole].
>>>> The radius of a sphere would be measured inside the sphere, but
>>>> the causal structure of the manifold inside the horizon of
>>>> a black hole does not permit that.
>>> I don’t know about you, but I can measure the radius of a sphere from
>>> outside the sphere just as well.
>>
>> Sure. But in this context the MEANING of the word "radius" is a distance
>> or line from the center to the surface,
> 
> Not necessarily.  It can also be easily defined as, e.g., half the diameter,
> or the circumference divided by 2π.

Not without a serious PUN on "radius" here -- those are equivalent in 
Euclidean space, but not in Schw. spacetime.

At the "center" of a Schwarzschild black hole is a singularity, and the 
distance from it to the horizon is not well defined. Instead of the 
singularity one can construct a 2-d spacelike surface from the union of 
the limit points of all geodesics; but that surface has infinite area -- 
attempting to consider it a "point at the center of the horizon" is 
hopeless.

My basic point (sorry for the pun) is that common geometrical terms, 
like "radius", were defined in flat space, and attempting to apply them 
to highly-curved spacetime is confusing at best, and in general useless.

	One can compute the area of the horizon in Schw. spacetime:
	4 pi (2M)^2. So _IF_ this were Euclidean space, such a sphere
	would have a radius = 2M. But this is NOT Euclidean space,
	and calling that a "radius" brings expectations that simply
	do not hold.

>> and that is simply not applicable to a black hole.
> 
> Nonsense.  (Google is your friend. [psf 6.1])

Google is not populated by experts in GR. There is LOTS of 
misinformation there (not only in politics).

Tom Roberts

[toc] | [prev] | [next] | [standalone]

#453345

Tom Roberts wrote:

> On 3/19/18 6:56 PM, Thomas 'PointedEars' Lahn wrote:
>> Tom Roberts wrote:
>>> and that is simply not applicable to a black hole.
>> 
>> Nonsense.  (Google is your friend. [psf 6.1])
> 
> Google is not populated by experts in GR. There is LOTS of
> misinformation there (not only in politics).

There is also a lot of information there.  You should read it sometime.

I will not accept your shifting the burden of proof, and not show you
the statements by *specialists* on black holes (which you are not) that 
contradict your claims and that you can find easily.


PointedEars
-- 
Q: What did the female magnet say to the male magnet?  
A: From the back, I found you repulsive, but from the front
   I find myself very attracted to you.
(from: WolframAlpha)

[toc] | [prev] | [next] | [standalone]

#453497

On 3/20/18 12:56 PM, Thomas 'PointedEars' Lahn wrote:
> Tom Roberts wrote:
> 
>> On 3/19/18 6:56 PM, Thomas 'PointedEars' Lahn wrote:
>>> Tom Roberts wrote:
>>>> and that is simply not applicable to a black hole.
>>> 
>>> Nonsense.  (Google is your friend. [psf 6.1])
>> 
>> Google is not populated by experts in GR. There is LOTS of 
>> misinformation there (not only in politics).
> 
> There is also a lot of information there.  You should read it
> sometime.
> 
> I will not accept your shifting the burden of proof, and not show
> you the statements by *specialists* on black holes (which you are
> not) that contradict your claims and that you can find easily.

Well, I *am* an expert on black holes.  Tom is basically right
here; to some extent it's a question of terminology, but the
terminology is pretty standard.

In flat space, there are multiple equivalent definitions of a
radial coordinate.  It can be the distance from the origin; a
quantity proportional to the circumference; a quantity proportional
to the square root of the area; a quantity proportional to the
cube root of he volume; or the square root of the sum of the
squares of Cartesian coordinate differences.

In a curved space (or spacetime), these are typically all
different.  For a black hole, they are *drastically* different
once one approaches the horizon.  Some of them can be measured
from the outside, while others can't.

The standard terminology is that while all of these can be called
"radial coordinates," the "radius" refers to a particular quantity:
the proper distance from the center.  This can't be measured
from the outside.  In fact, it has no meaning for an uncharged,
nonrotating black hole -- at any finite time, the "center" is to
the future, not at soe position in space at the same time.

It's true that the "areal radial coordinate" at the horizon --
the "radius" determined from the square root of the area -- is
often called the "Schwarzschild radius."  But this is historical
accident, coming from a time that the distinctions among different
coordinates was not very well understood.  I think I can safely
say that few, if any, experts on GR would actually say that the
"Schwarzschild radius" was the radius of a black hole.

Steve Carlip

[toc] | [prev] | [next] | [standalone]

#453498

Steven Carlip wrote:

> On 3/20/18 12:56 PM, Thomas 'PointedEars' Lahn wrote:
> Well, I *am* an expert on black holes.  Tom is basically right here; to
> some extent it's a question of terminology, but the terminology is
> pretty standard.
> 
> The standard terminology is that while all of these can be called
> "radial coordinates," the "radius" refers to a particular quantity:
> the proper distance from the center.  This can't be measured from the
> outside.  In fact, it has no meaning for an uncharged, nonrotating black
> hole -- at any finite time, the "center" is to the future, not at soe
> position in space at the same time.

Please be careful, you are about arguing with a known uneducated imbecile. 
Not that good.

[toc] | [prev] | [next] | [standalone]

#453501

Steven Carlip wrote:

> It's true that the "areal radial coordinate" at the horizon --
> the "radius" determined from the square root of the area -- is
> often called the "Schwarzschild radius."  But this is historical
> accident, coming from a time that the distinctions among different
> coordinates was not very well understood. 

Thank you for your explanation.  However:

> I think I can safely say that few, if any, experts on GR would actually
> say that the "Schwarzschild radius" was the radius of a black hole.

As one example of many that, AISB, can be found easily with a 
Google/whatever Web search keywords “black hole radius”:

Stephen W. Hawking, Malcolm J. Perry, Andrew Strominger (2016).  
Superrotation Charge and Supertranslation Hair on Black Holes.
<https://arxiv.org/abs/1611.09175>

| 2.3 Discussion
| 
| […]
| In this type of situation, however, peeling can typically be restored by
| adding incoming radiation in just such a finetuned way that the solution
| is exactly Schwarzschild outside some arbitrarily large but finite radius
| [105–107].  […]

I leave it to you to check the references.


PointedEars
-- 
«Nec fasces, nec opes, sola artis sceptra perennant.»
(“Neither high office nor power, only the scepters of science survive.”)

  —Tycho Brahe, astronomer (1546-1601), inscription at Hven

[toc] | [prev] | [next] | [standalone]

#453599

On Thursday, March 22, 2018 at 10:10:46 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> Steven Carlip wrote:
> 
> > It's true that the "areal radial coordinate" at the horizon --
> > the "radius" determined from the square root of the area -- is
> > often called the "Schwarzschild radius."  But this is historical
> > accident, coming from a time that the distinctions among different
> > coordinates was not very well understood. 
> 
> Thank you for your explanation.  However:
> 
> > I think I can safely say that few, if any, experts on GR would actually
> > say that the "Schwarzschild radius" was the radius of a black hole.
> 
> As one example of many that, AISB, can be found easily with a 
> Google/whatever Web search keywords “black hole radius”:
> 
> Stephen W. Hawking, Malcolm J. Perry, Andrew Strominger (2016).  
> Superrotation Charge and Supertranslation Hair on Black Holes.
> <https://arxiv.org/abs/1611.09175>

But I bet this is simply a shorthand for the longer and awkward phrase
(presumed understood by the reader), "the square root of the horizon area 
divided by 4 pi".

--
Jan

[toc] | [prev] | [next] | [standalone]

#453519

On Thursday, March 22, 2018 at 11:17:47 AM UTC-5, Steven Carlip wrote:
> On 3/20/18 12:56 PM, Thomas 'PointedEars' Lahn wrote:
> > Tom Roberts wrote:
> > 
> >> On 3/19/18 6:56 PM, Thomas 'PointedEars' Lahn wrote:
> >>> Tom Roberts wrote:
> >>>> and that is simply not applicable to a black hole.
> >>> 
> >>> Nonsense.  (Google is your friend. [psf 6.1])
> >> 
> >> Google is not populated by experts in GR. There is LOTS of 
> >> misinformation there (not only in politics).
> > 
> > There is also a lot of information there.  You should read it
> > sometime.
> > 
> > I will not accept your shifting the burden of proof, and not show
> > you the statements by *specialists* on black holes (which you are
> > not) that contradict your claims and that you can find easily.
> 
> Well, I *am* an expert on black holes.  Tom is basically right
> here; to some extent it's a question of terminology, but the
> terminology is pretty standard.
> 
> In flat space, there are multiple equivalent definitions of a
> radial coordinate.  It can be the distance from the origin; a
> quantity proportional to the circumference; a quantity proportional
> to the square root of the area; a quantity proportional to the
> cube root of he volume; or the square root of the sum of the
> squares of Cartesian coordinate differences.
> 
> In a curved space (or spacetime), these are typically all
> different.  For a black hole, they are *drastically* different
> once one approaches the horizon.  Some of them can be measured
> from the outside, while others can't.
> 
> The standard terminology is that while all of these can be called
> "radial coordinates," the "radius" refers to a particular quantity:
> the proper distance from the center.  This can't be measured
> from the outside.  In fact, it has no meaning for an uncharged,
> nonrotating black hole -- at any finite time, the "center" is to
> the future, not at soe position in space at the same time.
> 
> It's true that the "areal radial coordinate" at the horizon --
> the "radius" determined from the square root of the area -- is
> often called the "Schwarzschild radius."  But this is historical
> accident, coming from a time that the distinctions among different
> coordinates was not very well understood.  I think I can safely
> say that few, if any, experts on GR would actually say that the
> "Schwarzschild radius" was the radius of a black hole.

Thanks. It's always a treat when you post. I usually find myself being
corrected on something that I *thought* that I understood... 
sort of...
maybe... 
:-)

 

[toc] | [prev] | [next] | [standalone]

#453547

On Thursday, March 22, 2018 at 9:17:47 AM UTC-7, Steven Carlip wrote:

> I *am* an expert on black holes...

Well, the only thing that Koobee Wublee gets out of professor Carlip’s post is that he is an expert on black holes.  Similarly to deciphering a holy book from the medieval age, the rest reads like explanations to the holy scripts and more explanations on the explanation to that same holy scripts.  <shrug>

With Koobee Wublee’s compliment to professor Carlip’s comment raised, Koobee Wublee shall point out a simpler explanation below that follows the Occam’s Razor.  <shrug>

**  ds² = g_ij dq^i dq^j = [g]_ij d[q]^i d[q]^j = [g] * d[q]²

Where

**  ds = line element of spacetime geometry
**  g_ij = [g]_ij = elements of the matrix [g]
**  [g] = matrix representing the metric
**  [q] = matrix representing the coordinate system of the observer
**  [a] * [b] = [a]_ij [b]^ij, dot product of matrices [a] and [b]

The geometry is just ds.  What does that mean?  Well, ds is what it is but can only mean something if a coordinate system that everyone understands is introduced.  In this case, such coordinate system is [q].  Following this simple logic, the radius to this illusive black hole, that professor Carlip is an expert on, can easily be understand by anyone using this polar coordinate system.  <shrug>

[toc] | [prev] | [next] | [standalone]

Page 1 of 3  [1] 2 3  Next page →

Back to top | Article view | sci.physics.relativity

csiph-web