On May 8, 1:23 am, JanPB wrote:
On May 8, 12:21 am, Koobee Wublee wrote:

ds^2 = G c^2 dt^2 / (1 + K^2 / r^2) – 4 r^2 (1 + K^2 / r^2) dr^2 / K^2
– r^4 dO^2 / K^2

The Schwarzschild metric has the following form.

ds^2 = c^2 dt^2 (1 + K / r) – dr^2 / (1 + K / r) – r^2 dO^2

For the queer of England to continue living in that fat castle in the
air, he/she/it needs to talk himself/herself/itself into believing
both of the above equations are exactly the same.

Both coordinate systems are exactly the same. shrug

These solutions are solved after the specific forms of
the field equations are laid out.

Not "after the specific forms of the field equations are laid out" but
after a coordinate system has been chosen. This choice is only a
computational convenience, not anything fundamental.

You are still wrong. shrug

These solutions are solved after the specific forms ofthe field
equations are laid out.

At this moment, the choice of
coordinate system should be well established, and no one can change
the coordinate. shrug

What you've just said is like: once the choice of inches as units has
been made during the calculation, no one can convert the result to
centimetres.

No, that is not what I said. Of course, you are free to convert it to
whatever coordinate system of your choice after the solutions are
derived. However, at these solutions only apply to one same
particular set of coordinate system. shrug

I beg your pardon. Is there a typo on my part?

It's not a solution if the (t,r,theta,phi) are the same as in the
second (Schwarzschild's) formula.

Have you personally plug it into the field equations and verify that.
Eric Gisse has the software to do so. I am sure if that is not a
solution, someone would have complained long ago. So, the first
equation is still a valid solution to the field equations using the
same coordinate system of (t, r, theta, phi) as the second equation
(the Schwarzschild metric).

Both should satisfy G_ij = 0, and thus R_ij = 0.

No, the first one doesn't if its (t,r,theta,phi) are the same as those
in the second formula.

shrug

On the other hand, if you intended the first formula to be obtained by
substituing r in the second, then you are also WRONG: in that case
both formulas describe the same dot product (i.e., the same solution).

There you go again worshipping that dot product as if a true God.
shrug

Saying "both formulas describe the same dot product" is worshipping
dot product? How?

Because you believe in nonsense. shrug

Both equations do not describe the same dot product.

It's exactly the same with dr in polar coordinates and x/
sqrt(x^2+y^2)dx + y/sqrt(x^2+y^2)dy in Cartesian -- they are equal
covectors. Different formulas summing up to the same value. Same thing
when these covectors sit inside a formula for ds^2.

Yes?

Well, if they are equal, then what miracle suddenly makes them unequal
when they are inserted in the expression for ds^2?

But both equations do not specify the coordinate system being (t, x,
y, z). shrug

Accusation is very cheap. shrug

So are the two formulas written wrt to one coordinate system or two?
If two, what transformation did you use?

I am telling you both equations employ the same coordinate system.
Now, I see you are resorting back to your trollish behavior. There is
no point to continue any further, and in the future, please don’t
bring up that you have discussed this issue thoroughly with me because
it never did. You always resort to this kind of trollish behavior.
Now, go back to that fat castle in the air that you call GR and
fantasize about yourself being the queer of England, you majesty.