SHELL GAMES and coordinate transforms

Where is the pea?  At first, developing the Kerr metric with the Eddington transform between time and radial coordinates, the entire source or disturbance is expressed in the second term, whose coefficient is ‘2m’. Then after five more coordinate transforms, there are some terms in ‘m’, but some in the much larger ‘a’… HOW IS THIS MAGIC???  We could have thrown out the baby with the bathwater and ended up with no physics for SPIN…  however now we have a choice, and may drop terms in ‘m’ when they are added to terms in ‘a’.  Whence this alchemy?  I suspect there are zeroes in denominators, which underneath the very small ‘m’, still change relationships. I will report back when I pin this down. [[[SURPRISING ANSWER, see 2nd COMMENT]]]

3 thoughts on “SHELL GAMES and coordinate transforms

  1. ‘m’ is something like forty orders of magnitude smaller than ‘a’ !!! Thus I think GR describes a tendency of spacetime that CANNOT HAPPEN. Alexander Burinskii saves the day at the classical radius… In achieving the math solution, we followed our noses in eliminating cross-terms. WE PRODUCED A GEOMETRY very new and different, and it is one where SPIN rules as of the angular momentum radius, ‘a’.

    Like

  2. SURPRISING ANSWER: SHELL GAMES: The original expression written by Kerr for the GR solution including SPIN, is a curious mix of rectilinear -type coordinates, along with the REAL part of the newly complexified radius. As soon as we let ourselves sensibly redefine spherical angles and substitute these for all the spatial differentials, and regroup terms, whoa Betty, THERE IT IS ALREADY!!! Not even in denominators, in metric terms for the time, and also for ‘phi’, we see addition of terms in ‘a’, and in ‘m’. BINGO. In going on with further coord. transforms, we eliminate the final cross-terms (except the last d(phi)dt term). Then we get denominators, but it is not critical, they never go to zero, in the subsequent forms. In the first equation we can see the inconsistency in the coefficient, since both ‘z’ and ‘rho’ may go strictly to zero. This is smaller yet than ‘m’ as a very small quantity. This algebra will make you look stuipid sometimes, often even.

    Like

  3. The term in ‘m’ in the time differential coefficient, is not so relevant, since it multiplies the entire geometric ‘disturbance’ compared to the ‘1’ of flat spacetime. Later I will type in the equation in its final form after another few transforms.

    Like

Leave a comment