How to vary the Schwartzschild Metric

[Aethelwulf]

No. The SC metric is not inconsistent. It is a perfectly admisible solution to the Hilbert & Einstein equations under well-defined physical assumptions. And, as already said before, the SC metric has been well tested in half dozen of different tests. In fact, the SC metric is probably the best tested metric of general relativity. Your claim that "the Schwartzschild metric does not really purport to a real type of object" is unfounded.

 

Modifications to the SC metric are known as well.

 

Are you trying to be obtuse?

 

We have already agreed that it is inconsistent inasmuch that it cannot describe changing energy, taking into details like the loss of radiation. We've established this, and this is why I say it's inconsistent over periods of time.

 

As has been noted, it is an approximation which works well. Now, it has also been noted that it's like dust off a golf ball, but I've argued that radiation may not be very smooth in this sense, we might be talking about an object which releases gamma energy in the form of jet bursts.

 

Then surely in that kind of case, radiation will be given up a lot quicker.

 

So I am not saying that it is inconsistent that we can't make approximations, I am saying it is inconsistent that it does not describe the energy given up over periods of time. This is why it cannot purport to a real object 100% accurately - it doesn't take into details of the energy given up through natural processes which would be expected from a metric.

 

Now you have also said yourself that modifications are not unknown to the SC metric. This is exactly what my OP is attempting to do, but I need to find a way round the timelike killing vector, which won't be easy.

 

Just highlighting this problem mathematically, the SC metric is invariant under the tranformation [math]t \rightarrow t+dt[/math] in the spherical coordinate system [math](t,r,\theta, \phi)[/math]. You split the vector field [math](dt,0,0,0)[/math] into two factors, the finite vector field [math]\Sigma[/math] and some infinitesimal scalar, then the displacement vector is

 

[math]\zeta dt = (1,0,0,0) dt[/math]

 

And this is the Killing vector. When all the points in the space are displaced they do not flow with any expansion or compression. And has been discussed, it contains a specific symmetry [math]t \rightarrow -t[/math].

 

 

I don't think my approach will be able to solve a way around the killing vector, its almost entwined in the definition of the SC metric... which means I need to look for a different modified approach.

Edited June 14, 2012 by Aethelwulf