Undergrad Klein-Gordon: Schwarzschild Metric, Physically Acceptable?

[Vitani1]

Does this give solutions which are physically acceptable?

 

[jambaugh]

Yes.

 

[PeterDonis]

Moderator's note: Moved thread to relativity forum.

 

[haushofer]

A bit of context could help.

 

[Vitani1]

If you use the Schwarzschild metric in the Klein-Gordon equation (see attached) and derive the equation for the particle as a function of its position in time and space, do you get physically realizable solutions? This is my question.

 

[jambaugh]

Understand that the Klein-Gordon equation encodes the propagation of waves for massive fields in the absence of non-gravitational interactions with the field. If you can physically realize those assumptions (and GR) and you can physically realize a massive (including special case m=0) field. Thus: "Yes."

Failure to satisfy K-G is failure to conserve local momentum-energy. That's not impossible, the system can be "bleeding" momentum-energy into or out of some other field via interaction but one must assume it may also not do so.

 

[Vitani1]

When you say absence of non-gravitational interactions within the field you mean to say that solving this for the Schwarzschild is effective in explaining wave-like phenomena in the presence of gravity exclusively?

 

[Vitani1]

I meant to include in the previous post the presence of gravity or the absence of a field.