Equations of Motion in Relativistic Gravity by Dirk Puetzfeld Claus Lämmerzahl & Bernard Schutz

Author:Dirk Puetzfeld, Claus Lämmerzahl & Bernard Schutz
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.1 Skeletal Stress-Energy

Consider the solution (59) extended down to . For reasons described in Sect. 1.2, there is no known distributional source for this solution on a domain that includes . However, we can devise the following setup: each of the seed solutions can be thought of as being sourced by a pointlike stress-energy supported on . Everything else in the general solution then grows from these seeds, either being generated by nonlinearities or in the case of the free fields, being determined by global boundary conditions.

I refer to the stress-energy for the seed solutions as the skeletal stress energy, taking after a similar phrase in Ref. [35]; the idea is that in some sense, the object (or body) can be replaced by a skeleton. That skeleton is made up of multipole moments living on the object’s worldline.

For each seed solution , I roughly follow the approach taken by Gralla and Wald at first order [18], defining the (trace-reversed) distributional stress-energy tensor

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