What is the actual importance of Dixon's extended bodies theory for fundamental physics?

Disclaimer: I'm unsure if this question fits here. If it doesn't please let me know if it can be modified so that it does. In the end if it simply doesn't fit here, I'll delete it.

The motivation for the question is as follows: I've started a graduate course in Physics to obtain a master's degree. I wanted to work with QFT on curved spacetimes or something related to quantum gravity, but my advisor passed away and I ended up assigned to work with dynamics of extended bodies in GR and I'm finding it quite uninteresting. I'm trying to find something on the topic which ends up interesting me.

So, the point here is: in 1970 W. G. Dixon developed three papers explaining one approach to describe the dynamics of extended bodies in GR. These papers are:

1. Dynamics of extended bodies in general relativity. I. Momentum and angular momentum - In this paper, considering one extended body of energy-momentum tensor $T_{ab}$ on a spacetime $(M,g)$ with electromagnetic field $F_{ab}$ with Killing vector fields $K_a$ preserving $F_{ab}$ Dixon proposes, on the analysis of the conservation laws induced by $K_a$, definitions for momentum and angular momentum for the extended body.
2. Dynamics of extended bodies in general relativity - II. Moments of the charge-current vector - In this paper, Dixon develops one general definition for multipole moments of tensor fields describing properties of extended bodies. He discusses uniqueness and existence. The main result is that there is one set of multipole moments for the charge-current vector $J_a$ called the reduced set of moments, which encodes in the simples possible manner the conservation condition $\nabla_a J^a =0$.
3. Dynamics of extended bodies in general relativity III. Equations of motion - In this paper, Dixon reviews the result for the existence and uniqueness of the reduced multipole moments of $J_a$ and develops the analogous construction for $T_{ab}$ finding reduced moments for the energy-momentum tensor. In terms of these moments the conservation condition $\nabla_{a}T^{ab}=J_a F^{ab}$ yields the definitions from the first paper, together with the equations of motion that can be expanded to any desired multipole order.

The issue is: I can't simply find any real importance, specially from a fundamental physics point of view, in any of this. The amount of effort to construct this theory is enormous, and in the end, what it provides is just a way to analyze extended objects, that most of the time we have seem imagined as point particles, giving already good results.

Some people try to support that this is important by talking about e.g., the swimming effect, but this for me is just a mathematical curiosity. My advisor even just wants me to use all this to solve one exercise about a dumbell falling in Schwarzschild spacetime.

I don't actually see much physical motivation behind all this, nor any real need from observations to build this whole theory, which seems just to give some corrections due to considering the size of an object.

For someone who wanted to work with QFT on curved spacetimes, quantum gravity, etc (all of which have quite a few implications in fundamental physics) this is being extremely frustrating.

So my question here is: what is actualy the importance of developing this dynamics of extended bodies in GR? Does it have any important implications in fundamental physics and in the understanding of GR?

Is there some actual system in nature which requires one to develop this to explain observations?

Or in the end, it is just as I'm seeing it now, a mathematical curiosity which just yields some corrections to the point-particle results and that can be used just to solve some examples (that were imagined just to be examples, instead of being motivated for occuring in nature)?

• Have you asked your advisor why they want you to do this? Maybe it’s partly meant as a training exercise? – knzhou Mar 10 '18 at 19:56
• I've tried a few times. His answer was that "he finds it interesting" and that "he likes solving examples". I've asked also why he finds it important and his answer is just: "if one wants to solve the problem of one articulated robot on spacetime one needs this". I don't think he sees this as a training exercise, as he wants to publish one paper with the example he gave me to solve. – user1620696 Mar 10 '18 at 23:05
• To be clear, I don't find anything wrong with this kind of research. It is just that I prefer themes related to fundamental physics or to actual systems ocurring in nature, instead of imagined for problem solving. I'm trying thus to understand why this is one relevant research theme and if I can find something on this area that interests me, because certainly the theme "extended bodies in GR" seems quite broad. – user1620696 Mar 10 '18 at 23:06

One of the interesting aspects of EMRIs, is that unlike the binary black holes observable by LIGO, there evolution (controlled by the ratio of the masses) is very slow, meaning that we observe many ($\sim m_1/m_2$) gravitational wave cycles while the binary is in the sensitivity band of the detectors. As a result, the properties of the binary can be measured to very high accuracy ($\sim m_2/m_1$). This also means that EMRIs can be used as very sensitive probes of alternative theories of gravity. (e.g. by probing whether the primary black hole is described by the Kerr metric).