On gravity : a study of analytical and computational approaches to problem solving in collisionless systems

Abstract

I present an overview of the tools and methods of gravitational dynamics motivated by a variety of dynamics problems. Particular focus will be given to the development of dynamic phase-space configurations as well as the distribution functions of collisionless systems.

Chapter 1 is a short review of the descriptions of a gravitational system examining Poisson's equations, the probability distribution of particles, and some of the most popular model groups before working through the challenges of introducing anisotropy into a model.

Chapter 2 covers the work of Barber2014b which looks at the relations between quantities in collisionless systems. Analytical methods are employed to describe a model that can violate the GDSAI, a well-known result connecting the density slope to the velocity anisotropy. We prove that this inequality cannot hold for non-separable systems and discuss the result in the context of stability theorems.

Chapter 3 discusses the background for theories of gravity beyond Newton and Einstein. It covers the `dark sector' of modern astrophysics, motivates the development of MOND, and looks at some small examples of these MONDian theories in practice. Chapter 4 discusses how to perform detailed numerical simulations covering code methods for generating initial conditions and simulating them accurately in both Newtonian and MONDian approaches. The chapter ends with a quick look at the future of N-body codes.

Chapters 5 and 6 contain work from Barber 2012 and Barber 2014a which look at the recent discovery of an attractor in the phase-space of collisionless systems and present a variety of results to demonstrate the robustness of the feature. Attempts are then made to narrow down the necessary and sufficient conditions for the effect while possible mechanisms are discussed.

Finally, the epilogue is a short discussion on how best to communicate scientific ideas to others in a lecturing or small group setting. Particular focus is given to ideas of presentation and the relative importance of formality versus personality.