Mass and Motion in General Relativity

Our current perspective has arisen over millennia, through falling apples, elevator thought experiments and stars spiralling into black holes; Free fall and self-force in general relativity.

In fact, we do not have in mind to make a 1:1 reflection of the school. The ordering has been rearranged to tie articles together more coherently. We also propose to ask authors to focus their contributions according to the title we have suggested and to give a more complete description of current and future directions. We expect this will add to the volume’s value for all anticipated readers. This volume has the unique feature of presenting a multifaceted approach to mass, which is intended mainly for graduate students and young doctoral researchers in the field of gravitation, who might be hoping to find a concise and introductory presentation of advanced topics outside their research field.

It is true that research from the infinitesimal scale of particle physics to the cosmic scale of the universe is concerned with the mass. While there have been spectacular advances in physics during the past century, mass still remains as a mysterious entity at the forefront of current research. Particle accelerators in the quest for the Higgs boson, laser interferometers sensitive enough to respond to gravitational waves, equivalence principle tests and detectors for dark matter are among the most ambitious and expensive experiments that fundamental physics has ever envisaged, and strongly attest to this fact. Both the self-force and radiation reaction are, in fact, lively topics of research. Related to the nature of motion, they have been hotly debated within general relativity from the inception of the theory. Recent developments have shown that radiation reaction is unavoidable in determining the gravitational waveforms emitted from a source such as the capture of a solar mass star by super-massive black hole (EMRI).

The main theme of this volume is mass and its motion within general relativity (and other theories of gravity), particularly for compact bodies, to which many articles directly refer. Within this framework, there are chapters on post-Newtonian and related methods (Blanchet, Gourgoulhon and Jaramillo, Nagar, Schäfer), as well as on the self-force approach to the analysis of motion (Barack, Detweiler, Gal’tsov, Poisson, Wald, Whiting), summarised along with an historic development of the field (Spallicci) and a snapshot on the state of the art (Burko). Note that self-acceleration depends directly on the mass of the body experiencing it. Mass itself is essential for this effect on motion.

Auxiliary chapters set the context for these theoretical contributions within the wider context of experimental physics. The space mission LISA (Jennrich) has been designed to detect the gravitational waves from EMRI captures, while other LISA sources may have electromagnetic counterparts (van Putten). Motion in modern gravitation must confront alternative theories (Esposito-Farèse) and it must to be comprehensible within a quantum context (Noui), and demands an account of the relation between vacuum fluctuations and inertia (Jaekel and Reynaud). A volume centred on the fundamental role of mass in physics should face issues related to the basic laws of mechanics proposed by Newton (Lämmerzahl) and precision measurements (Davis).

The role of the Higgs boson within physics is to give a mass to elementary particles (Djouadi), by interacting with all particles required to have a mass and thereby inducing inertia.

Moreover, most mass in the universe is dark, and only indirectly detected. A proposed alternative to dark matter theories is due to a modified theory of gravity (Esposito-Farèse) such as MOND (MOdified Newtonian Dynamics). Even if general relativity does not explain gravity, there still remains the fundamental problem of reconciling any theory of gravity with the physics of quantum fields (Noui), itself so well verified experimentally.