This month, Living Reviews in Relativity has published two major updates of the reviews “The Einstein-Vlasov System/Kinetic Theory” by Håkan Andréasson and “Analogue Gravity” by Carlos Barceló, Stefano Liberati and Matt Visser. Both articles substantially revise previous versions from 2005.
Please find the abstract and further details below.
“The Einstein-Vlasov System/Kinetic Theory”
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This is a revised and updated version of the article from 2005. A number of new sections on the Einstein-Vlasov system have been added, e.g., on the formation of black holes and trapped surfaces, on self-similar solutions, on the structure of static solutions, on Buchdahl type inequalities, on the stability of cosmological solutions, and on axisymmetric solutions. Some of the previous sections have been significantly extended. The number of references has increased from 121 to 197.
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein–Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein–Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
Barceló Serón, Carlos and Liberati, Stefano and Visser, Matt
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Completely revised and updated previous version. Significantly extended Sections 2.4, 3, 4.1, 4.2, 5, and 7. Introduced new Section 6. Eight new figures have been added. The number of references increased from 434 to 702.
Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).
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