James Read

Modular Subgroups, Dessins d’Enfants and Elliptic K3 Surfaces

We consider the 33 conjugacy classes of genus zero, torsion-free modular subgroups, computing ramification data and Grothendieck’s dessins d’enfants. In the particular case of the index 36 subgroups, the corresponding Calabi–Yau threefolds are identified, in analogy with the index 24 cases being associated to K3 surfaces. In a parallel vein, we study the 112 semi-stable elliptic fibrations over P1 as extremal K3 surfaces with six singular fibres. In each case, a representative of the corresponding class of subgroups is identified by specifying a generating set for that representative.

Clarifying possible misconceptions in the foundations of general relativity

We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the Einstein equivalence principle and the ability to “transform away” gravity in local inertial coordinate systems.

Dessins d’enfants in \( \mathcal{N}=2 \) generalised quiver theories

A bstractWe study Grothendieck’s dessins d’enfants in the context of the N=2

Clocks and Chronogeometry: Rotating Spacetimes and the relativistic null hypothesis

\mathcal{N}=2

Two Miracles of General Relativity

supersymmetric gauge theories in (3 + 1) dimensions with product SU (2) gauge groups which have recently been considered by Gaiotto et al.. We identify the precise context in which dessins arise in these theories: they are the so-called ribbon graphs of such theories at certain isolated points in the moduli space. With this point in mind, we highlight connections to other work on trivalent dessins, gauge theories, and the modular group.

Hecke Groups, Dessins d'Enfants, and the Archimedean Solids

Does the gravitational field described in general relativity possess genuine stress-energy? We answer this question in the affirmative, in (i) a weak sense applicable in a certain class of models of the theory, and (ii) arguably also in a strong sense, applicable in all models of the theory. In addition, we argue that one can be a realist about gravitational stress-energy in general relativity even if one is a relationist about spacetime ontology. In each case, our reasoning rests upon a functionalist approach to the definition of physical quantities. 1 Introduction 2 Dramatis Personae   2.1 General relativity   2.2 Differential and integral conservation laws   2.3 Conservation equations in special and general relativity   2.4 Killing vector fields and spacetime isometries   2.5 The gravitational stress-energy pseudotensor 3 Interpreting Conservation Laws for Total Stress-Energy   3.1 The differential conservation law for total stress-energy   3.2 The integral conservation law for total stress-energy   3.3 Gravitational stress-energy 4 Gravitational Stress-Energy and Spacetime Ontology   4.1 Relationism and gravitational stress-energy   4.2 The cosmological constant 5 Conclusion 1 Introduction 2 Dramatis Personae   2.1 General relativity   2.2 Differential and integral conservation laws   2.3 Conservation equations in special and general relativity   2.4 Killing vector fields and spacetime isometries   2.5 The gravitational stress-energy pseudotensor   2.1 General relativity   2.2 Differential and integral conservation laws   2.3 Conservation equations in special and general relativity   2.4 Killing vector fields and spacetime isometries   2.5 The gravitational stress-energy pseudotensor 3 Interpreting Conservation Laws for Total Stress-Energy   3.1 The differential conservation law for total stress-energy   3.2 The integral conservation law for total stress-energy   3.3 Gravitational stress-energy   3.1 The differential conservation law for total stress-energy   3.2 The integral conservation law for total stress-energy   3.3 Gravitational stress-energy 4 Gravitational Stress-Energy and Spacetime Ontology   4.1 Relationism and gravitational stress-energy   4.2 The cosmological constant   4.1 Relationism and gravitational stress-energy   4.2 The cosmological constant 5 Conclusion

In defence of Everettian decision theory

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1. Introduction2. Fletchers Theorem2.1. Maudlin on the clock hypothesis in special relativity2.2. Fletcher’s result in special relativity2.3. Fletcher’s theorem in general relativity3. Electromagnetism and the Geometrical-Optical Limit 3.1. Maxwell’s equations in curved spacetime3.2. The geometrical-optical limit3.3. Rotating spacetimes3.4. Aren’t Gödel spacetimes unphysical?4. The Clock Hypothesis and Chronogeometry 4.1. Natural and mathematical observations4.2. Clock registry discord4.3. Chronogeometry5. Conclusion Introduction Fletchers Theorem Maudlin on the clock hypothesis in special relativity Fletcher’s result in special relativity Fletcher’s theorem in general relativity Electromagnetism and the Geometrical-Optical Limit Maxwell’s equations in curved spacetime The geometrical-optical limit Rotating spacetimes Aren’t Gödel spacetimes unphysical? The Clock Hypothesis and Chronogeometry Natural and mathematical observations Clock registry discord Chronogeometry Conclusion