Maxwell's equations in curved spacetime

Abstract: We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N = 8 world volume (rigid) supersymmetry in a “physical” gauge; we also present the field equations and transformation rules in a “lightcone” gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowski)4 × (flat 7-torus), and review some mathematical results that are relevant for path integral quantization.

Abstract: 1 Special relativity 2 Scalar and electromagnetic fields in special relativity 3 Gravity and spacetime geometry: the inescapable connection 4 Metric tensor, geodesics and covariant derivative 5 Curvature of spacetime 6 Einstein's field equations and gravitational dynamics 7 Spherically symmetric geometry 8 Black holes 9 Gravitational waves 10 Relativistic cosmology 11 Differential forms and exterior calculus 12 Hamiltonian structure of general relativity 13 Evolution of cosmological perturbations 14 Quantum field theory in curved spacetime 15 Gravity in higher and lower dimensions 16 Gravity as an emergent phenomenon Notes Index

Abstract: Algebraically degenerate solutions of the Einstein and Einstein‐Maxwell equations are studied Explicit solutions are obtained which contain two arbitrary functions of a complex variable, one function being associated with the gravitational field and the other mainly with the electromagnetic field

Abstract: We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our construction essentially completes the analysis of the existence, uniqueness, and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime. As a byproduct of our analysis, we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times Lorentz invariant distributions, plus a remainder term of arbitrarily low scaling degree.

Abstract: Starting from a completely general standpoint, we find the most general brane-universe solutions for a 3-brane in a five-dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.