Sustainability in the theology curriculum

This is the author's PDF version of a book chapter available in Sustainability education: Perspectives and practice across higher education. Edited by Paula Jones, David Selby, and Stephen Sterling. London: Earthscan, 2010. This book chapter was reproduced with the kind permission of EasthScan.This book chapter discusses how theology has the potential to contribute to education for sustainable development

Boundary description of Planckian scattering in curved spacetimes

We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of shock-waves up to the point of evolution at which the forward light-cone of a collision meets the boundary of the space-time. The conclusions are quite general and in particular generalize the previous work of E. and H. Verlinde. The role of the off-diagonal Einstein action in removing the bulk part of the action is emphasised. We discuss the sense in which our result is a particular example of holography and also the relation of our solutions in $AdS$ to those of Horowitz and Itzhaki

Implementing holographic projections in Ponzano--Regge gravity

We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a semi-classical limit while the boundary state functional remains quantum-mechanical. The properties of the resulting boundary theory are discussed.Comment: 20 pages, late

Penrose Limits and Spacetime Singularities

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction