Degenerate Solutions of General Relativity from Topological Field Theory

Degenerate Solutions of General Relativity from Topological Field Theory

Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional BF theory on any framed surface Σ embedded in M . In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Σ, while inside this neighborhood the connection A and the field E = e∧e sa...

Exact solutions of the field equations of the general theory of relativity

The series of papers now being reprinted as Golden Oldies were the product of Pascual Jordan’s strong relativity group at Hamburg University in the immediate postwar period, initially comprising Jordan, Jürgen Ehlers, andWolfgang Kundt, and later also Rainer Sachs andManfred Trümper. Jordanmademajor contributions to quantum mechanics and quantum field theory1 (Jordan algebras are named after hi...

A Topological Extension of General Relativity

A set of algebraic equations for the topological properties of space-time is derived, and used to extend general relativity into the Planck domain. A unique basis set of three-dimensional prime manifolds is constructed which consists of S, S × S, and T . The action of a loop algebra on these prime manifolds yields topological invariants which constrain the dynamics of the four-dimensional space...

Non-locality in quantum field theory due to general relativity

We show that general relativity coupled to a quantum field theory generically leads to non-local effects in the matter sector. These non-local effects can be described by non-local higher dimensional operators which remarkably have an approximate shift symmetry. When applied to inflationary models, our results imply that small nonGaussianities are a generic feature of models based on general re...

Einstein’s General Theory of Relativity