We contrast the two approaches to ‘‘classical’’ signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward’s distributional approach is based on a postulated modified form of the field equations. We make an...
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
The divergence theorem as usually stated cannot be applied across a change of signature unless it is reexpressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be ‘‘modified,’’ and therefore insistence on conservation of matter across such a surface cannot...
We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no...
We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
Multiagent approaches are well suited to designing autonomous solutions for systems that feature complex interactions between many individuals such as in autonomous traffic systems and multi-robot exploration systems. However, creating autonomous agents that function effectively in these systems is a challenging task. In these complex environments, agents need informative reward...