arXiv subjects

J. Brian Pitts

Publications and source records attributed to J. Brian Pitts.

40 records · Page 3Linked to original sources

arXiv2004

Null Cones and Einstein's Equations in Minkowski Spacetime

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector formalism reduce the configuration space to the causality-respecting part. In this smaller space, gauge transformations do not form a group, but only a groupoid. The flat metric removes the difficulty of defining equal-time commutation relations in quantum gravity and guarantees global hyperbolicity.

gr-qc↗

arXiv2002

Null Cones in Lorentz-Covariant General Relativity

The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After reviewing the history of this problem, we introduce a generalized eigenvector formalism to give a kinematic description of the relation between the two null cones, based on the Segre' classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a method to enforce special relativistic causality by using the naive gauge freedom to restrict the configuration space suitably. A set of new variables just covers this smaller configuration space and respects the flat metric's null cone automatically. In this smaller space, gauge transformations do not form a group, but only a groupoid. Respecting the flat metric's null cone ensures that the spacetime is globally hyperbolic, indicating that the Hawking black hole information loss paradox does not arise.

gr-qc↗

arXiv2001

Flat Spacetime Gravitation with a Preferred Foliation

Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional ``parametrized'' and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on $τ$ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, but find a need for one in the process (``flowing'') theory of time. We then suggest why such a foliation might reasonably be unobservable.

gr-qc↗

arXiv2001

Light Cone Consistency in Bimetric General Relativity

General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then gravity is not just another field in flat spacetime after all. Here we discuss recent progress in describing the conditions for consistency and prospects for satisfying those conditions.

gr-qc↗