136 research outputs found
How many futures on Finsler spacetime?
No full textSome recent results by the author on the geometry and dynamics of Finsler spacetimes are reviewed. It is shown that in Finslerian generalizations of general relativity the number of predicted lightlike cones is two, one past and one future, as in general relativity. This result is non-trivial as it can fail, for instance, in spacetime dimension two. It is also shown that suitable versions of the reverse Cauchy-Schwarz and reverse triangle inequalities hold on Finsler spacetimes. Finally, a long standing problem of Finslerian gravity concerns the development of dynamical equations which imply a conservation law. We make some progress following a recent proposal by the author according to which physical Finsler spacetimes have ane sphere indicatrices of hyperbolic type
Chronology violations and the origin of time
No full textWe review some results which relate chronology violations to singularities, and explain how the absence of both pathologies implies the existence of a cosmological time. Building on these mathematical ideas we then propose a causality argument in order to solve the homogeneity and entropy problems of cosmology. The solution is based on the replacement of the spacelike Big Bang boundary with a null boundary behind which stays a chronology violating region. This solution requiring a tilting of the light cones near the null boundary is based more on the behavior of the light cones and hence on causality, than on the behavior of the scale factor (expansion). The philosophical connection of this picture with Augustine of Hyppo famous discussion on time and creation is commented
Spacetime Metrics from Gauge Potentials
No full textI present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S3 cosmological metric
Orthogonal polynomial method and odd vertices in matrix models
No full textWe show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them
What Is a Reasonable Spacetime? Some Remarks on the Hole-Free Condition
No full textThe notion of hole-free spacetime, initially introduced by Geroch, is reformulated, improved and commented. It is argued that any reasonable spacetime should satisfy it
The representation of spacetime through steep time functions
No full textIn a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid for globally hyperbolic Lorentzian spacetime
From causality to time and back
No full textIn this work the problem of the existence of a (semi-)time function on spacetime is investigated together with the problem of recovering the causal structure from the set of time functions allowed by the spacetime. These problems are solved thanks also to a mathematical
correspondence with utility theory
Further observations on the definition of global hyperbolicity under low regularity
No full textThe definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on Lorentzian length spaces and Lorentzian optimal transport, suggesting possible corrections for the terminology adopted in these works. It is found that in Kunzinger-Samann's Lorentzian length spaces the definition of global hyperbolicity coincides with that valid for closed cone structures and, more generally, for topological preordered spaces: the causal relation is a closed order and the causally convex hull operation preserves compactness. In particular, it is independent of the metric, chronological relation or Lorentzian distance
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