1,721,071 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
Weak distinction and the optimal definition of causal continuity
No full textCausal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can actually replace distinction in the definition of causal continuity. An intermediate proof shows that feeble distinction and future (past) reflectivity imply past (resp. future) distinction. Some new characterizations of weak distinction and reflectivity are given
Rayleigh's dissipation function at work
No full textIt is shown that the Rayleigh's dissipation function can be successfully applied in the solution of mechanical problems involving friction non-linear in the velocities. Through the study of surfaces at contact we arrive at a simple integral expression which gives directly the Rayleigh dissipation function in terms of generalized coordinates. In this way the solutions of Lagrangian problems with friction are reduced to often elementary calculations of the kinetic energy, the potential energy and the Rayleigh dissipation function. Some examples of pedagogical interest are given
THE CONNECTIONS OF PSEUDO-FINSLER SPACES
No full textWe give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self-contained proofs. Our study of the Berwald nonlinear connection is framed into the theory of connections over general fibered spaces pioneered by Mangiarotti, Modugno and other scholars. The main identities for the linear Finsler connection are presented in the general case, and then specialized to some notable cases like Berwald’s, Cartan’s or Chern–Rund’s. In this way it becomes easy to compare them and see the advantages of one connection over the other. Since we introduce two soldering forms we are able to characterize the notable Finsler connections in terms of their torsion properties. As an application, the curvature symmetries implied by the compatibility with a metric suggest that in Finslerian generalizations of general relativity the mean Cartan torsion vanishes. This observation allows us to obtain dynamical equations which imply a satisfactory conservation law. The work ends with a discussion of yet another Finsler connection which has some advantages over Cartan’s and Chern–Rund’s
The vacuum conservation theorem
No full textA version of the vacuum conservation theorem is proved which does not assume the existence of a time function nor demands stronger properties than the dominant energy condition. However, it is shown that a stronger stable version plays a role in the study of compact Cauchy horizons
On the global existence of time
No full textQuesto saggio è arrivato terzo al concorso "The nature of time" bandito dal Foundational Questions Institute (FQXi
An equivalence of Finslerian relativistic theories
No full textIn Lorentz-Finsler geometry it is natural to define the Finsler Lagrangian over a cone (Asanov's approach) or over the whole slit tangent bundle (Beem's approach). In the former case one might want to add differentiability conditions at the boundary of the (timelike) cone in order to retain the usual definition of lightlike geodesics. It is shown here that if this is done then the two theories coincide, namely the `conic' Finsler Lagrangian is the restriction of a slit tangent bundle Lagrangian. Since causality theory depends on curves defined through the future cone, this work establishes the essential uniqueness of (sufficiently regular) Finsler spacetime theories and Finsler causality
Completeness of first and second order ODE flows and of Euler–Lagrange equations
No full textTwo results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to Lagrangian mechanics and gravitational waves are given
- …
