In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski nn-space. First, obtain the first order ordinary differential equations which determine En1E1n according to causal characters their meridian curves. Then, by finding general solutions, get explicit parametrizations such loxodromes. particular, investigate right En1E1n. Finally, give an ex...

We consider a simplicial minisuperspace model based on a cone over the α4 triangulation of the 3−sphere, in the presence of a massive scalar field, φ, with arbitrary scalar coupling term ηRφ. By restricting all the interior edge lengths and all the boundary edge lengths to be equivalent and the scalar field to be homogenous on the 3−space, we obtain a two dimensional minisuperspace model {si, φ...

We investigate models of (1 + d)-D Lorentzian semi-random lattices with one random (space-like) direction and d regular (time-like) ones. We prove a general inversion formula expressing the partition function of these models as the inverse of that of hard objects in d dimensions. This allows for an exact solution of a variety of new models including critical and multicritical generalized (1 + 1...

We investigate string theory on Lorentzian AdS3 in the minisuperspace approximation. The minisuperspace model reduces to the worldline theory of a scalar particle in the Lorentzian AdS3. The Hilbert space consists of normalizable wave functions, and we see that the unitarity of the theory (or the self-adjointness of the Hamiltonian) restricts the possible sets of wave functions. The restricted ...

We prove an extension of the Index Theorem for Morse–Sturm systems of the form −V ′′ + RV = 0, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in a Lorentzian manifold, obtaining an extension of the Morse Index Theorem ...

We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory for the wave equation on singular space-times.

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

Let X be a smooth manifold of dimension 1 + n endowed with a Lorentzian metric g. The energy tensor of a 2-form F is locally defined as Tab := − ( Fa Fbi − 1 4 F Fijgab ) . In this paper we characterize this tensor as the only 2-covariant natural tensor associated to a Lorentzian metric and a 2-form that is independent of the unit of scale and satisfies certain condition on its divergence. This...

We study the exact construction of D-branes in Lorentzian AdS3. We start by defining a family of conformal field theories that gives a natural Euclidean version of the SL(2,R) CFT and does not correspond to H3 , the analytic continuation of AdS3. We argue that one can recuperate the exact CFT results of Lorentzian AdS3, upon an analytic continuation in the moduli space of these conformal field ...