Juan Antonio Morales

Two-dimensional approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.

Covariant determination of the Weyl tensor geometry

We give a covariant and deductive algorithm to determine, for every Petrov type, the geometric elements associated with the Weyl tensor: principal and other characteristic 2-forms, Debever null directions and canonical frames. We show the usefulness of these results by applying them in giving the explicit characterization of two families of metrics: static type I spacetimes and type III metrics with a hypersurface-orthogonal Killing vector. PACS numbers: 0240M, 0420C

Intrinsic characterization of space-time symmetric tensors

This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.

Two-perfect fluid interpretation of an energy tensor

The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained.

Symmetric frames on Lorentzian spaces

Symmetric frames (those whose vectors are metrically indistinguishable) are studied both, from the algebraic and differential points of view. Symmetric frames which, in addition, remain indistinguishable for a given set of concomitants of the metric are analyzed, and the necessary and sufficient conditions for a space‐time to admit them are given. A new version of the cosmological principle then follows. Natural symmetric frames (induced by local charts) are also considered, and the space‐times admitting them are obtained.

199 Causal Classes of Space-Time Frames

It is shown that from the causal point of view Minkowskian space-time admits 199, and only 199, different classes of frames.

A kinematic method to obtain conformal factors

Radial conformal motions are considered in conformally flat space–times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson–Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi–Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson–Walker space–times.

Comments on space–time signature

In terms of three signs associated to two vectors and to a 2‐plane, a formula for the signature of any four‐dimensional metric is given. In the process, a simple expression for the sign of the Lorentzian metric signature is obtained. The relationship between these results and those already known are commented upon.

Radial conformal motions in Minkowski space–time

A study of radial conformal Killing fields (RCKF) in Minkowski space–time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.

Emission coordinates in Minkowski space‐time

The theory of relativistic positioning systems and their natural associated emission coordinates are essential ingredients in the analysis of navigation systems and astrometry. Here we study emission coordinates in Minkowski space‐time. For any choice of the four emitters (arbitrary space‐time trajectories) the relation between the corresponding emission coordinates and the inertial ones are explicitly given.