Searcharxiv⌕ Search

arXiv subjects

Joan Josep Ferrando

Publications and source records attributed to Joan Josep Ferrando.

49 records · Page 3Linked to original sources

On Newtonian frames

In Newtonian space-time there exist four, and only four, causal classes of frames. Natural frames allow to extend this result to coordinate systems, so that coordinate systems may be also locally classified in four causal classes. These causal classes admit simple geometric descriptions and physical interpretations. For example, one can generate representatives of the four causal classes by means of the {\em linear synchronization group}. Of particular interest is the {\em local Solar time synchronization}, which reveals the limits of the frequent use of the concept of `causally oriented oordinate', such as that of `time-like coordinate'. Classical {\em positioning systems}, based in sound or light signals, are, by themselves, interesting examples of location systems, i.e. of physically constructible coordinate systems. They show that one can locate events in Newtonian space-time {\em without} any use of the concept of synchronization. In fact, the coordinate systems associated to positioning systems, belong to all the classes but the standard one, i.e. the one based in the simultaneity synchronization. The relativistic analogs of these examples, emphasize the contrast between the four Newtonian and the one hundred and ninety nine Lorentzian causal classes of frames of classical and relativistic space-times, respectively.

gr-qc↗

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

gr-qc↗

Positioning with stationary emitters in a two-dimensional space-time

The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called {\em emission coordinates}, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out.

gr-qc↗

On the geometry of Killing and conformal tensors

The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type D solutions is offered. A generalization of these results to a wider family of type D space-times is also obtained. A generalization of these results to a wider family of type D space-times is also obtained.

gr-qc↗

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.

gr-qc↗

Coll Positioning systems: a two-dimensional approach

The basic elements of Coll positioning systems (n clocks broadcasting electromagnetic signals in a n-dimensional space-time) are presented in the two-dimensional case. This simplified approach allows us to explain and to analyze the properties and interest of these relativistic positioning systems. The positioning system defined in flat metric by two geodesic clocks is analyzed. The interest of the Coll systems in gravimetry is pointed out.

gr-qc↗

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $Ψ_2^T$, $Ψ_0^T$ and $Ψ_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.

gr-qc↗

Local thermal equilibrium and ideal gas Stephani universes

The Stephani universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined. Five classes of thermodynamic schemes are admissible, which give rise to five classes of regular models and three classes of singular models. No Stephani universes exist representing an exact solution to a classical ideal gas (one for which the internal energy is proportional to the temperature). But some Stephani universes may approximate a classical ideal gas at first order in the temperature: all of them are obtained. Finally, some features about the physical behavior of the models are pointed out.

gr-qc↗

Physics of Relativistic Perfect Fluids

A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. This criterion is applied to the class II Szafron-Szekeres perfect fluid space-times solutions, giving a very simple characterization of those that describe such thermal evolutions. For all of them, the significant thermodynamic variables are explicitly obtained. Also, the specific condition is given under which the divergence-free perfect fluid energy tensors may be interpreted as an ideal gas.

gr-qc↗

On the thermodynamics of inhomogeneous perfect fluid mixtures

It is shown that inhomogeneous Szekeres and Stephani universes exist corresponding to non-dissipative binary mixtures of perfect fluids in local thermal equilibrium. This result contradicts a recent statement by Zárate and Quevedo (2004 Class. Quantum Grav. {\bf 21} 197, {\it Preprint} gr-qc/0310087), which affirms that the only Szekeres and Stephani universes compatible with these fluids are the homogeneous Friedmann-Robertson-Walker models. Thus, contrarily to their conclusion, their thermodynamic scheme do not gives new indications of incompatibility between thermodynamics and relativity. Two of the points that have generated this error are commented.

gr-qc↗

Ideal Gas Stephani Universes

The Stephani Universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined, and the method to obtain the associated thermodynamic schemes is given

gr-qc↗

On the Leibniz bracket, the Schouten bracket and the Laplacian

The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them, is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.

gr-qc↗