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In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the bifurcation problem (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know independently the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, all of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system. [ABSTRACT FROM AUTHOR]

We analyze the field equations for the perfect fluid solutions admitting a group G3 of isometries acting on orbits S2 whose curvature has a gradient that is tangent to the fluid flow (T-models). We propose several methods to integrate the field equations and we present the general solution without the need to calculate any integral. [ABSTRACT FROM AUTHOR]

The perfect fluid solution admitting a group G3 of isometries acting on orbits S2 whose curvature has a gradient which is tangent to the fluid flow (T-models) are studied from a thermodynamic approach. All the admissible thermodynamic schemes are obtained, and the solutions compatible with the generic ideal gas equation of state are studied in detail. The possible physical interpretation of some previously known T-models is also analyzed. [ABSTRACT FROM AUTHOR]

The constraints imposed by the relativistic compressibility hypothesis on the square of the speed of sound in a medium are obtained. This result allows us to obtain purely hydrodynamic conditions for the physical reality of a perfect energy tensor representing the energetic evolution of a perfect fluid in local thermal equilibrium. The results are applied to the paradigmatic case of the generic ideal gases. Then the physical reality of the ideal gas Stephani models is analyzed and the Rainich-like theory for ideal gas solutions is built. [ABSTRACT FROM AUTHOR]

The necessary and sufficient condition for a conservative perfect fluid energy tensor to be the energetic evolution of a classical ideal gas is obtained. This condition forces the square of the speed of sound to have the form c²s=γp/ρ+p in terms of the hydrodynamic quantities, energy density ρ and pressure p, γ being the (constant) adiabatic index. The inverse problem for this case is also solved, that is, the determination of all the fluids whose evolutions are represented by a conservative energy tensor endowed with the above expression of c²s, and it shows that these fluids are, and only are, those fulfilling a Poisson law. The relativistic compressibility conditions for the classical ideal gases and the Poisson gases are analyzed in depth and the values for the adiabatic index γ for which the compressibility conditions hold in physically relevant ranges of the hydrodynamic quantities ρ, p are obtained. Some scenarios that model isothermal or isentropic evolutions of a classical ideal gas are revisited, and preliminary results are presented in applying our hydrodynamic approach to looking for perfect fluid solutions that model the evolution of a classical ideal gas or of a Poisson gas. [ABSTRACT FROM AUTHOR]

We write the known invariant definition of the Szekeres-Szafron family of solutions in an intrinsic, deductive, explicit and algorithmic form. We also intrinsically characterize the two commonly considered subfamilies, and analyze other subclasses, also defined by first-order differential conditions. Furthermore, we present a Rainich-like approach to these metrics. [ABSTRACT FROM AUTHOR]

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the bifurcation problem (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know independently the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, all of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system. [ABSTRACT FROM AUTHOR]