Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects

A method to construct interior axially symmetric metrics that appropriately match with any vacuum solution of the Weyl family is developed in Hernandez-Pastora etal. (Class Quantum Gravity 33:235005, 2016). It was shown,for the case of some vacuum solutions, that the simplestsolution for the interior metric leads to sources with well behaved energy conditions. Now, we integrate the field equa-tions to obtain the interior metric functions in terms of theanisotropies and pressures of the source. As well, the compatible equations of state for these global models are calculated. The interior metric and the suitable energy momentum tensor describing the source are constructed in terms of the exterior metric functions. At the boundary of the compact object,the behaviour of a pressure Tm, defined from the energy momentum tensor, is shown to be related with the exterior gravitational field. This fact allows us to explore the differences arising at the matter distribution when the sphericalsymmetry of the global metric is dropped. Finally, an equation derived from the matching conditions is obtained whichallows us to calculate the Weyl coefficients of the exteriormetric as source integrals. Hence the Relativistic MultipoleMoments of the global model can be expressed in terms ofthe matter distribution of the source

Linearized multipole solutions and their representation

The monopole solution of the Einstein vacuum field equations (Schwarzschild`s solution) in Weyl coordinates involves a metric function that can be interpreted as the gravitational potential of a bar of length $2m$ with constant linear density. The question addressed in this work is whether similar representations can be constructed for Weyl solutions other than the spherically symmetric one. A new family of static solutions of the axisymmetric vacuum field equations generalizing the M-Q$^{(1)}$ solution is developed. These represent slight deviations from spherical symmetry in terms of the relativistic multipole moments (RMM) we wish the solution to contain. A Newtonian object referred to as a dumbbell can be used to describe these solutions in a simple form by means of the density of this object, since the physical properties of the relativistic solution are characterized by its behaviour. The density profile of the dumbbell, which is given in terms of the RMM of the solution, allows us to distinguish general multipole Weyl solutions from the constant-density Schwarzschild solution. The range of values of the multipole moments that generate positive-definite density profiles are also calculated. The bounds on the multipole moments that arise from this density condition are identical to those required for a well-behaved infinite-redshift surface $g_{00}=0$.Comment: 32 pages, 2 figure

On the Solutions of infinite systems of linear equations

New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these systems is solved and applied in the field of the General Relativity Theory of Gravitation. The solution of the system is used to construct a relevant physical representation of certain static and axisymmetric solution of the Einstein vacuum equations. In addition, a newtonian representation of these relativistic solutions is recovered. It is shown as well that there exists a relation between this application and the classical Haussdorff moment problem.Comment: Accepted for publication in General Relativity and Gravitatio

Digital Demodulator for BFSK waveform based upon Correlator and Differentiator Systems

The present article relates in general to digital demodulation of Binary Frequency Shift Keying (BFSK waveform) . New processing methods for demodulating the BFSK-signals are proposed here. Based on Sampler Correlator, the hardware consumption for the proposed techniques is reduced in comparison with other reported. Theoretical details concerning limits of applicability are also given by closed-form expressions. Simulation experiments are illustrated to validate the overall performance

Locating the critical end point using the linear sigma model coupled to quarks

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.Comment: 8 pages, 2 figures, conference paper from ISMD 201

Study of semileptonic and nonleptonic decays of the Bc−B_c^- meson

We evaluate semileptonic and two--meson nonleptonic decays of the $B_c^-$ meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one--body current operators at the quark level. Our model reproduces the constraints of heavy quark spin symmetry obtained in the limit of infinite heavy quark mass. For the two--meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches.Comment: Talk given at the IVth International Conference on Quarks an Nuclear Physics, Madrid, June 5th-10th 200

Photometry of the eclipsing cataclysmic variable SDSS J152419.33+220920.0

Aims. We present new photometry of the faint and poorly studied cataclysmic variable SDSS J152419.33+220920.0, analyze its light curve and provide an accurate ephemeris for this system. Methods. Time-resolved CCD differential photometry was carried out using the 1.5m and 0.84m telescopes at the Observatorio Astronomico Nacional at San Pedro Martir. Results. From time-resolved photometry of the system obtained during six nights (covering more than twenty primary eclipse cycles in more than three years), we show that this binary presents a strong primary and a weak secondary modulation. Our light curve analysis shows that only two fundamental frequencies are present, corresponding to the orbital period and a modulation with twice this frequency. We determine the accurate ephemeris of the system to be HJD(eclipse)= 2454967.6750(1) + 0.06531866661(1) E. A double-hump orbital period modulation, a standing feature in several bounce-back systems at quiescence, is present at several epochs. However, we found no other evidence to support the hypothesis that this system belongs to the post-minimum orbital-period systems