Real sector of the nonminimally coupled scalar field to self-dual gravity

A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes non-polynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the constraints, an alternative method preventing the use of Dirac brackets, is discussed. It consists of converting all second class constraints into first class by adding extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the corrections to many misprints of v1 and also the ones of the published version. The conceptual and technical parts of the paper are not altere

A new look inside Planetary Nebula LoTr 5: A long-period binary with hints of a possible third component

LoTr 5 is a planetary nebula with an unusual long-period binary central star. As far as we know, the pair consists of a rapidly rotating G-type star and a hot star, which is responsible for the ionization of the nebula. The rotation period of the G-type star is 5.95 days and the orbital period of the binary is now known to be $\sim$2700 days, one of the longest in central star of planetary nebulae. The spectrum of the G central star shows a complex H$\alpha$ double-peaked profile which varies with very short time scales, also reported in other central stars of planetary nebulae and whose origin is still unknown. We present new radial velocity observations of the central star which allow us to confirm the orbital period for the long-period binary and discuss the possibility of a third component in the system at $\sim$129 days to the G star. This is complemented with the analysis of archival light curves from SuperWASP, ASAS and OMC. From the spectral fitting of the G-type star, we obtain a effective temperature of $T_{\rm eff}$ = 5410$\pm$250 K and surface gravity of $\log g$ = 2.7$\pm$0.5, consistent with both giant and subgiant stars. We also present a detailed analysis of the H$\alpha$ double-peaked profile and conclude that it does not present correlation with the rotation period and that the presence of an accretion disk via Roche lobe overflow is unlikely.Comment: 12 pages, 12 figures, accepted for publication in MNRA

Kepler-91b: a planet at the end of its life. Planet and giant host star properties via light-curve variations

The evolution of planetary systems is intimately linked to the evolution of their host star. Our understanding of the whole planetary evolution process is based on the large planet diversity observed so far. To date, only few tens of planets have been discovered orbiting stars ascending the Red Giant Branch. Although several theories have been proposed, the question of how planets die remains open due to the small number statistics. In this work we study the giant star Kepler-91 (KOI-2133) in order to determine the nature of a transiting companion. This system was detected by the Kepler Space Telescope. However, its planetary confirmation is needed. We confirm the planetary nature of the object transiting the star Kepler-91 by deriving a mass of $M_p=0.88^{+0.17}_{-0.33} ~M_{\rm Jup}$ and a planetary radius of $R_p=1.384^{+0.011}_{-0.054} ~R_{\rm Jup}$. Asteroseismic analysis produces a stellar radius of $R_{\star}=6.30\pm 0.16 ~R_{\odot}$ and a mass of $M_{\star}=1.31\pm 0.10 ~ M_{\odot}$. We find that its eccentric orbit ($e=0.066^{+0.013}_{-0.017}$) is just $1.32^{+0.07}_{-0.22} ~ R_{\star}$ away from the stellar atmosphere at the pericenter. Kepler-91b could be the previous stage of the planet engulfment, recently detected for BD+48 740. Our estimations show that Kepler-91b will be swallowed by its host star in less than 55 Myr. Among the confirmed planets around giant stars, this is the planetary-mass body closest to its host star. At pericenter passage, the star subtends an angle of $48^{\circ}$, covering around 10% of the sky as seen from the planet. The planetary atmosphere seems to be inflated probably due to the high stellar irradiation.Comment: 21 pages, 8 tables and 11 figure