Near-horizon modes and self-adjoint extensions of the Schroedinger operator

We investigate the dynamics of scalar fields in the near-horizon exterior region of a Schwarzschild black hole. We show that low-energy modes are typically long-living and might be considered as being confined near the black hole horizon. Such dynamics are effectively governed by a Schroedinger operator with infinitely many self-adjoint extensions parameterized by $U(1)$, a situation closely resembling the case of an ordinary free particle moving on a semiaxis. Even though these different self-adjoint extensions lead to equivalent scattering and thermal processes, a comparison with a simplified model suggests a physical prescription to chose the pertinent self-adjoint extensions. However, since all extensions are in principle physically equivalent, they might be considered in equal footing for statistical analyses of near-horizon modes around black holes. Analogous results hold for any non-extremal, spherically symmetric, asymptotically flat black hole.Comment: 10 pages, 1 fig, contribution submitted to the volume "Classical and Quantum Physics: Geometry, Dynamics and Control. (60 Years Alberto Ibort Fest)" Springer (2018

Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Plank "constant" is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.Comment: 29 pages, latex, no figures. New Section on semiclassical limit of wave equation added; old references rearranged; new references, remarks, comments, and acknowledgments added; typos correcte

On the renormalization of the electroweak chiral Lagrangian with a Higgs

We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral expansion. The complete off-shell renormalization procedure is implemented, including one loop corrections stemming from the leading two-derivative terms, for finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. Furthermore, new counterterms involving the Higgs particle which are apparently chiral non-invariant are identified in the perturbative analysis. A novel general parametrization of the pseudoescalar field redefinitions is proposed, which reduces to the various usual ones for specific values of its parameter; the non-local field redefinitions reabsorbing all chiral non-invariant counterterms are then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.Comment: 9 pages, 6 figures, final version to appear in PR

Stability aspects of relativistic thin magnetized disks

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA E DESENVOLVIMENTO DO ESTADO DE SÃO PAULOWe adapt the well-known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely supported by surface polar currents on the disk. Our starting point is the Gutsunaev-Manko axisymmetric solution describing massive magnetic dipoles in general relativity, from which we obtain a continuous three-parameter family of asymptotically flat static magnetized disks with finite mass and energy. For strong magnetic fields, the disk surface density profile resembles some well-known self-gravitating ringlike structures. We show that many of these solutions can be indeed stable and, hence, they could be in principle useful for the study of the abundant astrophysical situations involving disks of matter and magnetic fields9512110CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA E DESENVOLVIMENTO DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA E DESENVOLVIMENTO DO ESTADO DE SÃO PAULOsem informaçãoE-26/200.279/2015 , 2013/09357-

Quantum dynamics of non-relativistic particles and isometric embeddings

It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where M has been assumed to be a hypersurface of $R^{d+1}$. We show, contrary to recent claims, that constrained systems theory does not contribute to the elimination of the ambiguities present in the canonical and path integral formulations of the problem. These discrepancies with recent works are discussed.Comment: Revtex, 14 page

Neutron star in presence of torsion-dilaton field

We develop the general theory of stars in Saa's model of gravity with propagating torsion and study the basic stationary state of neutron star. Our numerical results show that the torsion force decreases the role of the gravity in the star configuration leading to significant changes in the neutron star masses depending on the equation of state of star matter. The inconsistency of the Saa's model with Roll-Krotkov-Dicke and Braginsky-Panov experiments is discussed.Comment: 29 pages, latex, 24 figures, final version. Added: 1)comments on different possible mass definitions; 2)new sections: a)the inconsistency of the Saa's model with Roll-Krotkov-Dicke and Braginsky-Panov experiments; b)stability analysis via catastrophe theory; 3)new figers added and some figures replaced. 4)new reference

Quantum effects and superquintessence in the new age of precision cosmology

Recent observations of Type Ia supernova at high redshifts establish that the dark energy component of the universe has (a probably constant) ratio between pressure and energy density $w=p/\rho=-1.02(^{+0.13}_{-0.19})$. The conventional quintessence models for dark energy are restricted to the range $-1\le w < 0$, with the cosmological constant corresponding to $w=-1$. Conformally coupled quintessence models are the simplest ones compatible with the marginally allowed superaccelerated regime ($w<-1$). However, they are known to be plagued with anisotropic singularities. We argue here that the extension of the classical approach to the semiclassical one, with the inclusion of quantum counterterms necessary to ensure the renormalization, can eliminate the anisotropic singularities preserving the isotropic behavior of conformally coupled superquintessence models. Hence, besides of having other interesting properties, they are consistent candidates to describe the superaccelerated phases of the universe compatible with the present experimental data.Comment: 7 pages. Essay selected for "Honorable Mention" in the 2004 Awards for Essays on Gravitation, Gravity Research Foundatio

A note on a third order curvature invariant in static spacetimes

We consider here the third order curvature invariant $I=R_{\mu\nu\rho\sigma;\delta}R^{\mu\nu\rho\sigma;\delta}$ in static spacetimes ${\cal M}=R\times\Sigma$ for which $\Sigma$ is conformally flat. We evaluate explicitly the invariant for the $N$-dimensional Majumdar-Papapetrou multi black-holes solution, confirming that $I$ does indeed vanish on the event horizons of such black-holes. Our calculations show, however, that solely the vanishing of $I$ is not sufficient to locate an event horizon in non-spherically symmetric spacetimes. We discuss also some tidal effects associated to the invariant $I$.Comment: 5 pages, 3 figures. Extra material available at http://vigo.ime.unicamp.br/in