121207295
Spaces of positive and negative frequency solutions of field equations in curved space–times. II. The massive vector field equations in static space–times
The space–times considered in this article are static, Vn×R, with compact space‐section manifolds without boundary, Vn, and such that the trajectories of the Killing vector field are geodesics. For the physical field of spin 1 and mass m≳0 in these space–times, field equations are solved in any adapted atlas, by the one‐parameter groups of unitary operators generated by scalar and vector Hamiltonians, i−1Tj−1, j=0,1, in Sobolev spaces Hjl−1(Vn) ×Hjl 1(Vn), leR. Hilbert spaces of positive energy solutions of field equations, as well as those of reduced solutions and their canonical symplectic and complex structures, are determined. The existence and the uniqueness of Lichnerowicz’s (1−1) current on space–time are established, and the corresponding frequency‐solution Hilbert spaces are constructed. Within the framework of Segal, a definition of quantum field operators is given, leading to the postulated commutator for the physical field concerned.
119721670
On quantization of free fields in stationary space-times
In Section 1 we analyse the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections; we give an existence and uniqueness theorem for the Lichnerowicz distribution kernelG1 together with its proper Fourier expansion, and we construct the Hilbert spaces of frequency-part solutions defined by means ofG1.In Section 2 an analysis, a theorem and a construction similar to the above are formulated for thefree real field spin 1, massm>0, in one kind of static space-times.In this letter, only results are given. For detailed proofs and further results, see reference [9], [10] and [11].
121404671
Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times
In stationary space–times Vn×R with compact space‐section manifold without boundary Vn, the Klein–Gordon equation is solved by the one‐parameter group of unitary operators generated by the energy operator i−1T−1 in the Sobolev spaces Hl(Vn) ×Hl−1(Vn). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency‐part solutions defined by means of this kernel are constructed.
15903445
GRAVITATIONAL PERTURBATIONS OF THE KERR BLACK HOLE DUE TO ARBITRARY SOURCES
We describe the Kerr black hole in the ingoing and outgoing Kerr–Schild horizon penetrating coordinates. Starting from the null vector naturally defined in these coordinates, we construct the null tetrad for each case, as well as the corresponding geometrical quantities allowing us to explicitly derive the field equations for the perturbed scalar projections Ψ0(1) and Ψ4(1) of the Weyl tensor, including arbitrary source terms. This perturbative description, including arbitrary sources, described in horizon penetrating coordinates is desirable in several lines of research on black holes, and contributes to the implementation of a formalism aimed to study the evolution of the spacetime in the region where two black holes are close together.
119252183
Gravitational waves during inflation from a 5D large-scale repulsive gravity model
Abstract We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during the early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild–de Sitter metric on cosmological scales. This metric is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza–Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that it is possible to derive the dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity–antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.
30618258
Present accelerated expansion of the universe from new Weyl-integrable gravity approach
We investigate if a recently introduced formulation of general relativity on a Weyl-integrable geometry contains cosmological solutions exhibiting acceleration in the present cosmic expansion. We derive the general conditions to have acceleration in the expansion of the universe and obtain a particular solution for the Weyl scalar field describing a cosmological model for the present time in concordance with the data combination Planck + WP + BAO + SN.
121636708
Topological origin of the coupling constants hierarchy in Kaluza-Klein approach
We consider an Abelian BF-model in the frame of ten-dimensional Kaluza–Klein approach on the space T2×X×M, where X belongs to the class of four-dimension decorated plumbed cobordisms (dp-cobordisms) and M is an An-1-singularity resolution manifold homeomorphic to a compactified ALE space. These four-dimensional manifolds with boundaries possess nontrivial cohomology properties that lead to a specific generalization of the Dirac quantization conditions and enables us to express classical partition functions in terms of 4-form fluxes through the direct product of nontrivial 2-cycles associated with the manifolds X and M. The intersection matrices of these manifolds play the role of coupling constants for the fluxes. We build several examples of dp-cobordisms containing in their intersection matrices the hierarchy of dimensionless low-energy coupling constants of interactions which are available in the real universe. We also consider the phenomenon of "running coupling constants," in particular the cosmological constant evolution induced by the topology changes of internal space X.
119111308
Gravitational waves from scalar field accretion
Our aim in this work is to outline some physical consequences of the interaction between black holes and scalar field halos in terms of gravitational waves. In doing so, the black hole is taken as a static and spherically symmetric gravitational source, {\it i. e.} the Schwarzschild black hole, and we work within the test field approximation, considering that the scalar field lives in the curved space-time outside the black hole. We focused on the emission of gravitational waves when the black hole is perturbed by the surrounding scalar field matter. The symmetries of the spacetime and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one dimensional description. Some properties of such gravitational waves are discussed as a function of the parameters of the infalling scalar field, and allow us to make the conjecture that the gravitational waves carry information on the type of matter that generated them.