arXiv subjects
Publications and source records attributed to M. D. Maia.
We present an updated review of Kraichnan's derivation of Einstein's equations from quantum field theory, including the period after the discovery of the Higgs mechanism. Gravitation in the Einstein sense is seen to be renormalizable and consistent with the Standard Model of Fundamental Interactions.
Using the observational properties of Einstein's gravitational field it is shown that a minimum of four non-coplanar mass probes are necessary for the Michelson and Morley interferometer to detect gravitational waves within the context of General Relativity. With fewer probes, some alternative theories of gravitation can also explain the observations. The conversion of the existing gravitational wave detectors to four probes is also suggested.
Based on the Szekeres-Pirani gravitational compass we suggest the addition of a fourth, non-coplanar mass/mirror to the presently existing laser based gravitational wave observatories, enabling them to operate omnidirectionally, to filter out ambiguous interpretations and to point out the direction of the gravitational wave source.
The Cauchy-Kowalevski theorem is applied to the solutions of Einstein's equations and to cosmology. Three fundamental requirements of the theorem: the use of analytic series; the existence of the boundary surfaces; and the setting of the independent initial data are revised, using methods of geometric analysis. It is shown that during its relativistic phase, the standard model of the universe is governed by Einstein's gravitation described as a massless spin-2 field, but it is necessarily complemented by massive spin-2 field, which responds for the dark sector of the universe. On the other hand, at the inflationary phase, the exponential growth of the volume of the universe is shown to be consistent with a thermal, non-relativistic expansion. These two phases are separated by the last inflationary surface.
The non-Abelian Kaluza-Klein unification of gravitation with gauge fields theory is reformulated, with the inclusion of a massive spin-2 field defined by the extrinsic curvature. The internal space is non-compact, characterized by the group of rotations of vectors orthogonal to the space-time. The non-compactness of the internal space warrants the solution of the fermion chirality problem of the original Kaluza-Klein theory and makes it closer to the more recent Brane World paradigm, in special to the so called DGP model. However, the access of gravitation to the extra dimensions is defined by the mentioned massive spin-2 field obeying the Fierz-Pauli equation. The existence of a short range gravitational component makes possible to apply the modified Kaluza-Klein unification to the Tev scale of energies.
It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes appear in General Relativity and how it leaves an observable footprint in space-time. In cosmology we show that such topological observable is the cosmic radiation produced by the acceleration of the universe. The cosmological constant is a very particular case which occurs when the expansion of the universe into the vacuum occurs only in the direction of the cosmic time flow.
The topological structure of Schwarzschild's space-time and its maximal analytic extension are investigated in context of brane-worlds. Using the embedding coordinates, these geometries are seen as different states of the evolution of a single brane-world. Comparing the topologies and the embeddings it is shown that this evolution must be followed by a signature change in the bulk.
The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown that space-times are deformable in the sense of local change of shape. These deformations leave an observable signature in the space-time, characterized by a conserved tensor, associated with a tangent acceleration, defined by the extrinsic curvature of the space-time. In the applications to cosmology, we find that the accelerated expansion of the universe is the observable effect of the deformation, dispensing with the cosmological constant and its problems.
The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincaré conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.
Coalescing binary systems (eg pulsars, neutron stars and black holes) are the most likely sources of gravitational radiation, yet to be detected on or near Earth, where the local gravitational field is negligible and the Poincaré symmetry rules. On the other hand, the general theory of gravitational waves emitted by axially symmetric rotating sources predicts the existence of a non-vanishing news function. The existence of such function implies that, for a distant observer, the asymptotic group of isometries, the BMS group, has a translational symmetry that depends on the orbit periodicity of the source, thus breaking the isotropy o the Poincaré translations. These results suggest the application of the asymptotic BMS-covariant wave equation to obtain a proper theoretical basis for the gravitational waves observations.
Until recently the study of the gravitational field of dark matter was primarily concerned with its local effects on the motion of stars in galaxies and galaxy clusters. On the other hand, the WMAP experiment has shown that the gravitational field produced by dark matter amplifies the higher acoustic modes of the CMBR power spectrum, more intensely than the gravitational field of baryons. Such a wide range of experimental evidences from cosmology to local gravity suggests the necessity of a comprehensive analysis of the dark matter gravitational field per se, regardless of any other attributes that dark matter may eventually possess. In this paper we introduce and apply Nash's theory of perturbative geometry to the study of the dark matter gravitational field alone, in a higher-dimensional framework. It is shown that the dark matter gravitational perturbations in the early universe can be explained by the extrinsic curvature of the standard cosmology. Together with the estimated presence of massive neutrinos, such geometric perturbation is compatible not only with the observed power spectrum in the WMAP experiment but also with the most recent data on the accelerated expansion of the universe. It is possible that the same structure formation exists locally, such as in the cases of young galaxies or in cluster collisions. In most other cases it seems to have ceased when the extrinsic curvature becomes negligible, leading to Einstein's equations in four dimensions. The slow motion of stars in galaxies and the motion of plasma substructures in nearly colliding clusters are calculated with the geodesic equation for a slowly moving object in a gravitational field of arbitrary strength.
It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a justification for quaternion quantum gravity at the Tev energy scale.
General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily conceived. On the other hand, experimental evidences show that there exists a non-zero cosmological constant, which implies in a deSitter space-time, not compatible with the assumed Minkowski structure. Such inconsistency is shown to be a consequence of the lack of a application independent curvature standard in Riemann's geometry, leading eventually to the cosmological constant problem in general relativity. We show how the curvature standard in Riemann's geometry can be fixed by Nash's theorem on locally embedded Riemannian geometries, which imply in the existence of extra dimensions. The resulting gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than being a a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity is a gravitational contribution which propagates in the extra dimensions. Therefore, the comparison between the vacuum energy and the cosmological constant in general relativity ceases to be. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.
The acceleration of the universe is described as a dynamical effect of the extrinsic curvature of space-time. By extending previous results, the extrinsic curvature is regarded as an independent spin-2 field, determined by a set of non-linear equations similar to Einstein's equations. In this framework, we investigate some cosmological consequences of this class of scenarios and test its observational viability by performing a statistical analysis with current type Ia Supernova data.
The cosmological constant problem is seen as a symptom of the ambiguity of the Riemann curvature in general relativity. The solution of that ambiguity provided by Nash's theorem on gravitational perturbations along extra dimensions eliminate the direct comparison between the vacuum energy density and Einstein's cosmological constant, besides being compatible with the formation of structures and the accelerated expansion of the universe.
The eventual production of mini black holes by proton-proton collisions at the LHC is predicted by theories with large extra dimensions resolvable at the Tev scale of energies. It is expected that these black holes evaporate shortly after its production as a consequence of the Hawking radiation. We show that for theories based on the ADS/CFT correspondence, the produced black holes may have an unstable horizon, which grows proportionally to the square of the distance to the collision point.
The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.
The dark matter constraint imposed by the recent WMAP experiment on gravitational theories is analyzed. Using the non-linearity of the vacuum Einstein's equations, it is shown that when the slow motion condition is applied to the geodesic equations, the resulting nearly Newtonian gravitational field describes nearly flat velocity curves for rotating stars in the vicinity of thin disk galaxies.