On the Stability of Black Holes at the LHC

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.Comment: 3 page

Applications of Nash's Theorem to Cosmology

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.Comment: 7 pages, Latex 0ne figure, Talk Presented at the II Indo-Brazilian Workshop on Gravitation and Cosmolog

On The Topological Nature of the Cosmological Constant

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.Comment: 5 pages Latex no figure

Cosmology of Spin-2 Fields

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.Comment: 9 pages, no figures, Latex. Several typos were corrected, some arguments have been simplified, new references and one acknowledgement adde

Brane-worlds and Cosmology

The Friedmann equation for a FRW-brane-world in a flat bulk is derived and applied to the accelerated expansion of the universe.Comment: Essay in honor of Mario Novello, 8 pages, latex. Typo correcte

Cosmology and Gravitation: Summary talk at the XXIV Brazilian Meeting on Particles and Fields

This is a brief summary with comments on selected contributions to the Cosmology and Gravitation section at the $24^{th}$ Brazilian Meeting on Particle and Fields (ENFPC XXIV), held at Caxambu, from September 30 to October 4, 2003.Comment: 7 pages, no figures, revtex 4. Brazilian Journal of Physics (to appear 2004

Spin and Isospin in Quaternion Quantum Mechanics

The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The latter corresponds to a vector boson in space-time, interpreted as a SU(2) gauge field. The existence of quaternionic spinor fields implies in a quaternionic Hilbert space and its necessary mathematical analysis. It is shown how to obtain a unique representation of a quaternion function by a convergent positive power series.Comment: 7 pages revte

Estimating the index of summability of pairs of Banach spaces

Let $E_{1},...,E_{m},F$ be Banach spaces. The index of summability of $\left(E_{1}\times\cdots\times E_{m},F\right)$ is a kind of measure of how far the $m$-linear operators $T:E_{1}\times\cdots\times E_{m}\rightarrow F$ are from being multiple summing. In this paper we estimate the index of summability of several pairs of Banach spaces$.

Covariant Analysis of Experimental Constraints on the Brane-world

Some observational constraints on the brane-world based on predictions from specific models in five dimensions, have been recently reported, both on local and cosmological scales. In order to identify the origins of these constraints, the equations of motion of the brane-world are translated to the most general, model-independent (or "covariant"), formulation of the theory, based only on the Einstein-Hilbert action for the bulk geometry, the confinement of the standard gauge interactions and the exclusive probing of the extra dimensions by the gravitational field. In the case of the binary pulsar PSR1913+16, it is found that gravi-vectors and gravi-scalars do not appear in the covariant equations, but they are replaced by vector and scalar fields related to the extrinsic curvature of the brane-world. Only the latter one impose a condition on the binary pulsar orbits. A general solution for this problem is proposed, based on results from differential geometry, suggesting a stable bulk geometry, whose existence requires higher dimensions. On the cosmological scale, it is shown that the high energy inflation constraint originating from the square of the energy density term in the modified Friedman's equation is mainly due to the assumption of the reflection symmetry across the brane-world. It is shown that this symmetry is not consistent with the regularity of the brane-world. These results suggest that the two constraints can be lifted by increasing the number of extra dimensions.Comment: Six pages, revtex4, no figures, Added references, typos corrected, one co-author added, improved abstract, introduction, better derivation of the covariant equations and a longer discussion on Z_2 symmetry. Better pdf output. Have a look

The Signature Problem for Embedded Space-times

The compatibility between the general relativity and the mathematical property that the space-times are embedded manifolds are further examined. In particular we study the uniqueness of the signature of the embedding space for a given space-time. The interpretation of the twisting vector as a gauge potential is also implemented.Comment: 13 pages, Late