10 research outputs found
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
Mathematical Support to Braneworld Theory
The braneworld theory appear with the purpose of solving the problem of the
hierarchy of the fundamental interactions. The perspectives of the theory
emerge as a new physics, for example, deviation of the law of Newton's gravity.
One of the principles of the theory is to suppose that the braneworld is local
submanifold in a space of high dimension, the bulk, solution of Einstein's
equations in high dimension. In this paper we approach the mathematical
consistency of this theory with a new proof of the fundamental theorem of
submanifolds for case of semi-Riemannian manifolds. This theorem consist an
essential mathematical support for this new theory. We find the integrability
conditions for the existence of space-time submanifolds in a pseudo-Euclidean
space.
Keywords: Submanifolds, Braneworld, Pseudo-Riemannian geometryComment: 10 page
What is the topology of a Schwarzschild black hole?
We investigate the topology of Schwarzschild's black hole through the
immersion of this space-time in spaces of higher dimension. Through the
immersions of Kasner and Fronsdal we calculate the extension of the
Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with
arXiv:1102.446
The Embedding of Schwarzschild in Braneworld
The braneworlds models were inspired partly by Kaluza-Klein's theory, where
both the gravitational and the gauge fields are obtained from the geometry of a
higher dimensional space. The positive aspects of these models consist in
perspectives of modifications it could bring in to particle physics, such as:
unification in a TeV scale, quantum gravity in this scale and deviation of
Newton's law for small distances. One of the principles of these models is to
suppose that all space-times can be embedded in a bulk of higher dimension. The
main result in these notes is a theorem showing a mathematical inconsistency of
the Randall-Sundrum braneworld model, namely that the Schwarzschild space-time
cannot be embedded locally and isometrically in a five dimensional bulk with
constant curvature,(for example AdS-5). From the point of view of
semi-Riemannian geometry this last result represents a serious restriction to
the Randall-Sundrum's braneworld model.Comment: Published in the Int. J. Theor. Phys, 200
Geometry of Brane-Worlds
The most general geometrical scenario in which the brane-world program can be
implemented is investigated. The basic requirement is that it should be
consistent with the confinement of gauge interaction, the existence of quantum
states and the embedding in a bulk with arbitrary dimensions, signature and
topology.
It is found that the embedding equations are compatible with a wide class of
Lagrangians, starting with a modified Einstein-Hilbert Lagrangian as the
simplest one, provided minimal boundaries are added to the bulk.
A non-trivial canonical structure is derived, suggesting a canonical
quantization of the brane-world geometry relative to the extra dimensions,
where the quantum states are set in correspondence with high frequency
gravitational waves. It is shown that in the cases of at least six dimensions,
there exists a confined gauge field included in the embedding structure. The
size of extra dimensions compatible with the embedding is calculated and found
to be different from the one derived with product topology.Comment: Minor changes and a correction to equation (22). 9 pages twocolumn
Revte
The Deformable Universe
The concept of smooth deformations of a Riemannian manifolds, recently
evidenced by the solution of the Poincar\'e 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.Comment: 20 pages, LaTeX, 3 figure
The accelerating universe in brane-world cosmology
The standard Friedmann universe embedded in a five dimensional and constant
curvature bulk is examined without any a priori junction condition between the
brane and the bulk. A geometrical explanation for the accelerated expansion of
the universe is derived by using a minimum set of assumptions consistent with
the brane-world program. It is shown that the extrinsic curvature of the brane
can be associated to the dark energy which presumably drives the universe
expansion.Comment: Revtex, 4 page