On spectral types of semialgebraic sets

In this work we prove that a semialgebraic set $M\subset{\mathbb R}^m$ is determined (up to a semialgebraic homeomorphism) by its ring ${\mathcal S}(M)$ of (continuous) semialgebraic functions while its ring ${\mathcal S}^*(M)$ of (continuous) bounded semialgebraic functions only determines $M$ besides a distinguished finite subset $\eta(M)\subset M$. In addition it holds that the rings ${\mathcal S}(M)$ and ${\mathcal S}^*(M)$ are isomorphic if and only if $M$ is compact. On the other hand, their respective maximal spectra $\beta_s M$ and $\beta_s^* M$ endowed with the Zariski topology are always homeomorphic and topologically classify a `large piece' of $M$. The proof of this fact requires a careful analysis of the points of the remainder $\partial M:=\beta_s^* M\setminus M$ associated with formal paths.Comment: 22 page

On gauge invariant regularization of fermion currents

We compare Schwinger and complex powers methods to construct regularized fermion currents. We show that although both of them are gauge invariant they not always yield the same result.Comment: 10 pages, 1 figur

An alternative well-posedness property and static spacetimes with naked singularities

In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular time-like boundary is well posed, if we only demand the waves to have finite energy, although no boundary condition is required. This feature does not come from essential self-adjointness, which is false in these cases, but from a different phenomenon that we call the alternative well-posedness property, whose origin is due to the degeneracy of the metric components near the boundary. Beyond these examples, in the second part, we characterize the type of degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra

Motion and Trajectories of Particles Around Three-Dimensional Black Holes

The motion of relativistic particles around three dimensional black holes following the Hamilton-Jacobi formalism is studied. It follows that the Hamilton-Jacobi equation can be separated and reduced to quadratures in analogy with the four dimensional case. It is shown that: a) particles are trapped by the black hole independently of their energy and angular momentum, b) matter alway falls to the centre of the black hole and cannot understake a motion with stables orbits as in four dimensions. For the extreme values of the angular momentum of the black hole, we were able to find exact solutions of the equations of motion and trajectories of a test particle.Comment: Plain TeX, 9pp, IPNO-TH 93/06, DFTUZ 93/0

Proper Polynomial Maps - The Real Case

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu