The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page

Short-range nuclear effects on axion emissivities by nucleon-nucleon bremsstrahlung

The rates of axion emission by nucleon-nucleon (NN) bremsstrahlung are reconsidered by taking into account the NN short range correlations. The analytical formulas for the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes with the inclusion of the full momentum dependence of an one- and two- pion exchange nuclear potentials, in the non-degenerate limit, are explicitly given. We find that the two-pion exchange (short range) effects can give a significant contribution to the emission rates, and are temperature dependent. Other short range nuclear effects like effective nucleon mass, polarization effects and use of correlated wave functions, are discused as well. The trend of all these nuclear effects is to diminish the corresponding axion emission rates. Further, we estimate that the values of the emission rates calculated with the inclusion of all these effects can differ from the corresponding ones derived with constant nuclear matrix elements by a factor of $\sim 24$. This leads to an uncertainty factor of $\sim 4.9$ when extracting bounds of the axion parametersComment: 11 pages, 4 figure

The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved

We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.Comment: 10 pages, 5 figure

Pion mass effects on axion emission from neutron stars through NN bremsstrahlung processes

The rates of axion emission by nucleon-nucleon bremsstrahlung are calculated with the inclusion of the full momentum contribution from a nuclear one pion exchange (OPE) potential. The contributions of the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes in both the nondegenerate and degenerate limits are explicitly given. We find that the finite momentum corrections to the emissivities are quantitatively significant for the non-degenerate regime and temperature-dependent, and should affect the existing axion mass bounds. The trend of these nuclear effects is to diminish the emissivities

High-energy black hole production

Black hole production in high-energy collisions is briefly surveyed. Included is a summary of recent developments and open problems relevant to collider (LHC) production, as well as of some theoretical issues pointing towards fundamental principles of quantum gravity.Comment: Talk at PASCOS 2007, to appear in the proceedings. v2: minor improvements, added refs. v3: reference correction. 11 pages, late

Spontaneous breaking of discrete symmetries in QCD on a small volume

In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C), spatial reflection (P) and time reversal (T) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show that a physical signature for the symmetry breaking is a persistent baryonic current wrapping in the compact directions. The existence of such a current is derived analytically at first order in perturbation theory and confirmed in the non-perturbative regime by lattice simulations.Comment: 4 pages, 2 figures, based on the poster presented by B. Lucini at Pascos 0

Shell-model calculations of two-neutrino double-beta decay rates of 48^{48}Ca with GXPF1A interaction

The two-neutrino double beta decay matrix elements and half-lives of $^{48}$Ca, are calculated within a shell-model approach for transitions to the ground state and to the $2^+$ first excited state of $^{48}$Ti. We use the full $pf$ model space and the GXPF1A interaction, which was recently proposed to describe the spectroscopic properties of the nuclei in the nuclear mass region A=47-66. Our results are $T_{1/2}(0^{+}\to 0^{+})$ = $3.3\times 10^{19}$ $yr$ and $T_{1/2}(0^{+}\to 2^{+})$ = $8.5\times 10^{23}$ $yr$. The result for the decay to the $^{48}$Ti 0$^+$ ground state is in good agreement with experiment. The half-life for the decay to the 2$^+$ state is two orders of magnitude larger than obtained previously.Comment: 6 pages, 4 figure