On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics

de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium.Comment: 18 pages latex, 1 figur

Exact solution for the interior of a black hole

Within the Relativistic Theory of Gravitation it is shown that the equation of state $p=\rho$ holds near the center of a black hole. For the stiff equation of state $p=\rho-\rho_c$ the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range beyond the horizon. The solution is regular everywhere, with a specific shape at the origin. The gravitational redshift at the horizon remains finite but is large, $z\sim 10^{23}$$M_\odot/M$. Time keeps its standard role also in the interior. The energy of the Schwarzschild metric, shown to be minus infinity in the General Theory of Relativity, is regularized in this setup, resulting in $E=Mc^2$.Comment: 12 pages newFNLstyle. 4 figure

Explanation of the Helium-3 problem

One of the tests of nucleosynthesis theory is the $^3$He abundance in the Galaxy. $^3$He$^+$ is observed through its 3.46 cm hyperfine level in Hii regions and the $^3$He/H ratio compares well with theory. Since $^3$He can be created or destroyed in nuclear reactions, one would expect that its abundance shows a trend with the amount of such reactions, so with distance to the Center of the Galaxy and with metallicity. Such trends are lacking in observations. This is explained by assuming that the Hii clouds are recently formed out of the primordial micro brown dwarfs of earth mass predicted by gravitational hydrodynamics. If indeed existing, they would preserve their primordial $^3$He/H ratio and spread this when evaporating into Hii clouds, independent of the location in the Galaxy. In the development of the argument, it is also explained that wide binaries do not rule out the MACHO dark matter predicted by gravitational hydrodynamics, but are rather immersed as visible partners in Jeans clusters of dark micro brown dwarfs.Comment: 4 page

Prediction for the neutrino mass in the KATRIN experiment from lensing by the galaxy cluster A1689

The KATRIN experiment in Karlsruhe Germany will monitor the decay of tritium, which produces an electron-antineutrino. While the present upper bound for its mass is 2 eV/$c^2$, KATRIN will search down to 0.2 eV$/c^2$. If the dark matter of the galaxy cluster Abell 1689 is modeled as degenerate isothermal fermions, the strong and weak lensing data may be explained by degenerate neutrinos with mass of 1.5 eV$/c^2$. Strong lensing data beyond 275 kpc put tension on the standard cold dark matter interpretation. In the most natural scenario, the electron antineutrino will have a mass of 1.5 eV/$c^2$, a value that will be tested in KATRIN.Comment: 13 pages, 5 figure

Observational Derivation of Einstein's``Law of the Constancy of the Velocity of Light in Vacuo"

On the basis of Galilean invariance and the Doppler formula, combined with an observational condition, it is shown that the constancy of the velocity of light {\it in vacuo} can be derived, together with time-dilatation and Lorentz contraction. It is not necessary to take the constancy as a postulate.Comment: 5 pages AIP-tex. Conference "Quantum Theory: Reconsideration of Foundations 3", Vaxjo Sweden, June 2005. To appear in AIP conference serie

Are observations of the galaxy cluster Abell 1689 consistent with a neutrino dark matter scenario?

Recent weak and strong lensing data of the galaxy cluster A1689 are modelled by dark fermions that are quantum degenerate within some core. The gas density, deduced from X-ray observations up to 1 Mpc and obeying a cored power law, is taken as input, while the galaxy mass density is modelled. An additional dark matter tail may arise from cold or warm dark matter, axions or non-degenerate neutrinos. The fit yields that the fermions are degenerate within a 430 kpc radius. The fermion mass is a few eV and the best case involves 3 active plus 3 sterile neutrinos of equal mass, for which we deduce $1.51 \pm 0.04$ eV. The eV mass range will be tested in the KATRIN experiment.Comment: 5 pages latex, 5 figures. Accepted for MNRAS Letter