D. Grigoriou

Microscopic black hole stabilization via the uncertainty principle

Due to the Heisenberg uncertainty principle, gravitational confinement of two- or three-rotating particle systems can lead to microscopic Planckian or sub-Planckian black holes with a size of order their Compton wavelength. Some properties of such states are discussed in terms of the Schwarzschild geodesics of general relativity and compared with properties computed via the combination of special relativity, equivalence principle, Newtons gravitational law and Compton wavelength. It is shown that the generalized uncertainty principle (GUP) provides a satisfactory fit of the Schwarzschild radius and Compton wavelength of such microscopic, particle-like, black holes.

Gravitational mass and Newton's universal gravitational law under relativistic conditions

We discuss the predictions of Newtons universal gravitational law when using the gravitational, mg, rather than the rest masses, mo, of the attracting particles. According to the equivalence principle, the gravitational mass equals the inertial mass, mi, and the latter which can be directly computed from special relativity, is an increasing function of the Lorentz factor, γ, and thus of the particle velocity. We consider gravitationally bound rotating composite states, and we show that the ratio of the gravitational force for gravitationally bound rotational states to the force corresponding to low (γ ≈ 1) particle velocities is of the order of (mPl/mo)2 where mpi is the Planck mass (ħc/G)1/2. We also obtain a similar result, within a factor of two, by employing the derivative of the effective potential of the Schwarzschild geodesics of GR. Finally, we show that for certain macroscopic systems, such as the perihelion precession of planets, the predictions of this relativistic Newtonian gravitational law differ again by only a factor of two from the predictions of GR.

Computation of masses and binding energies of some hadrons and bosons according to the rotating lepton model and the relativistic Newton equation

We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newtons relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (~ 0.9 to 1 GeV/c2), while ground states comprising two neutrinos have masses in the meson mass range (~ 0.4 to 0.8 GeV/c2). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (~ 81 GeV/c2) corresponds to the mass of a rotating gravitationally confined e± — ve pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.