An imaginary temperature far away from a stationary spinning star

Masood-ul-Alam A.K.M.

Yau Mathematical Sciences Center, Tsinghua University, Beijing

E-mail: Masood-ul_Alam

By what appears to be a natural extension a temperature is assigned to the vacuum spacetime outside an isolated rigidly rotating star in an asymptotically flat stationary axisymmetric spacetime. This temperature becomes imaginary far away from the axis of the star turning the equation for the concentration of test particles in the few particles limit in this region into a Schrödinger type equation. A distance from the axis where the temperature gives Planck’s constant is crudely estimated for various gravitating objects assuming linear and quadratic temperature dependence of the diffusion coefficient to argue for a gravitational origin of basic quantum mechanics. For a uniform density classical object having the mass and angular momentum comparable to that of a neutron and assuming quadratic temperature (magnitude) dependence of the diffusion coefficient with the proportionality constant bk_B and with mobility b = 2a/m (m mass of the test particle) we get Planck’s constant roughly at 0.2 Bohr radius on the equatorial plane. In view of the crudeness of the various estimations involved it must be a remarkable coincidence and it calls for detail analysis using expertise from several branches of mathematical physics.

Keywords: Gravity, Quantum mechanics, Imaginary temperature, Rotating star.

DOI: 10.18698/2309-7604-2015-1-374-383

Article file: Masood-ul-Alam.pdf