Variational principle for Thermodynamics, application to Rotational motion in General Relativity
OKC/Nordita High-Energy Physics Theory seminar
Monday 27 April 2015
to 14:15 at
Christian Fronsdal (UCLA)
I am interested in the structure of stars and galaxies, with very strict criteria for what constitutes a dynamical metric-matter system. We need a variational formulation with a Lagrangian for the total system.
It implies an underlying variational principle for thermodynamics and this the problem becomes one of much wider interest. I believe I am solving this problem, of interest to thermodynamics and fluid dynamics, numerous applications to classical and modern problems in hydrodynamics, thermodynamics and chemistry. The key to the solution is to take seriously the representation of the velocity field as the time derivative of a vector "potential".
When this becomes really interesting is when we lift the idea to the relativistic domain. The velocity field here becomes an antisymmetric tensor field, a field that is known since 1964 as the "notoph", and in string
theory as the Kalb-Ramond field. The relativistic energy momentum tensor of this field is just what is needed
to describe rotating stars and galaxies. At present I am solving the field equations on the Kerr background.
Of special interest is the fact that this approach predicts a (very small) photon mass and the existence of magnetic fields in the neighbourhood of rotating masses; this will affect the predictions of gravitational lensing. It also affects the shape of the orbits in a Kerr geometry, including the rotation curves in our galaxy. So that there are at least 2 implications for Dark Matter.