Seminário no dia 10/09 às 10h

Resumo: To analyze the dynamics of a single spiral galaxy, we will discuss the known class of exact stationary axially-symmetric solutions to Einstein gravity coupled with neutral dust. Differently from the Newtonian description of the same system where all the quantities are completely fixed once the velocity or the matter distribution are known, the class of the relativistic solutions provides additional degrees of freedom, making the applications of this system much more interesting and wide. Up to now, from the relativistic perspective the already proposed models for galaxies are the co-rotating and the differentially rotating model. While in the first case the velocity of the dust satisfies L_u(g) = 0, in the second case it differs from zero. What is interesting about these solutions is that the low energy limits are non equivalent to the Newtonian theory. In particular, the differentially rotating case generalize the known results of Balasin and Grumiller and further highlights the discrepancy between Newtonian theory of gravity and general relativity at low velocities and energy densities. Using these exact solutions, we push forward the idea that the “inertia” of the gravitational field can simulate dark matter effects. In fact, we show that non co-rotance further reduces the amount of energy density required to explain the rotation curves for spiral galaxies.