Tuesdays 10:30 - 11:30 | Fridays 11:30 - 12:30
Showing votes from 2016-02-02 11:30 to 2016-02-05 12:30 | Next meeting is Friday May 8th, 11:30 am.
The study of cosmology, galaxy formation and exoplanetary systems has now advanced to a stage where a cosmic inventory of terrestrial planets may be attempted. By coupling semi-analytic models of galaxy formation to a recipe that relates the occurrence of planets to the mass and metallicity of their host stars, we trace the population of terrestrial planets around both solar-mass (FGK type) and lower-mass (M dwarf) stars throughout all of cosmic history. We find that the mean age of terrestrial planets in the local Universe is $8\pm1$ Gyr and that the typical planet of this type is located in a spheroid-dominated galaxy with total stellar mass about twice that of the Milky Way. We estimate that hot Jupiters have depleted the population of terrestrial planets around FGK stars at redshift $z=0$ by no more than $\approx 10\%$, and predict that $\approx 1/3$ of the terrestrial planets in the local Universe are orbiting stars in a metallicity range for which such planets have yet to be been detected. When looking at the inventory of planets throughout the whole observable Universe (i.e. in all galaxies on our past light cone) we argue for a total of $\approx 2\times 10^{19}$ and $\approx 7\times 10^{20}$ terrestrial planets around FGK and M stars, respectively. Due to the hierarchical formation of galaxies and lookback-time effects, the average terrestrial planet on our past light cone has an age of just $1.7\pm 0.2$ Gyr and is sitting in a galaxy with a stellar mass a factor of $\approx 2$ lower than that of the Milky Way. These results are discussed in the context of cosmic habitability, the Copernican principle and the prospects of searches for extraterrestrial intelligence at cosmological distances.
The generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1] is extended to the system of Fermion fields. We first find the regular wave solution of Fermion field which has arbitrary frequency and mode number on the BTZ spacetime, and then use it to calculate the exact gravitational entropy. The results show that there is a threshold frequency below which the Fermion fields could not contribute the generalized gravitational entropy. Also, the static and zero-mode solutions have not entropy, contrast to that in scalar field. We also found that the entropy of the static scalar fields and non-static fermions is an increasing function of mode number and, after arriving the maximum entropy it becomes a deceasing function and is derived to the asymptotic value.