# Introduction:

I am interested in study critical phenomena for the Eisntein-Vlasov system.
I am working in maximal slicing condition with areal coordinates. I use two
methods to attack this problem: particle-mesh (PM) method and solve the
Boltzmman equation directly (using RNPL) on the tangent bundle of the spacetime.
In the next PS file you can have a look at the equations in both cases.
- :

**Measure of the angular momentum for different
critical solutions**:

# Particle-Mesh Code:

##

- Tests:
- Flatspace:
- One particle in Schwarzschild backgroud:
- Comparation with analytic geodesic for a
particle initially at r=10 moving around a BH with M=1. The plot shows the
radial position with respect the time for an observer at infinity. The level of
discretization is 8.

- pt (t component of the covariant
4-momentum), for different levels of discretization and the same particle as
before.(theoretically should be constant)

- Oppenheimmer-Snyder Collapse:
- ADM mass at infinity for diferent levels, for
2000 particles, total mass equal to 1 and constant initial density up to r=10.

- Particles with angular momentum:
### Dispersion:

# Solving Boltzmman Equation:

### Dispersion:

- Movie of one Isosurface of the distribution function in
phase space.(1.0 MB MPEG)
- Movie of one slice of the phase space for constant L.
(1.0 MB MPEG)

# References: