Sumários

Event and Apparent Horizons

11 maio 2018, 13:30 • David Hilditch

Following on from last time we studied different characterizations of a black hole.

 - The Event Horizon was given as the formal definition of the boundary of a black hole.
 - The notion of the apparent horizon was explained as a proxy for the event-horizon in applications
   where it is not feasible to locate the event horizon.

Initial Data and Binary Black Hole spacetimes

7 maio 2018, 17:00 • David Hilditch

Finished our study of the constraint equations by looking at moving-puncture initial data.

Explained the basic methods for treating black holes: moving-punctures and excision.

Discussed superficially the main codes and methods used in each case.

Initial Data

4 maio 2018, 13:30 • David Hilditch

Continued studying the constraints formulated as an Elliptic system.

- Looked at other formulations of the constraints including  the conformal thin Sandwich equations. 
- Looked at simple exact solutions, and the Bowen-York extrinsic curvature.


Initial Data

30 abril 2018, 17:00 • David Hilditch

Initial Data

 - Demonstrated the York-Lichneroricz conformal decomposition as a reformulation of the constraints.
 - Studied the transverse-traceless decomposition of symmetric tensors.
 - Used these methods to rewrite the constraints as a set of coupled Elliptic equations.

Well-posedness and hyperbolicity

27 abril 2018, 13:30 • David Hilditch

Well-posedness and hyperbolicity

 - Worked with a first order, linear constant coefficient PDE system.
 - Introduced weak, strong and symmetric hyperbolicity.
 - Showed (morally) that strong-hyperbolicity implies well-posedness.

Moving on to GR:

 - Demonstrated weak hyperbolicity of ADM in geodesic slicing.
 - Introduced the harmonic gauge (wave gauge) formulation of GR.