Courses I'm teaching can be found on
Also Salman Khan
is a way better teacher than I'll ever be. Go learn from his
videos. They're incredible.
CMC Cauchy surfaces play an important role in mathematical relativity. Sadly they don't always
BUT they do exist if gravity is attractive in all directions.
Invisibility of trapped surfaces in asymptotically flat spacetimes is a classical result (here classical is defined as any result obtained before I started doing research). We prove an analogous statement
for asymptotically de Sitter spacetimes.
I accidentally made a controversial physical discovery, and now I don't know what to do.
In spacetimes with below Lipschitz regularity, maximizers between causally
related points can contain parts that are timelike AND parts that are null. This is fascinating because it drastically
from classical theory, but it's also annoying
when developing low regularity causality theory. Fortunately maximizers in spacetimes with Lipschitz regularity
must be either completely timelike or completely null.
Most singularity theorems assume the strong energy condition. However evidence of dark energy (or a belief in inflationary theory)
shows that the strong energy condition does not strictly hold. We obtain singularities without the strong energy condition, but in its place, we assume
the existence of a Cauchy surface exapnding in all directions.
Should timelike completeness imply C 0-inextendibility? Yes. Yes it should. Does it? We don't know.
BUT timelike completess plus global hyperbolicity does imply C 0-inextendibility.
We generalize some of Sbierski's methods from his pioneering
on the C 0-inextendibility
of the Schwarzschild spacetime. We obtain a structural result on spacetime boundaries and prove some inextendibility theorems
within the class of spherically symmetric spacetimes.