Abstract:
The initial value problem is well-defined on a class of spacetimes
broader than the globally hyperbolic geometries for which existence
and uniqueness theorems are traditionally proved. Simple examples
are the time-nonorientable spacetimes whose orientable
double cover is globally hyperbolic. These spacetimes have generalized
Cauchy surfaces on which smooth initial data sets yield unique solutions.
A more difficult problem is to characterize the class of spacetimes with
closed timelike curves that admit a well-posed initial value problem.
Examples of spacetimes with closed timelike curves are given for which
initial data at past null infinity has been recently shown to yield unique
solutions. Other examples show that confining closed timelike curves to
compact regions is not sufficient to guarantee uniqueness. An approach
to the characterization problem is suggested by the behavior of
congruences of null rays. Interacting fields have not yet been studied,
but particle models suggest that uniqueness (and possibly existence)
is likely to be lost as the strength of the interaction increases.
Title of lecture 2: Open problems in general relativistic astrophysics
Abstract: The talk reviews a set of unsolved problems that arise from studies of
relativistic stars and black holes. Stated in a way that reflects
the author's bias on what is likely to be true, the list is:
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The slide times are completely random this stage.
The pdf file with the slides might be very slow to start in the video window (50Mo for the first lecture, 15Mo for the second).