Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetimes with Singularities   We report on some advances made in the problem of singularities in general
relativity.
  First is introduced the singular semi-Riemannian geometry for metrics which
can change their signature (in particular be degenerate). The standard
operations like covariant contraction, covariant derivative, and constructions
like the Riemann curvature are usually prohibited by the fact that the metric
is not invertible. The things become even worse at the points where the
signature changes. We show that we can still do many of these operations, in a
different framework which we propose. This allows the writing of an equivalent
form of Einstein's equation, which works for degenerate metric too.
  Once we make the singularities manageable from mathematical viewpoint, we can
extend analytically the black hole solutions and then choose from the maximal
extensions globally hyperbolic regions. Then we find space-like foliations for
these regions, with the implication that the initial data can be preserved in
reasonable situations. We propose qualitative models of non-primordial and/or
evaporating black holes.
  We supplement the material with a brief note reporting on progress made since
this talk was given, which shows that we can analytically extend the
Schwarzschild and Reissner-Nordstrom metrics at and beyond the singularities,
and the singularities can be made degenerate and handled with the mathematical
apparatus we developed.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci