Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The finite volume method on a Schwarzschild background   We introduce a class of nonlinear hyperbolic conservation laws on a
Schwarzschild black hole background and derive several properties satisfied by
(possibly weak) solutions. Next, we formulate a numerical approximation scheme
which is based on the finite volume methodology and takes the curved geometry
into account. An interesting feature of our model is that no boundary
conditions is required at the black hole horizon boundary. We establish that
this scheme converges to an entropy weak solution to the initial value problem
and, in turn, our analysis also provides us with a theory of existence and
stability for a new class of conservation laws.

33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph