Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational-wave dynamics and black-hole dynamics: second
  quasi-spherical approximation   Gravitational radiation with roughly spherical wavefronts, produced by
roughly spherical black holes or other astrophysical objects, is described by
an approximation scheme. The first quasi-spherical approximation, describing
radiation propagation on a background, is generalized to include additional
non-linear effects, due to the radiation itself. The gravitational radiation is
locally defined and admits an energy tensor, satisfying all standard local
energy conditions and entering the truncated Einstein equations as an effective
energy tensor. This second quasi-spherical approximation thereby includes
gravitational radiation reaction, such as the back-reaction on the black hole.
With respect to a canonical flow of time, the combined energy-momentum of the
matter and gravitational radiation is covariantly conserved. The corresponding
Noether charge is a local gravitational mass-energy. Energy conservation is
formulated as a local first law relating the gradient of the gravitational mass
to work and energy-supply terms, including the energy flux of the gravitational
radiation. Zeroth, first and second laws of black-hole dynamics are given,
involving a dynamic surface gravity. Local gravitational-wave dynamics is
described by a non-linear wave equation. In terms of a complex gravitational-
radiation potential, the energy tensor has a scalar-field form and the wave
equation is an Ernst equation, holding independently at each spherical angle.
The strain to be measured by a distant detector is simply defined.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
23
The categories of this paper are: solv-int