Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservation laws for dynamical black holes   An essentially complete new paradigm for dynamical black holes in terms of
trapping horizons is presented, including dynamical versions of the physical
quantities and laws which were considered important in the classical paradigm
for black holes in terms of Killing or event horizons. Three state functions
are identified as surface integrals over marginal surfaces: irreducible mass,
angular momentum and charge. There are three corresponding conservation laws,
expressing the rate of change of the state function in terms of flux integrals,
or equivalently as divergence laws for associated conserved currents. The
currents of energy and angular momentum include the matter energy tensor in a
physically appropriate way, plus terms attributable to an effective energy
tensor for gravitational radiation. Four other state functions are derived: an
effective energy, surface gravity, angular speed and electric potential. There
follows a dynamical version of the so-called first law of black-hole mechanics.
A corresponding zeroth law holds for null trapping horizons.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math