Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective field theory of modified gravity on the spherically symmetric
  background: leading order dynamics and the odd-type perturbations   We consider perturbations of a static and spherically symmetric background
endowed with a metric tensor and a scalar field in the framework of the
effective field theory of modified gravity. We employ the previously developed
2+1+1 canonical formalism of a double Arnowitt-Deser-Misner (ADM) decomposition
of space-time, which singles out both time and radial directions. Our building
block is a general gravitational action that depends on scalar quantities
constructed from the 2+1+1 canonical variables and the lapse. Variation of the
action up to first-order in perturbations gives rise to three independent
background equations of motion, as expected from spherical symmetry. The
dynamical equations of linear perturbations follow from the second-order
Lagrangian after a suitable gauge fixing. We derive conditions for the
avoidance of ghosts and Laplacian instabilities for the odd-type perturbations.
We show that our results not only incorporates those derived in the most
general scalar-tensor theories with second-order equations of motion (the
Horndeski theories) but they can be applied to more generic theories beyond
Horndeski.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin