Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant Renormalization-Group improvement   Renormalization-Group (RG) improvement has been frequently applied to capture
the effect of quantum corrections on cosmological and black-hole spacetimes.
This work utilizes an algebraically complete set of curvature invariants to
establish that: On the one hand, RG improvement at the level of the metric is
coordinate-dependent. On the other hand, a newly proposed RG improvement at the
level of curvature invariants is coordinate-independent. Spherically-symmetric
and axially-symmetric black-hole spacetimes serve as physically relevant
examples.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn