Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How appropriate are the gravitational entropy proposals for traversable
  wormholes?   In this paper we have examined the validity of some proposed definitions of
gravitational entropy (GE) in the context of traversable wormhole solutions of
the Einstein field equations. Here we have adopted two different proposals of
GE and checked for their applicability in the case of these wormholes. The
first one is the phenomenological approach proposed by Rudjord et al
\cite{entropy1} and expanded by Romero et al in \cite{entropy2}, which is a
purely geometric method of measuring gravitational entropy. The latter one is
the Clifton-Ellis-Tavakol (CET) proposal \cite{CET} for the gravitational
entropy which arises in relativistic thermodynamics and is based on the
Bel-Robinson tensor, which represents the effective super-energy-momentum
tensor of free gravitational fields. Considering some of the Lorentzian
traversable wormholes along with the Brill solution for NUT wormholes and the
AdS wormholes, we have evaluated the gravitational entropy for these systems.
Incidentally, the application of the CET proposal can provide unique
gravitational entropies for spacetimes of Petrov type D and N only, whereas the
geometric method can be applied to almost every kind of spacetime, although it
has no relation with thermodynamics. For any traversable wormhole to be
physically realistic, it should have a viable GE. We found that the GE
proposals do give us a consistent measure of GE in several of them. This means
that the existence of a viable gravitational entropy strictly depends on its
definition.

11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas