https://doi.org/10.1140/epjc/s10052-018-6494-5
Regular Article - Theoretical Physics
On the classification of consistent boundary conditions for 
-gravity
1
Department of Physics, University of Tehran, Tehran, Iran
2
Foundations of Physics Group, School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
3
Department of Physics, Isfahan University of Technology, Isfahan, Iran
4
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
* e-mail: fshojai@ut.ac.ir
Received:
1
October
2018
Accepted:
2
December
2018
Published online:
10
December
2018
Using a completely covariant approach, we discuss the role of boundary conditions (BCs) and the corresponding Gibbons–Hawking–York (GHY) terms in 
-gravity in arbitrary dimensions. Following the Ostrogradsky approach, we can introduce a scalar field in the framework of Brans–Dicke formalism to the system to have consistent BCs by considering appropriate GHY terms. In addition to the Dirichlet BC, the GHY terms for both Neumann and two types of mixed BCs are derived. We show the remarkable result that the 
-gravity is itself compatible with one type of mixed BCs, in D dimension, i.e. it doesn’t require any GHY term. For each BC, we rewrite the GHY term in terms of Arnowit–Deser–Misner (ADM) variables.
© The Author(s), 2018
