https://doi.org/10.1140/epjc/s10052-023-12072-y
Regular Article - Theoretical Physics
The role of the boundary term in f(Q, B) symmetric teleparallel gravity
1
Dipartimento di Fisica “E. Pancini”, Universitá di Napoli “Federico II”, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
2
Scuola Superiore Meridionale, Largo San Marcellino 10, 80138, Naples, Italy
3
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy
Received:
26
July
2023
Accepted:
23
September
2023
Published online:
10
October
2023
In the framework of metric-affine gravity, we consider the role of the boundary term in Symmetric Teleparallel Gravity assuming f(Q, B) models where f is a smooth function of the non-metricity scalar Q and the related boundary term B. Starting from a variational approach, we derive the field equations and compare them with respect to those of f(Q) gravity in the limit of 
. It is possible to show that 
models are dynamically equivalent to f(R) gravity as in the case of teleparallel 
gravity (where 
). Furthermore, conservation laws are derived. In this perspective, considering boundary terms in f(Q) gravity represents the last ingredient towards the Extended Geometric Trinity of Gravity, where f(R), 
, and f(Q, B) can be dealt under the same standard. In this perspective, we discuss also the Gibbons–Hawking–York boundary term of General Relativity comparing it with B in f(Q, B) gravity.
© The Author(s) 2023
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