result is similar to the higher dimensional asymptotically AdS black holes and different from the Lifshitz and the hyperscaling violating geometries that this bound has violated [@Alishahiha:2018tep]. This shows that although BMSFTs are ultrarelativistic theories, they are more similar to the relativistic theories than to the nonrelativistic ones.

The idea presented in this paper for the definition of the suggested spacetime region on which the gravitational action is evaluated may help us to study the complexity of formation [@Brown:2015bva; @Brown:2015lvg; @Chapman:2016hwi] in the context of flat/BMSFT correspondence. This is a potentional open problem that could be addressed in future works.

Acknowledgements {#acknowledgements .unnumbered}
================

The authors thank S. M. Hosseini and Sh. Karimi for useful comments on the manuscript. We are also grateful to M. R. Mohammadi Mozaffar, A. Faraji Astaneh and Yang Run Qiu for the useful comments. We have used xAct [@xAct] and its package[@Nutma:2013zea] during this work and for Penrose-Cartan diagrams we have used the code by E. Gourgoulhon [@sage].

 Non-symmetric evolutions in past and future null infinities
============================================================

In this appendix, we discuss the nonsymmetric scenario when the boundary times on future and past null infinities develop individually. We show the parameter that render nonsymmetricity by 