Do we know how to define energy in general relativity?

Abstract

This essay is dedicated to Prof. K.K. Phua on the occasion of his 80th birthday. While the contents of this essay are based on our recent papers${}^{1,2}$ published in the International Journal of Modern Physics A, I have added many personal opinions, so that I am solely responsible for all statements in this essay. 1. S. Aoki, T. Onogi and S. Yokoyama, Int. J. Mod. Phys. A36 (2021) no.10, 2150098. 2. S. Aoki, T. Onogi and S. Yokoyama, Int. J. Mod. Phys. A36 (2021) no.29, 2150201.

8 pages. In "Looking Beyond the Frontiers of Science - Dedicated to the 80th Birthday of KK Phua", https://doi.org/10.1142/13065, Eds.: L Brink, N-P Chang, D H Feng, K Fujikawa, M-L Ge, L C Kwek , C H Oh and S R Wadia