In Sect. 10.3 we discussed the construction of Newtonian field theory of gravitation based on a scalar gravitational potential satisfying a linear (elliptic) partial differential equation and alluded to solutions to the Poisson equation with sources that could give rise to gradient forces leading to terrestrial tides. In this chapter we argue that such phenomena can be given a geometric interpretation in terms of approximate solutions of Einstein’s tensor field equation with particular sources. The argument is based on a perturbative approach where Einsteinian gravitation is considered to be a local perturbation of Minkowski spacetime. The chapter concludes by drawing attention to the relevance of “tidal forces” for limiting the application of the “strong equivalence principle” that historically was a cornerstone in Einstein’s thinking about non-Newtonian gravitation.

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An Interpretation of “Tidal Strains” from the Einstein-Minkowski Paradigm

  • Robin W. Tucker,
  • Timothy J. Walton

摘要

In Sect. 10.3 we discussed the construction of Newtonian field theory of gravitation based on a scalar gravitational potential satisfying a linear (elliptic) partial differential equation and alluded to solutions to the Poisson equation with sources that could give rise to gradient forces leading to terrestrial tides. In this chapter we argue that such phenomena can be given a geometric interpretation in terms of approximate solutions of Einstein’s tensor field equation with particular sources. The argument is based on a perturbative approach where Einsteinian gravitation is considered to be a local perturbation of Minkowski spacetime. The chapter concludes by drawing attention to the relevance of “tidal forces” for limiting the application of the “strong equivalence principle” that historically was a cornerstone in Einstein’s thinking about non-Newtonian gravitation.