Gravitational Time Dilation in L1 Point: Summed, Canceled or Else?

[Chris Miller]

TL;DR Summary

Gravitational time dilation at Lagrangian points

In the Lagrangian (L1) point between two hypothetically massive (and close) objects , is gravitational time dilation effect summed or canceled, or something else?

 

[PeroK]

Summary:: Gravitational time dilation at Lagrangian points

In the Lagrangian (L1) point between two hypothetically massive (and close) objects , is gravitational time dilation effect summed or canceled, or something else?

https://astronomy.stackexchange.com/questions/14367/gravitational-time-dilation-multiple-sources

 

[pervect]

Summary:: Gravitational time dilation at Lagrangian points

In the Lagrangian (L1) point between two hypothetically massive (and close) objects , is gravitational time dilation effect summed or canceled, or something else?

It's an approximation, but it more or less adds, as Perok says.

The L1 point itself is an approximation in GR (though it's exact in Newtonian theory). The Newtonian analysis doesn't take into account, for example, the gravitational radiation that would make an orbiting body inspiral. Usually this is quite negligible, for instance it's negligible in the solar system. But it's not necessarily negligible for the Hulse-Taylor binary, for another example. If there is no inspiral, one can argue that the solution is stationary, and in that case Perok's source's arguments apply for the weak field case.