Double Schwarzschild Black Hole Solution

In the article cited below, authors Pedro Cunha, Carlos Herdeiro and Maria Rodrigues report the existence of an exact solution to Einstein’s field equations for two static black holes held rigid by a singular strut. This solution shows that the potential between two black holes of equal mass is exactly zero, indicating there is no time dilation with respect to infinity at the center of mass of the system. The result has sparked heated arguments on the Science Forum platform, as it may defy intuition.

If you wish to check the calculations yourself, the equations are given below. The full text of the article is available on arXiv: click here.

Excerpts from Physical Review D 97, 084020 (2018):

Does the black hole shadow probe the event horizon geometry?

By Pedro V. P. Cunha, Carlos A. R. Herdeiro, and Maria J. Rodriguez

[The following images show the equations for the double black hole static metric. To enlarge for readability, type Ctrl + (control plus) several times. Undo with Ctrl -.]