A builder checks the strength of an arch not by running through all possible shapes in their head, but by mentally nudging it and seeing how much force is expended. That's essentially how the principle of virtual work works in mechanics. The authors of a new study have applied this approach to the very geometry of spacetime.
They constructed a covariant framework of virtual work for the metric. In it, Einstein's equations emerge not from the extremality of an action, but from the requirement that the total virtual work over admissible variations of the metric be zero. Spacetime, as it were, 'feels out' neighboring configurations and settles where all contributions are balanced.
In this view, the cosmological constant ceases to be a mysterious addition. It emerges as an ideal reaction to an isoperimetric condition — a global constraint on spacetime averages. The value of the constant is fixed not locally, but by the entire history of the universe, reflecting its nonlocal geometric nature.
The principle of virtual work, which came from the statics of structures, was first formulated by Johann Bernoulli back in 1717—long before the advent of general relativity.