Imaginary soaring branes: a hidden feature of non-extremal solutions

A key property of many BPS solutions of supergravity is the fact that certain probe branes placed in these solutions feel no force, essentially because electric repulsion and gravitational attraction balance one another. In this letter we show that the existence of brane probes that feel no force is also a property of many non-supersymmetric, non-extremal solutions of supergravity. This observation requires a new class of brane probes that move with constant velocity along one or several internal directions of the solution but the zero-force condition that makes the branes "float along" at constant speed, or soar, requires the velocity to be purely imaginary. While these probes are not physical, their no-force condition implies the existence of hidden relations between the warp factors and electric potentials of non-extremal solutions in certain duality frames, and this provides insight into the structure of such solutions and can greatly simplify the search for them.