taken to consist of the sum of the Einstein–Hilbert action with a Lagrange multiplier λ that ensures that the time vector is a unit vector and also with all of the covariant terms involving the time vector u but having at most two derivatives. In particular it is assumed that the action may be written as the integral of a local Lagrangian density where GN is Newton's constant and g is a metric with Minkowski signature. The Lagrangian density is Here R is the Ricci scalar, is the covariant derivative and the tensor K is defined by Here the ci are dimensionless adjustable parameters of the theory. Solutions Stars Several spherically symmetric solutions to ae-theory have been found. Most recently Christopher Eling and Ted Jacobson have found solutions resembling stars and solutions resembling black holes. In particular, they demonstrated that there are no spherically symmetric solutions in which stars are constructed entirely from the aether. Solutions without additional matter always have either naked singularities or else two asymptotic regions of spacetime, resembling a wormhole but with no horizon. They have argued that static stars must have static aether solutions, which means that the aether points in the direction of a timelike Killing vector. Black holes and potential problems However this is difficult to reconcile with static black holes, as at the event horizon there are no timelike Killing vectors available and so the black hole solutions cannot have static aethers. Thus when a star collapses to form a black hole, somehow the aether must eventually become static even very far away from the collapse. In addition the stress tensor does not obviously satisfy the Raychaudhuri equation, one needs to make recourse to the equations of motion. This is in contrast with theories with no aether, where this property is independent of the equations of motion. Experimental constraints In Universal Dynamics of Spontaneous Lorentz Violation and a New Spin-Dependent Inverse-Square Law Force Nima Arkani-Hamed, Hsin-Chia Cheng, Markus Luty and Jesse Thaler have examined experimental consequences of the breaking of boost symmetries inherent in aether theories. They have found that the resulting Goldstone boson leads to, among other things, a new kind of Cherenkov radiation. In addition they have argued that spin sources will interact via a new inverse square law force with a very unusual angular dependence. They suggest that the discovery of such a force would be very strong evidence