gravitation theories (in the ambient field of an isolated spherically symmetric object), and we will use the second to compare gravitational radiation in Nordström's theory and in Einstein's general theory of relativity. The static spherically symmetric asymptotically flat vacuum solution The static vacuum solutions in Nordström's theory are the Lorentzian manifolds with metrics of the form where we can take the flat spacetime Laplace operator on the right. To first order in , the metric becomes where is the metric of Minkowski spacetime (the flat background). The metric Adopting polar spherical coordinates, and using the known spherically symmetric asymptotically vanishing solutions of the Laplace equation, we can write the desired exact solution as where we justify our choice of integration constants by the fact that this is the unique choice giving the correct Newtonian limit. This gives the solution in terms of coordinates which directly exhibit the fact that this spacetime is conformally equivalent to Minkowski spacetime, but the radial coordinate in this chart does not readily admit a direct geometric interpretation. Therefore, we adopt instead Schwarzschild coordinates, using the transformation , which brings the metric into the form Here, r now has the simple geometric interpretation that the surface area of the coordinate sphere is just . Just as happens in the corresponding static spherically symmetric asymptotically flat solution of general relativity, this solution admits a four-dimensional Lie group of isometries, or equivalently, a four-dimensional (real) Lie algebra of Killing vector fields. These are readily determined to be (translation in time) (rotation about an axis through the origin) These are exactly the same vector fields which arise in the Schwarzschild coordinate chart for the Schwarzschild vacuum solution of general relativity, and they simply express the fact that this spacetime is static and spherically symmetric. Geodesics The geodesic equations are readily obtained from the geodesic Lagrangian. As always, these are second order nonlinear ordinary differential equations. If we set we find that test particle motion confined to the equatorial plane is possible, and in this case first integrals (first order ordinary differential equations) are readily obtained. First, we have where to first order in m we have the same result as for the Schwarzschild vacuum. This also shows that Nordström's theory agrees with the result of the Pound–Rebka experiment. Second, we have which is the same result as for the Schwarzschild vacuum. This expresses conservation of orbital angular momentum of