journal club on aspects of information, quantum theory, and gravity
08 Apr 2025
We present an explicit solution to the Einstein field equations sourced by a stress tensor with identically zero energy density. We refer to the solution as the “platypus metric” due to its intriguing properties. It exemplifies a key difference between Newton and Einstein gravity: while Newtonian gravity is sourced exclusively by mass, pressure alone can source relativistic gravitational fields. We also discuss various qualitative aspects of the platypus solution. For example, it has a stable photon ring, all non-radial null geodesics are bounded, it is locally conformally flat, spatially flat with vanishing extrinsic curvature, among other properties. While the platypus spacetime does not appear to represent any physical scenario in the universe, it is an interesting example of the strange behaviors one can obtain within general relativity.