What is Gödel metric?

The Gödel metric is a solution to Einstein's field equations of general relativity that describes a rotating universe. It was introduced by the logician and mathematician Kurt Gödel in 1949, and it is notable for containing closed time-like curves, which allow for the possibility of time travel within the spacetime it describes. The Gödel metric can be represented in a cylindrical coordinate system and is characterized by a constant rotation throughout the universe. The key features of the Gödel metric include: 1. **Rotation**: The solution involves a rotating universe, which means that the geometry of spacetime is not static. This rotation leads to peculiar properties, such as closed time-like curves where the pathways through spacetime can loop back on themselves. 2. **Cosmological constant**: The solution includes a cosmological constant, indicating that it features an expanding universe model. 3. **Time travel**: Due to the presence of closed time-like curves, if a person or an object travels along these curves, they could theoretically return to an earlier point in time. 4. **Implications**: The Gödel metric has been studied for its implications on the nature of time and causality in the framework of general relativity. It raises questions about determinism and the nature of time as understood in classical physics. Despite its mathematical interest, the Gödel metric does not correspond to our observable universe, which does not exhibit such large-scale rotating behavior or closed time-like curves. It serves primarily as a theoretical example to explore the implications of general relativity and the nature of time and space.