Would two dimensions be world enough for spacetime?. (August 2018) - Fletcher, Samuel C.; Manchak, J.B.; Schneider, Mike D.; Weatherall, James Owen
Abstract: We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions. Highlights: We collect and discuss several curious features of general relativity in two spacetime dimensions. We discuss the vanishing of the Einstein tensor and the non-vanishing of the Weyl tensor. We discuss the failure of an initial-value formulation of general relativity in two dimensions. We discuss the failure of the Newtonian limit in two dimensions. We discuss alternative ways of "generalizing" general relativity to different spacetime dimensions.