Extending the rigidity of general relativity

Understand

We give the most general conditions to date which lead to uniqueness of the general relativistic Hamiltonian.

• Namely, we show that all spatially covariant generalizations of the scalar constraint which extend the standard one while remaining quadratic in the momenta are second class.
• Unlike previous investigations along these lines, we do not require a specific Poisson bracket algebra, and the quadratic dependence on the momenta is completely general, with an arbitrary local operator as the kinetic term.