Covariant Noether charges for type IIB and 11-dimensional supergravities

Understand

The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism that, in principle, allows one to define and compute the energy, angular momenta, and chemical potentials of generic solutions of gravitational theories.

• However, it has been observed that for some supergravity solutions the variation of the Noether charge is not (at least manifestably) integrable, and as a result it is unclear whether there are well-defined thermodynamic charges for these solutions.
• In this work, we derive an expression for the variation of the covariant Noether charges for any solution of Type IIB 10-dimensional supergravity or 11-dimensional supergravity.
• Although this Noether quantity is not integrable in general, we show that for asymptotically scale-invariant solutions, it is.