Second law from the Noether current on null hypersurfaces

Understand

I study the balance law equation of surface charges in the presence of background fields.

• The construction allows a unified description of Noether's theorem for both global and local symmetries.
• From the balance law associated with some of these symmetries, I will discuss generalizations of Wald's Noether entropy formula and general entropy balance laws on null hypersurfaces based on the null energy conditions, interpreted as an entropy creation term.
• The entropy is generally the so-called improved Noether charge, a quantity that has recently been investigated by many authors, associated to null future-pointing diffeomorphisms.