Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes

Understand

In a general time-dependent (3+1)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers.

• However the Kodama vector does not by itself define any preferred notion of time.
• We first extract as much information as possible by invoking the "warped product" structure of spherically symmetric spacetime to study the Kodama vector, and the associated Kodama energy flux, in a coordinate independent manner.
• Using this formalism we construct a general class of conservation laws, generalizing Kodama's energy flux.