Quasilocal Corrections to Bondi's Mass-Loss Formula and Dynamical Horizons

In this work, a null geometric approach to the Brown-York quasilocal formalism is used to derive an integral law that describes the rate of change of mass and/or radiative energy escaping through a dynamical horizon of a non-stationary spacetime. The result thus obtained shows - in accordance with previous results from the theory of dynamical horizons of Ashtekar et al. - that the rate at which energy is transferred from the bulk to the boundary of spacetime through the dynamical horizon becomes zero at equilibrium, where said horizon becomes non-expanding and null. Moreover, it reveals previously unrecognized quasilocal corrections to the Bondi mass-loss formula arising from the combined variation of bulk and boundary components of the Brown-York Hamiltonian, given in terms of a bulk-to-boundary inflow term akin to an expression derived in an earlier paper by the author [#huber2022remark]. For clarity, this is discussed with reference to the Generalized Vaidya family of spacetimes, for which derived integral expressions take a particularly simple form.