Electromagnetic Radiations on Weakly Isolated Horizon and Study of Geometrical Properties

Third Maxwell’s scalar ϕ2 justifies why weakly isolated horizons stays in equilibrium evenif there is dynamical matter filed on and near horizon. To measure physical quantities suchas charge, mass, or energy of black hole, we do a relevant calculation on event horizon. Butit is global in nature, so we need to perform measurements on quasi-local horizons. Thesehorizons are studied in work of Abhay Ashtekar. This paper, first, focuses on review ofgeometrical properties of non-expanding (NEH) and weakly isolated horizons (WIH). Then,we find useful expressions for Maxwell’s scalars. We also calculate electric and magneticmonopole charges on horizon. We show that weakly isolated horizon allows radiative partof field to accumulate when spin coefficient π is not zero. This accumulation is treated asquantum excitation of field in QFT.