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We provide a direct proof for the positivity of Chen-Nester-Tung quasi-localenergy with analytic reference in spherical symmetry. A hoop-type theorem forthis energy is also established. Finally, the relation between Chen-Nester-Tungand Brown-York quasi-local energies will be discussed.

Positivity and Hoop Properties for Chen-Nester-Tung Quasi-local Energy with Analytic Reference in Spherical Symmetry