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Abstract:
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Isolated and Dynamical horizons are used to generate boundary conditions upon the lapse and shift vectors . Numerous results involving the Hamiltonian of General relativity are derived , including a self -contained derivation of the Hamiltonian equations of general relativity using both a direct 'brute force' method of directly computing Lie derivatives , as well as the standard Hamil - tonian approach . Conclusions are compared to numerous examples , including the Kerr , Schwarzschild -De Sitter , McVittie , and Vaiyda spacetimes . |