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We explore the surface charges and the associated symmetries when the boundary conditions are imposed at two arbitrary boundaries in spacetime. In particular, we consider Einstein AdS$_3$ gravity theory and impose boundary conditions at two different arbitrary constant radius surfaces. We show that (1) smooth interpolation between two boundaries is possible iff the mass and angular momentum measured at the two boundaries are equal and, (2) the other surface charges at each boundary depend only on the boundary condition imposed at that boundary and the two set of charges at the two boundaries are not correlated with each other. We explicitly construct such a family of solution geometries which smoothly interpolate between the two boundaries.
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