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Hosotani Replies: Hagen and Sudarshan 1 (HS) claim that (i) expression (9) of Ref. 2 does not solve the field equations and (ii) the Hamiltonian does not generate the correct time development of y/. I first show that both of these claims are incorrect.To be specific, we consider a nonrelativistic Abelian system on a torus:The boundary conditions (b.c.) are given by (4). The flux quantization condition follows for general /? 7 , but a special one, (5), has been adopted in Ref. 2, which is important in the discussion there.First we note a theorem: The general solution to V 2 /(/,x) =g(f,x), where both / and g are single valued on the torus and J dxg =0, is given byThe single-valued Green's function satisfies JdxDix) =0 and V 2 D(x)-5(x)-l/I|L 2 . (There was a typographical error in the latter in Ref. 2.) c(t) is arbitrary.With the b.c. (4) and (5), divA(x) is single valued and JVxdivA^O. Therefore, making use of (8), one can always choose a divA =0 gauge. Define Bo "^o and Bj^Aj+fij/eLj.The BJ's are single valued and satisfy divB=0. It follows from the field equations (6) with K:=0that,The theorem, then, implies that the BJ*s are uniquely solved in terms of J v up to x-independent terms. The residual gauge invariance may be employed to eliminate the x-independent term in Z?o-This leads to the expression (9) of Ref. 2. The ^-dependent terms in both Eq. (R3) and Eq. (9) of Ref. 2 originate from fij in the definition of Bj and therefore q is a onumber. [The parameter a in (5) of Ref. 2 is related to the total charge by q ^In^ia/e 2 .] HS incorrectly replaced this c-number q by the operator Q in their Eq.(1), which further leads to wrong manipulations. We also note that AQ in Eq. (2) of HS satisfies Aolhjix)] -/lokl + (l/e)0/ so that the b.c. (4) and (5) of Ref. 2 are not obeyed. Moreover, HS's b.c. involves the time derivatives of operators (0,), whose meaning is not clear at all in quantum theory.The dynamical variables are 0i, Qi, and y/, which have the commutation relations [0\,$2]-ie 2 /fj. and {yKx), y f (y)} =

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A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified by their mass and their non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields is shown to be stable against spherically symmetric linear perturbations.

A continuum of monopole, dyon and black hole solutions exist in the EinsteinYang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the ADM mass. The stability of the solutions which have no node in nonAbelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.