  We study the Yang-Mills-Higgs system within the framework of general
relativity. In the static situation, using Bogomol'nyi type analysis, we derive
a positive-definite energy functional which has a lower bound. Specializing to
the gauge group $SU(2)$ and the t'Hooft-Polyakov ansatz for the gauge and Higgs
fields, we seek static, spherically symmetric solutions to the coupled system
of equations in both the isotropic and standard coordinate systems. In both
cases, in the spontaneously broken symmetry situation, we find great
simplications reducing the solutions of the coupled system to the solution of a
single non-linear differential equation, different one in each case, but
well-known in other contexts of physics. We find abelian and non-abelian
monopole solutions with gravitational fields playing the role of Higgs fields
in providing attraction that balances the repulsion due to the gauge fields.
Numerical solutions indicate the possibility of blackhole horizons inside the
monopoles enclosing the singularity at the origin. Such non-abelian monopoles
are then the analogs of Reissner-Nordstr\"om blackholes with magnetic charge.
