  In backgrounds with compact dimensions there may exist several phases of
black objects including the black-hole and the black-string. The phase
transition between them raises puzzles and touches fundamental issues such as
topology change, uniqueness and Cosmic Censorship. No analytic solution is
known for the black hole, and moreover, one can expect approximate solutions
only for very small black holes, while the phase transition physics happens
when the black hole is large. Hence we turn to numerical solutions. Here some
theoretical background to the numerical analysis is given, while the results
will appear in a forthcoming paper. Goals for a numerical analysis are set. The
scalar charge and tension along the compact dimension are defined and used as
improved order parameters which put both the black hole and the black string at
finite values on the phase diagram. Predictions for small black holes are
presented. The differential and the integrated forms of the first law are
derived, and the latter (Smarr's formula) can be used to estimate the ``overall
numerical error''. Field asymptotics and expressions for physical quantities in
terms of the numerical ones are supplied. Techniques include ``method of
equivalent charges'', free energy, dimensional reduction, and analytic
perturbation for small black holes.
