  We explore the (non)-universality of Martinez's conjecture, originally
proposed for Kerr black holes, within and beyond general relativity. The
conjecture states that the Brown-York quasilocal energy at the outer horizon of
such a black hole reduces to twice its irreducible mass, or equivalently, to
\sqrt{A} /(2\sqrt{pi}), where `A' is its area. We first consider the charged
Kerr black hole. For such a spacetime, we calculate the quasilocal energy
within a two-surface of constant Boyer-Lindquist radius embedded in a constant
stationary-time slice. Keeping with Martinez's conjecture, at the outer horizon
this energy equals the irreducible mass. The energy is positive and
monotonically decreases to the ADM mass as the boundary-surface radius
diverges. Next we perform an analogous calculation for the quasilocal energy
for the Kerr-Sen spacetime, which corresponds to four-dimensional rotating
charged black hole solutions in heterotic string theory. The behavior of this
energy as a function of the boundary-surface radius is similar to the charged
Kerr case. However, we show that in this case it does not approach the
expression conjectured by Martinez at the horizon.
