  In this paper, we examine the emergence of conserved charges on the horizon
of a particular class of extremal non-dilatonic black $p$-branes (which reduce
to extremal dilatonic black holes in $D=4$ dimensions upon toroidal
compactification) in the presence of a probe massless scalar field in the bulk.
This result is achieved by writing the black $p$-brane geometry in a Gaussian
null coordinate system which allows us to get a non-singular near-horizon
geometry description. We find that the near-horizon geometry is
$AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal
structure which can be seen as a warped product of $AdS_{2}\times S^{p}$ in
Gaussian null coordinates. We show that the bulk scalar field satisfying the
field equations is expanded in terms of non-normalizable and normalizable
modes, which for certain suitable quantization conditions are well-behaved at
the boundary of $AdS_{p+2}$ space. Furthermore, we show that picking the
normalizable modes results in the existence of conserved quantities on the
horizon. We discuss the impact of these conserved quantities in the late time
regime.
