  This project explores the $D=11$ supergravity model and the properties of its
p-brane ansatz. The initial field content (graviton, gravitino and the
anti-symmetric tensor field) in the action of $D=11$ supergravity is explained
in the context of supersymmetry. The action is then decomposed to the bosonic
sector, which is compared with the $\sigma$-model in string theory at a low
energy limit $\alpha'\xrightarrow{}0$. The dilaton in the $D=10$ string theory
can be realised from the dimensional reduction of $D=11$ supergravity, which
gives the scalar contribution in the action to form the single-charge action.
The field equation of the single-charged action is then derived. An
$SO(D-d)\times Poincare_{d}$ ansatz is introduced to simplify the field
equation. The solution of the field equation bifurcates into the electric
ansatz and the magnetic ansatz. These ansatzes are called p-branes which are
string-like objects that exist in their p-dimensional world volume embedded in
the ambient spacetime. The BPS bounds are saturated for these p-branes, and
upon dimensional reduction, they are similar to extremal Riessner-Nordstrom
black holes up to the scalar. The branic motion is then derived and a special
case of parallel brane orbit is explored. Similar to the Riessner-Nordstrom
black hole, the circular orbit is found to require a specific angular momentum
that increases further from the central brane. The circular orbit always exists
for the extremal case, but the black branes that do not saturate the BPS bound
may not have a circular orbit below a threshold angular momentum.
