  The linear Boltzmann equation governs the absorption and scattering of a
population of particles in a medium with an ambient field, represented by a
Riemannian metric, where particles follow geodesics. In this paper, we study
the possible issues of uniqueness and stability in recovering the absorption
and scattering coefficients from the boundary knowledge of the albedo operator.
The albedo operator takes the incoming flux to the outgoing flux at the
boundary. For simple compact Riemannian manifolds of dimension $n \geq 2$, we
study the stability of the absorption coefficient from the albedo operator up
to a gauge transformation. We derive that when the absorption coefficient is
isotropic then the albedo operator determines uniquely the absorption
coefficient and we establish a stability estimate. We also give an
identification result for the reconstruction of the scattering parameter. The
approach in this work is based on the construction of suitable geometric optics
solutions and the use of the invertibility of the geodesic ray transform.
