LyST: a Scalar-Tensor Theory of Gravity on Lyra Manifold
  We present a scalar-tensor theory of gravity on a torsion-free and metric
compatible Lyra manifold. This is obtained by generalizing the concept of
physical reference frame by considering a scale function defined over the
manifold. The choice of a specific frame induces a local base, naturally
non-holonomic, whose structure constants give rise to extra terms in the
expression of the connection coefficients and in the expression for the
covariant derivative. In the Lyra manifold, transformations between reference
frames involving both coordinates and scale change the transformation law of
tensor fields, when compared to those of the Riemann manifold. From a direct
generalization of the Einstein-Hilbert minimal action coupled with a matter
term, it was possible to build a Lyra invariant action, which gives rise to the
associated Lyra Scalar-Tensor theory of gravity (LyST), with field equations
for $g_{\mu\nu}$ and $\phi$. These equations have a well-defined Newtonian
limit, from which it can be seen that both metric and scale play a role in the
description gravitational interaction. We present a spherically symmetric
solution for the LyST gravity field equations. It dependent on two parameters
$m$ and $r_{L}$, whose physical meaning is carefully investigated. We highlight
the properties of LyST spherically symmetric line element and compare it to
Schwarzchild solution.
