Variations in the fine structure constant constraining gravity theories
  In this paper, we investigate how the fine structure constant, $\alpha$, locally varies in the presence of a static and spherically symmetric gravitational source. The procedure consists in calculating the solution and the energy eigenvalues of a massive scalar field around that source, considering the weak-field regimen. From this result, we obtain expressions for an spatially variable fine structure constant by considering suitable modifications in the involved parameters admitting some scenarios of semi-classical and quantum gravities. Constraints on free parameters of the approached theories are calculated from astrophysical observations of the emission spectra of a white dwarf. Such constraints are finally compared with those ones obtained in the literature. 
V. B. Bezerra, M. S. Cunha, C. R. Muniz, M. O. Tahim, and H. S. Vieira
gr-qc astro-ph.SR hep-th