Variations in the fine-structure constant constraining gravity theories

¹ Departamento de Física, Universidade Federal da Paraíba - Caixa Postal 5008, CEP 58051-970, João Pessoa, PB, Brazil
² Grupo de Física Teórica (GFT), Centro de Ciências e Tecnologia, Universidade Estadual do Ceará CEP 60740-000, Fortaleza, Ceará, Brazil
³ Grupo de Física Teórica (GFT), Universidade Estadual do Ceará, Faculdade de Educação, Ciências e Letras de Iguatu - Iguatu, Ceará, Brazil
⁴ Grupo de Física Teórica (GFT), Universidade Estadual do Ceará, Faculdade de Educação, Ciências e Letras do Sertão Central - Quixadá, Ceará, Brazil
⁵ Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba - CEP 58233-000, Araruna, PB, Brazil

^(a) valdir@fisica.ufc.br
^(b) marcony.cunha@uece.br
^(c) celio.muniz@uece.br
^(d) makarius.tahim@uece.br
^(e) horacio.santana.vieira@hotmail.com

Received: 7 June 2016
Accepted: 29 August 2016

Abstract

In this paper, we investigate how the fine-structure constant, α, 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 regime. From this result, we obtain expressions for a 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 obtained in the literature.