Eur. Phys. J. C (2015) 75: 448
https://doi.org/10.1140/epjc/s10052-015-3671-7

Regular Article - Theoretical Physics

Space-time singularities in Weyl manifolds

¹ CAPES Foundation, Ministry of Education of Brazil, Brasilia, Brazil
² Departamento de Física, Universidade Federal da Paraíba, C. Postal 5008, João Pessoa, PB, 58051-970, Brazil
³ Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 5, 00185, Rome, Italy

^* e-mail: cromero@fisica.ufpb.br

Received: 13 August 2015
Accepted: 8 September 2015
Published online: 25 September 2015

Abstract

We extend one of the Hawking–Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame.