Eur. Phys. J. C (2009) 63: 149-155
https://doi.org/10.1140/epjc/s10052-009-1076-1

Regular Article - Theoretical Physics

Circular orbits in cosmic string and Schwarzschild–AdS spacetime with Fermi–Walker transport

¹ Departamento de Física, CCEN, Universidade Federal da Paraíba, Cidade Universitária, 58051-970, João Pessoa, PB, Brazil
² Departamento de Física, Universidade Estadual de Feira de Santana, BR116-Norte, Km 3, 44031-460, Feira de Santana, BA, Brazil

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

Received: 9 January 2009
Revised: 18 May 2009
Published online: 16 June 2009

Abstract

In this paper we discuss the Fermi–Walker transport of vectors along orbits in cosmic string and Schwarzschild–AdS spacetimes. We analyze the influence of acceleration on these holonomies. An effect similar to Thomas precession is observed within the process of Fermi–Walker transport along these circular orbits which are studied in the limit of vanishing cosmological constant in Schwarzschild–AdS case; also we obtain Fermi–Walker transport in a Schwarzschild background. In the case of a Schwarzschild spacetime, we analyze the quantized band holonomy invariance. In the limit of zero acceleration we recover the well-known results for holonomy matrix obtained by parallel transport in all these spacetimes.