Eur. Phys. J. C (2017) 77: 787
https://doi.org/10.1140/epjc/s10052-017-5378-4

Regular Article - Theoretical Physics

Thermal Casimir effect in Kerr spacetime with quintessence and massive gravitons

¹ Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5.008, João Pessoa, PB, CEP 58059-970, Brazil
² Departamento de Física, Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Av. Dr. Guarany, 317, Derby Clube, Sobral, CE, CEP 62042-030, Brazil
³ Grupo de Física Teórica (GFT), Universidade Estadual do Ceará, Av. Dr. Silas Munguba 1700, Fortaleza, CE, CEP 60714-903, Brazil
⁴ Universidade Estadual do Ceará, Faculdade de Educação, Ciências e Letras do Sertão Central, Planalto Universitário s/n, Quixadá, CE, Brazil

^* e-mail: marcony.cunha@uece.br

Received: 28 September 2017
Accepted: 6 November 2017
Published online: 21 November 2017

Abstract

Starting from an analytical expression for the Helmholtz free energy we calculate the thermal corrections to the Casimir energy density and entropy within nearby ideal parallel plates in the vacuum of a massless scalar field. Our framework is the Kerr spacetime in the presence of quintessence and massive gravitons. The high and low temperature regimes are especially analyzed in order to distinguish the main contributions. For instance, in the high temperature regime, we show that the force between the plates is repulsive and grows with both the quintessence and the massive gravitons. Regarding the Casimir entropy, our results are in agreement with the Nernst heat theorem and therefore confirm the third law of thermodynamics in the present scenario.