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Dynamics of perfect fluids in nonminimally coupled gravity

Orfeu Bertolami^*

António Martins^†

Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

^*Also at Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa. orfeu.bertolami@fc.up.pt
^†antonio.fpn.martins@gmail.com

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Phys. Rev. D 85, 024012 – Published 11 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024012

Abstract

In this work we explore the consequences that a nonminimal coupling between geometry and matter can have on the dynamics of perfect fluids. It is argued that the presence of a static, axially symmetric pressureless fluid does not imply a Minkowski space-time like as is in general relativity. This feature can be attributed to a pressure mimicking mechanism related to the nonminimal coupling. The case of a spherically symmetric black hole surrounded by fluid matter is analyzed, and it is shown that under equilibrium conditions the total fluid mass is about twice that of the black hole. Finally, a generalization of the Newtonian potential for a fluid element is proposed and its implications are briefly discussed.

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References (19)

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In fact, the same relation holds even for the axially symmetric case. See below.
There is a minor issue we have been ignoring so far: as pointed out earlier, $g_{t t}$ must depend on $λ$ , so that one recovers $g_{t t} = - 1$ when $λ \to 0$ . Making the substitution $r_{s}^{*} \to λ r_{s}^{*}$ is one way to deal with this problem. However, if $λ \neq 0$ , it can be absorbed into $f_{2}$ , which is the same as taking $λ = 1$ , so that no problem arises whatsoever. We will assume that $λ \neq 0$ throughout the rest of this paper.
Take, for example, the ratio $ρ (r_{s}^{*} / 2) / ρ (r_{s}^{*}) ≃ 8.5$
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Dynamics of perfect fluids in nonminimally coupled gravity

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