http://arxiv.org/abs/1611.03985
[Abridged] If gravitation is to be described by a hybrid metric-Palatini $f(\mathcal{R})$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous G\”odel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of $f(\mathcal{R})$ theories, we examine whether they admit G\”odel-type solutions for some physically well-motivated matter sources. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous solutions in $f(\mathcal{R})$ theories reduces to the problem of determining solutions of this type in $f(R)$ gravity in the metric formalism. Employing this result, we determine a perfect-fluid G\”odel-type solution in $f(\mathcal{R})$ gravity, and show that it is isometric to the G\”odel geometry, and therefore exhibits violation of causality. This extends a theorem on G\”odel-type models, which was established in the framework of general relativity. We also show that a single massless scalar field gives rise to the only ST-homogeneous G\”odel-type solution with no violation of causality. Since the perfect-fluid and scalar field solutions are in the hyperbolic family, i.e. the essential parameter is positive $m^{2} > 0$, we further determine a general G\”odel-type solution with a combination of a scalar with an electromagnetic field plus a perfect fluid as matter source, which contains G\”odel-type solutions with $m=0$ and with $m^{2} < 0$, as well as the previous solutions as special cases. The bare existence of these G\”odel-type solutions makes apparent that hybrid metric-Palatini $f(\mathcal{R})$ gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity.
J. Santos, M. Reboucas, T. Oliveira, et. al.
Tue, 15 Nov 16
46/86
Comments: 18 pages, no figures
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