Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity

Abstract

[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 Gödel-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 Gödel-type solutions for well-motivated matter source. 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 Einstein's field equations with a cosmological constant. Employing this far-reaching result, we determine a general Gödel-type whose matter source is a combination of a scalar with an electromagnetic field plus a perfect fluid. This general Gödel-type solution contains special solutions in which the essential parameter $m^2$ can be $m^2>0$, $m=0$, and $m^2<0$, covering thus all classes of homogeneous Gödel-type spacetimes. This general solution also contains all previously known solution as special cases. The bare existence of these Gödel-type solutions makes apparent that hybrid metric-Palatini gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity.

V2: Presentation of Sec.4 substantially improved, references added, version published in Eur.Phys.J.C

References in corpus (21)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Wormholes supported by hybrid metric-Palatini gravity
• The matter power spectrum in f(R) gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Violation of the Equivalence Principle in Modified Theories of Gravity
• Hydrogen atom in Palatini theories of gravity
• Gödel-type universes in f(R) gravity
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Dynamics of Linear Perturbations in the hybrid metric-Palatini gravity
• Experimental Simulation of Closed Timelike Curves
• Gödel-type universes in Palatini f(R) gravity
• The Gödel solution in the modified gravity
• Violation of causality in $f(T)$ gravity
• Gödel-type universes in f(T) gravity
• From black strings to black holes: nuttier and squashed AdS${}_5$ solutions

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• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Cosmic strings in generalized hybrid metric-Palatini gravity
• Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory
• Novel electrically charged wormhole, black hole and black bounce exact solutions in hybrid metric-Palatini gravity
• Gödel-type solutions in $f(R,T,R_{\mu \nu }{T}^{\mu \nu }$) gravity
• Wave Fronts in a Causality Violating Godel-Type Metric
• Weyl Fermions in a Linear Class of Gödel-Type Space-Time Backgrounds