Causal properties of nonlinear gravitational waves in modified gravity

Abstract

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments.Comment: 8 pages, 3 figures, 1 table. Accepted for publication in PR

Morphology control of SrBi2Nb2O9 prepared by a modified chemical method

“…The pressed pellets were then sintered at 1100 °C for 2 h. The sample synthesized through molten salt route evidenced the presence of plate-like grains, the thickness of which varied between 0.5 and 0.4 μm. The formation of plates in molten salt could be attributed to dissolution −precipita tion mechanism [18]. However, oxalate co-precipitation route allows the formation of a predominantly polygonal shaped, with grain size heterogeneity.…”

Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

“…The details of 'nearisospectrality' will be investigated in future work. It would also be worthwhile considering whether isospectral stars in modified theories of gravity can exist, since the properties of GWs can vary Suvorov & Melatos 2017). The solution generating techniques discussed by Suvorov & Melatos (2016) may be useful in this direction.…”

A family of solutions to the inverse problem in gravitation: building a theory around a metric

“…This implies that given any metric g, the conformal metric e 2ϕ g for conformal factor ϕ is a solution to some f (R) theory provided that the factor ϕ is chosen such that the conformal scalar curvature is constant; mathematically, this requires the existence of a solution to the Yamabe problem[35,36]. As such, practically any conceivable causal structure can arise in some f (R) theory[37], because a metric conformally related to any given metric can be admitted as an exact solution.…”