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Register a new userExact results on analogue gravity in optical Plebanski-Tamm media
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Exact results concerning ray-tracing methods in Plebanski-Tamm media are derived. In particular, Hamilton equations describing the propagation of quasi-plane wave electromagnetic fields in the geometrical optics regime are explicitly written down in terms of the 3-metric representing the properties of the optical analogue, anisotropic medium. We exemplify our results by obtaining the trajectories of light in the resulting analogue medium recreating Godels universe.
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Using the action for the instanton representation of Plebanski gravity (IRPG), we construct minisuperspace solutions restricted to diagonal variables. We have treated the Euclidean signature case with zero cosmological constant, depicting a gravitational analogy to free particle motion. This paper provides a testing ground for the IRPG for a simple case, which will be extended to the full theory in future work.
We show that the Plebanski-Demianski spacetime persists as a solution of General Relativity when the theory is supplemented with both, a conformally coupled scalar theory and with quadratic curvature corrections. The quadratic terms are of two types and are given by quadratic combinations of the Riemann tensor as well as a higher curvature interaction constructed with a scalar field which is conformally coupled to quadratic terms in the curvature. The later is built in terms of a four-rank tensor $S_{mu u}^{ lambdarho}$ that depends on the Riemann tensor and the scalar field, and that transforms covariantly under local Weyl rescallings. Due to the generality of the Plebanski-Demianski family, several new hairy black hole solutions are obtained in this higher curvature model. We pay particular attention to the C-metric spacetime and the stationary Taub-NUT metric, which in the hyperbolic case can be analytically extended leading to healthy, asymptotically AdS, wormhole configurations. Finally, we present a new general model for higher derivative, conformally coupled scalars, depending on an arbitrary function and that we have dubbed Conformal K-essence. We also construct spherically symmetric hairy black holes for these general models.
Using the instanton representation method, we re-construct graviton solutions about DeSitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known solutions. This paper is a precursor for its application to the construction of new General Relativity solutions in future work.
General Relativitys Kerr metric is famous for its many symmetries which are responsible for the separability of the Hamilton-Jacobi equation governing the geodesic motion and of the Teukolsky equation for wave dynamics. We show that there is a unique stationary and axisymmetric Newtonian gravitational potential that has exactly the same dual property of separable point-particle and wave motion equations. This `Kerr metric analogue of Newtonian gravity is none other than Eulers 18th century problem of two-fixed gravitating centers.
Ultrashort laser pulse filaments in dispersive nonlinear Kerr media induce a moving refractive index perturbation which modifies the space-time geometry as seen by co-propagating light rays. We study the analogue geometry induced by the filament and show that one of the most evident features of filamentation, namely conical emission, may be precisely reconstructed from the geodesics. We highlight the existence of favorable conditions for the study of analogue black hole kinematics and Hawking type radiation.
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