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Register a new userTunneling approach and thermality in dispersive models of analogue gravity
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We set up a tunneling approach to the analogue Hawking effect in the case of models of analogue gravity which are affected by dispersive effects. An effective Schroedinger-like equation for the basic scattering phenomenon IN->P+N*, where IN is the incident mode, P is the positive norm reflected mode, and N* is the negative norm one, signalling particle creation, is derived, aimed to an approximate description of the phenomenon. Horizons and barrier penetration play manifestly a key-role in giving rise to pair-creation. The non-dispersive limit is also correctly recovered. Drawbacks of the model are also pointed out and a possible solution ad hoc is suggested.
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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.
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.
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.
We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this critical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.
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