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The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation…
Fluid analog models for gravity are based on the idea that any spacetime geometry admits a reinterpretation in which space is thought of as a fluid flowing with a prescribed velocity. This fluid picture is a restatement of the ADM…
The search for regular black hole solutions in classical gravity leads us to consider a core of Euclidean signature in the interior of a black hole. Solutions of Lorentzian and Euclidean general relativity match in such a way that energy…
It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. This question can be answered by invoking the language of Lorentzian differential geometry: If the fluid is barotropic and…
In this work a new family of black hole solutions in Lovelock gravity is discussed. These solutions describe anisotropic fluids which extend to the spatial infinity. Though far from the horizon their geometries approach some previously…
Lorentz-symmetry and the notion of light cones play a central role in the definition of horizons and the existence of black holes. Current observations provide strong indications that astrophysical black holes do exist in Nature. Here we…
The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid onto black holes are solved in Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary…
We study the wave equation for a stationary Lorentzian metric in the case of two space dimensions. Assuming that the metric has a singularity of the appropriate form, surrounded by an ergosphere which is a smooth Jordan curve, we prove the…
We review the Analogue Gravity description of a unidirectional water wave system, assuming no prior knowledge of General Relativity or differential geometry. In so doing, we generalize established results concerning an effective curved…
Quite recently, some new mathematical approaches to black holes have appeared in the literature. They do not rely on the classical concept of event horizon -- which is very global, but on the local concept of hypersurfaces foliated by…
The curved geometry of a spacetime manifold arises as a solution of Einstein's gravitational field equation. We show that the metric of a spherically symmetric gravitational field configuration can be viewed as an optical metric created by…
What is going on (as of August 2008) at the interface between theoretical general relativity, string-inspired models, and observational astrophysics? Quite a lot. In this mini-survey I will make a personal choice and focus on four specific…
We introduce the notion of fluid approximation of a quantum spherical black hole in the context of Loop Quantum Gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations $s_i$ which typically…
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs)…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
In this paper we abandon the idea that even a "quantum" black hole, of Planck size, can still be described as a classical, more or less complicated, geometry. Rather, we consider a genuine quantum mechanical approach where a Planckian black…
This paper is concerned with several not-quantum aspects of black holes, with emphasis on theoretical and mathematical issues related to numerical modeling of black hole space-times. Part of the material has a review character, but some new…
We provide an explicit construction of classical strings that have endpoints on the horizons of the 2D Lorentzian black hole. We argue that this is a dual description of geodesics that are localized around the horizon which are the…
In [cond-mat/9906332; Phys. Rev. Lett. 84, 822 (2000)] and [physics/9906038; Phys. Rev. A 60, 4301 (1999)] Leonhardt and Piwnicki have presented an interesting analysis of how to use a flowing dielectric fluid to generate a so-called…
Strong gravity in the immediate vicinity of compact objects (e.g., black holes, neutron stars) necessitates inclusion of general relativistic effects. Traditionally, pseudo-Newtonian potential representation of gravity were favored to…