Related papers: Black Holes as Incompressible Fluids on the Sphere
The Schwarzschild metric has a divergent energy density at the horizon, which motivates a new approach to black holes. If matter is spread uniformly throughout the interior of a supermassive black hole, with mass $M\sim M_\star= 2.34…
These lecture notes, based on a course given at the Zurich Clay Summer School (June 23-July 18, 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this…
The presence of dark matter around a black hole remarkably affects its spacetime. We consider the effects of dark matter on the shadow of a new solution to the Einstein equations that describes a rotating black hole in the background of…
The prediction of spacetime singularities, regions of infinite curvature where classical physics breaks down, is one of the most profound challenges in General Relativity (GR). In particular, black hole solutions such as the Schwarzschild…
Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter…
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a…
In this work, we derive rigorous and universal bounds on the geometric characteristics of black holes in asymptotically flat spacetimes under assumptions that weak energy condition is satisfied. We prove that the event horizon radius, the…
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant…
We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational…
We construct a scattering theory for the spin $\pm2$ Teukolsky equations on the exterior of the Schwarzschild spacetime, as a first step towards developing a scattering theory for the linearised Einstein equations in double null gauge. This…
One of the challenges of today's theoretical physics is to fully understand the connection between a geometrical object like area and a thermostatistical one like entropy, since area behaves analogously like entropy. The Bekenstein bound…
Deformed Reissner-Nordstr\"om, as well as Reissner-Nordstr\"om de Sitter, solutions are obtained in a noncommutative gauge theory of gravitation. The gauge potentials (tetrad fields) and the components of deformed metric are calculated to…
In spherical symmetry, solutions of the semiclassical Einstein equations belong to one of two possible classes. Both classes contain solutions that -- depending on the dynamic behavior of the horizon -- describe evaporating physical black…
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in…
With the question, ``Can relativistic charged spheres form extremal black holes?" in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the…
We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution.…
In this paper we consider spacetimes in vacuum general relativity --possibly coupled to a scalar field-- with a positive cosmological constant $\Lambda$. We employ the Isolated Horizons (IH) formalism where the boundary conditions imposed…
We consider the Burgers equation posed on the outer communication region of a Schwarzschild black hole spacetime. Assuming spherical symmetry for the fluid flow under consideration, we study the propagation and interaction of shock waves…
We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based…
The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods…