Related papers: Local energy estimate on Kerr black hole backgroun…
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…
Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein…
This note surveys how energy generation and strengthening has been used to prove Morawetz estimates for various field equations in Minkowski space, the exterior of the Schwarzschild spacetime, and the exterior of the Kerr spacetime. It…
This work makes the first ever attempt to understand the influence of the black hole background space-time in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, the role of the…
We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force…
In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model…
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated to the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar.…
We provide an invariant characterization of the physical properties of the Kerr spacetime. We introduce two dimensionless invariants, constructed out of some known curvature invariants, that act as detectors for the event horizon and…
We investigate the accretion of a collisionless, relativistic kinetic gas by a rotating Kerr black hole, assuming that at infinity the state of the gas is described by a distribution function depending only on the energy of the particles.…
In this paper we treat the black hole horizon as a physical boundary to the spacetime and study its dynamics following from the Gibbons-Hawking-York boundary term. Using the Kerr black hole as an example we derive an effective action that…
In this article we calculate the total angular momentum for Kerr space-time for slow rotations. In order to analyze the role of such quantity we apply Weyl quantization method to obtain a quantum equation for the z-component of the angular…
We calculate the energy distribution of a charged regular black hole by using the energy-momentum complexes of Einstein and M{\o}ller.
We analyze the extraction of the rotational energy of a Kerr black hole (BH) endowed with a test charge and surrounded by an external test magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin,…
Using distributional techniques we calculate the energy--momentum tensor of the Schwarzschild geometry. It turns out to be a well--defined tensor--distribution concentrated on the $r=0$ region which is usually excluded from space--time.…
Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but the actual nature of these objects has still to be proven. The analysis of the electromagnetic radiation emitted by a…
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These…
We use the Bergmann energy-momentum complex to calculate the energy of a charged regular black hole. The energy distribution is the same as we obtained in the Einstein prescription. Also, we get the expression of the energy in the Bergmann…
The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major obstacle in the black hole stability problem is that the…
In a previous work, we constructed a positive-definite total energy functional for the axially symmetric linear perturbative theory of Kerr black hole spacetimes. That work is based on the dimensional reduction of dynamical axisymmetric…
In this article we prove optimal pointwise bounds for solutions to the semilinear wave equation with integer powers $p\geq 3$ on Kerr backgrounds with small angular momentum and small initial data.