The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the mode harmonic number, and $V$ has a second order pole at $r_s$. This is irrelevant to the black hole exterior stability problem, where $r>2M>0$, and $r_s <0$, but it introduces a non trivial problem in the naked singular case where $M0$, and the singularity appears in the relevant range of $r$. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related to $\Psi_z$ by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of $M$}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

A path to radio-loudness through gas-poor galaxy mergers and the role of retrograde accretion

In this proceeding we explore a pathway to radio-loudness under the hypothesis that retrograde accretion onto giant spinning black holes leads to the launch of powerful jets, as seen in radio loud QSOs and recently in LAT/Fermi and BAT/Swift Blazars. Counter-rotation of the accretion disc relative to the BH spin is here associated to gas-poor galaxy mergers progenitors of giant (missing-light) ellipticals. The occurrence of retrograde accretion enters as unifying element that may account for the radio-loudness/galaxy morphology dichotomy observed in AGN.Comment: To appear in the proceedings of the conference "Accretion and Ejection in AGN: A global view, June 22-26 2009 - Como, Italy

On the orientation and magnitude of the black hole spin in galactic nuclei

Massive black holes in galactic nuclei vary their mass M and spin vector J due to accretion. In this study we relax, for the first time, the assumption that accretion can be either chaotic, i.e. when the accretion episodes are randomly and isotropically oriented, or coherent, i.e. when they occur all in a preferred plane. Instead, we consider different degrees of anisotropy in the fueling, never confining to accretion events on a fixed direction. We follow the black hole growth evolving contemporarily mass, spin modulus a and spin direction. We discover the occurrence of two regimes. An early phase (M <~ 10 million solar masses) in which rapid alignment of the black hole spin direction to the disk angular momentum in each single episode leads to erratic changes in the black hole spin orientation and at the same time to large spins (a ~ 0.8). A second phase starts when the black hole mass increases above >~ 10 million solar masses and the accretion disks carry less mass and angular momentum relatively to the hole. In the absence of a preferential direction the black holes tend to spin-down in this phase. However, when a modest degree of anisotropy in the fueling process (still far from being coherent) is present, the black hole spin can increase up to a ~ 1 for very massive black holes (M >~ 100 million solar masses), and its direction is stable over the many accretion cycles. We discuss the implications that our results have in the realm of the observations of black hole spin and jet orientations.Comment: 14 pages, 7 figures, accepted for publication in Ap

Probing the formation history of the nuclear star cluster at the Galactic Centre with millisecond pulsars

The origin of the Nuclear Star Cluster in the centre of our Galaxy is still unknown. One possibility is that it formed after the disruption of stellar clusters that spiralled into the Galactic Centre due to dynamical friction. We trace the formation of the Nuclear Star Cluster around the central black hole, using state-of-the-art N-body simulations, and follow the dynamics of the neutron stars born in the clusters. We then estimate the number of Millisecond Pulsars (MSPs) that are released in the Nuclear Star Cluster, during its formation. The assembly and tidal dismemberment of globular clusters lead to a population of MSPs distributed over a radius of about 20 pc, with a peak near 3 pc. No clustering is found on the sub-parsec scale. We simulate the detectability of this population with future radio telescopes like the MeerKAT radio telescope and SKA1, and find that about of order ten MSPs can be observed over this large volume, with a paucity of MSPs within the central parsec. This helps discriminating this scenario from the in-situ formation model for the Nuclear Star Cluster that would predict an over abundance of MSPs closer to the black hole. We then discuss the potential contribution of our MSP population to the gamma-ray excess at the Galactic Centre.Comment: 11 pages, 8 figures, accepted for publication in MNRA

Growing massive black holes through super-critical accretion of stellar-mass seeds

The rapid assembly of the massive black holes that power the luminous quasars observed at $z \sim 6-7$ remains a puzzle. Various direct collapse models have been proposed to head-start black hole growth from initial seeds with masses $\sim 10^5\,\rm M_\odot$, which can then reach a billion solar mass while accreting at the Eddington limit. Here we propose an alternative scenario based on radiatively inefficient super-critical accretion of stellar-mass holes embedded in the gaseous circum-nuclear discs (CNDs) expected to exist in the cores of high redshift galaxies. Our sub-pc resolution hydrodynamical simulations show that stellar-mass holes orbiting within the central 100 pc of the CND bind to very high density gas clumps that arise from the fragmentation of the surrounding gas. Owing to the large reservoir of dense cold gas available, a stellar-mass black hole allowed to grow at super-Eddington rates according to the "slim disc" solution can increase its mass by 3 orders of magnitudes within a few million years. These findings are supported by simulations run with two different hydro codes, RAMSES based on the Adaptive Mesh Refinement technique and GIZMO based on a new Lagrangian Godunov-type method, and with similar, but not identical, sub-grid recipes for star formation, supernova feedback, black hole accretion and feedback. The low radiative efficiency of super-critical accretion flows are instrumental to the rapid mass growth of our black holes, as they imply modest radiative heating of the surrounding nuclear environment.Comment: 12 pages, 8 figures, 2 tables. Accepted for publication in MNRA

Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schr\"odinger-like stability equation. As an immediate application we prove that for $D \neq 6$ and $\alpha >0$, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case $D =6$, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for $\alpha < 0$.Comment: 7 pages, 1 figure, minor corrections, references adde

Hyperk\"ahler torsion structures invariant by nilpotent Lie groups

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of ${\frak sp}(n)$ to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.Comment: LateX, 12 page