Bounds for axially symmetric linear perturbations for the extreme Kerr black hole

We obtain remarkably simple integral bounds for axially symmetric linear perturbations for the extreme Kerr black hole in terms of conserved energies. From these estimates we deduce pointwise bounds for the perturbations outside the horizon.Comment: 15 page

On the linear stability of the extreme Kerr black hole under axially symmetric perturbations

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the particular case of Minkowski, using this energy we also prove pointwise boundedness of the perturbation in a remarkable simple way.Comment: 35 pages. 2 figures. Relevant improvement in the presentation in section 2.

Construction of the Lyapunov spectrum in a chaotic system displaying phase synchronization

We consider a three-dimensional chaotic system consisting of the suspension of Arnold's cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relative phase between the suspension flow and the clock locks to a special value, thus making the motion fall onto a lower dimensional attractor. More specifically, we construct the attractive invariant manifold, of dimension smaller than three, using a convergent perturbative expansion. Moreover, we compute via convergent series the Lyapunov exponents, including notably the central one. The result generalizes a previous construction of the attractive invariant manifold in a similar but simpler model. The main novelty of the current construction relies in the computation of the Lyapunov spectrum, which consists of non-trivial analytic exponents. Some conjectures about a possible smoothening transition of the attractor as the coupling is increased are also discussed.Comment: 24 pages, 10 figure

Mass models from high-resolution HI data of the dwarf galaxy NGC 1560

We present HI observations performed at the GMRT of the nearby dwarf galaxy NGC 1560. This Sd galaxy is well-known for a distinct "wiggle" in its rotation curve. Our new observations have twice the resolution of the previously published HI data. We derived the rotation curve by taking projection effects into account, and we verified the derived kinematics by creating model datacubes. This new rotation curve is similar to the previously published one: we confirm the presence of a clear wiggle. The main differences are in the innermost ~100 arcsec of the rotation curve, where we find slightly (<~ 5 km/s) higher velocities. Mass modelling of the rotation curve results in good fits using the core-dominated Burkert halo (which however does not reproduce the wiggle), bad fits using the a Navarro, Frenk & White halo, and good fits using MOND (Modified Newtonian Dynamics), which also reproduces the wiggle.Comment: Accepted for publication in MNRAS. 11 pages, 13 figures. High-resolution version available at http://users.ugent.be/~ggianfra/1560_final.pd

Modified gravity models and the central cusp of dark matter haloes in galaxies

The N-body dark matter (DM) simulations point that DM density profiles, e.g. the Navarro Frenk White (NFW) halo, should be cuspy in its centre, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves close to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, Modified Newtonian Dynamics (MOND) and a more recent approach renormalization group effects in general relativity (RGGR). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that (i) there is a radius, given by half the disc scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; (ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have, respectively, two and one more free parameters than MOND)

Supernova neutrino physics with a nuclear emulsion detector

The existence of the coherent neutrino-nucleus scattering reaction requires to evaluate, for any detector devoted to WIMP searches, the irreducible background due to conventional neutrino sources and at same time, it gives a unique chance to reveal supernova neutrinos. We report here a detailed study concerning a new directional detector, based on the nuclear emulsion technology. A Likelihood Ratio test shows that, in the first years of operations and with a detector mass of several tens of tons, the observation of the supernova signal can be achieved. The determination of the distance of the supernova from the neutrinos and the observation of $^8$B neutrinos are also discussed.Comment: 22 pages, 12 figure

Remarks on the properties of elliptical galaxies in modified Newtonian dynamics

Two incorrect arguments against MOND in elliptical galaxies could be that the equivalent circular velocity curves tend to become flat at much larger accelerations than in spiral galaxies, and that the Newtonian dark matter halos are more concentrated than in spirals. Here, we compare published scaling relations for the dark halos of elliptical galaxies to the scaling relations expected for MONDian phantom halos. We represent the baryonic content of galaxies by spherical profiles, and their corresponding MONDian phantom halos by logarithmic halos. We then derive the surface densities, central densities, and phase space densities and compare them with published scaling relations. We conclude that it is possible to get flat circular velocity curves at high acceleration in MOND, and that this happens for baryonic distributions described by Jaffe profiles in the region where the circular velocity curve is flat. Moreover, the scaling relations of dark halos of ellipticals are remarkably similar to the scaling relations of phantom halos of MOND.Comment: Accepted for publication in A and

Isolated and non-isolated dwarfs in terms of modified Newtonian dynamics

Within the framework of modified Newtonian dynamics (MOND) we investigate the kinematics of two dwarf spiral galaxies belonging to very different environments, namely KK 246 in the Local Void and Holmberg II in the M81 group. A mass model of the rotation curve of KK 246 is presented for the first time, and we show that its observed kinematics are consistent with MOND. We re-derive the outer rotation curve of Holmberg II, by modelling its HI data cube, and find that its inclination should be closer to face-on than previously derived. This implies that Holmberg II has a higher rotation velocity in its outer parts, which, although not very precisely constrained, is consistent with the MOND prediction.Comment: Accepted in A&A as a Research Note. 6 pages, 3 figure