Quasars: a supermassive rotating toroidal black hole interpretation

A supermassive rotating toroidal black hole (TBH) is proposed as the fundamental structure of quasars and other jet-producing active galactic nuclei. Rotating protogalaxies gather matter from the central gaseous region leading to the birth of massive toroidal stars whose internal nuclear reactions proceed very rapidly. Once the nuclear fuel is spent, gravitational collapse produces a slender ring-shaped TBH remnant. These events are typically the first supernovae of the host galaxies. Given time the TBH mass increases through continued accretion by several orders of magnitude, the event horizon swells whilst the central aperture shrinks. The difference in angular velocities between the accreting matter and the TBH induces a magnetic field that is strongest in the region of the central aperture and innermost ergoregion. Due to the presence of negative energy states when such a gravitational vortex is immersed in an electromagnetic field, circumstances are near ideal for energy extraction via non-thermal radiation including the Penrose process and superradiant scattering. This establishes a self-sustaining mechanism whereby the transport of angular momentum away from the quasar by relativistic bi-directional jets reinforces both the modulating magnetic field and the TBH/accretion disk angular velocity differential. Quasar behaviour is extinguished once the BH topology becomes spheroidal. Similar mechanisms may be operating in microquasars, SNe and GRBs when neutron density or BH tori arise. In certain circumstances, long-term TBH stability can be maintained by a negative cosmological constant, otherwise the classical topology theorems must somehow be circumvented. Preliminary evidence is presented that Planck-scale quantum effects may be responsible.Comment: 26 pages, 14 figs, various corrections and enhancements, final versio

Sparse geometric graphs with small dilation

Given a set S of n points in R^D, and an integer k such that 0 <= k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, maximum degree five, and dilation O(n / (k+1)) can be computed in time O(n log n). For any k, we also construct planar n-point sets for which any geometric graph with n-1+k edges has dilation Omega(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position

Inner Size of a Dust Torus in the Seyfert 1 Galaxy NGC 4151

The most intense monitoring observations yet made were carried out on the Seyfert 1 galaxy NGC 4151 in the optical and near-infrared wave-bands. A lag from the optical light curve to the near-infrared light curve was measured. The lag-time between the V and K light curves at the flux minimum in 2001 was precisely 48+2-3 days, as determined by a cross-correlation analysis. The correlation between the optical luminosity of an active galactic nucleus (AGN) and the lag-time between the UV/optical and the near-infrared light curves is presented for NGC 4151 in combination with previous lag-time measurements of NGC 4151 and other AGNs in the literature. This correlation is interpreted as thermal dust reverberation in an AGN, where the near-infrared emission from an AGN is expected to be the thermal re-radiation from hot dust surrounding the central engine at a radius where the temperature equals to that of the dust sublimation temperature. We find that the inner radius of the dust torus in NGC 4151 is $\sim$ 0.04 pc corresponding to the measured lag-time, well outside the broad line region (BLR) determined by other reverberation studies of the emission lines.Comment: Accepted for publication in ApJ Letters, 13 pages, 3 figures; Corrected typo

Pulsar timing in extreme mass ratio binaries: a general relativistic approach

The detection of a pulsar (PSR) in a tight, relativistic orbit around a supermassive or intermediate mass black hole - such as those in the Galactic centre or in the centre of Globular clusters - would allow for precision tests of general relativity (GR) in the strong-field, non-linear regime. We present a framework for calculating the theoretical time-frequency signal from a PSR in such an Extreme Mass Ratio Binary (EMRB). This framework is entirely relativistic with no weak-field approximations and so able to account for all higher-order strong-field gravitational effects, relativistic spin dynamics, the convolution with astrophysical effects and the combined impact on the PSR timing signal. Specifically we calculate both the spacetime path of the pulsar radio signal and the complex orbital and spin dynamics of a spinning pulsar around a Kerr black hole, accounting for spacetime curvature and frame dragging, relativistic and gravitational time delay, gravitational light bending, temporal and spatial dispersion induced by the presence of plasma along the line of sight and relativistic aberration. This then allows for a consistent time-frequency solution to be generated. Such a framework is key for assessing the use of PSR as probes of strong field GR, helping to inform the detection of an EMRB system hosting a PSR and, most essentially, for providing an accurate theoretical basis to then compare with observations to test fundamental physics.Comment: 19 pages, 15 Figures. Accepted for publication in MNRA