After a brief discussion of the σ-hole concept and the significance of molecular electrostatic potentials in noncovalent interactions, we draw attention to some common misconceptions that are encountered in that context: (1) Since the electrostatic potential reflects the contributions of both the nuclei and the electrons, it cannot be assumed that negative potentials correspond to “electron-ric...

The residuals about the standard Mbh-σ relation correlate with the effective radius, absolute magnitude, and Sérsic index of the host bulge. Although, it is noted here that the elliptical galaxies do not partake in such correlations. Moreover, it is revealed that barred galaxies (with their relatively small, faint, and low stellar concentration bulges) can deviate from the Mbh-σ relation by δ l...

We consider corrections to the entropy of a black hole from an O(N) invariant linear σ-model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the σ-model entropy depends on scale. At short distances, ...

Early-type galaxy velocity dispersions and luminosities are correlated. The correlation estimated in local samples (≤ 100 Mpc) differs from that measured more recently in the SDSS. We show that this is also true for the ENEAR sample if galaxy luminosities are estimated using distances which have been corrected for peculiar motions. We then show that, because the estimate of the ‘true’ distance ...

We calibrate reverberation-based black hole masses in active galactic nuclei (AGNs) by using the correlation between black hole mass, MBH, and bulge/spheroid stellar velocity dispersion, σ∗. We use new measurements of σ∗ for 6 AGNs and published velocity dispersions for 10 others, in conjunction with improved reverberation mapping results, to determine the scaling factor required to bring rever...

We present the results of deep spectroscopy for the central region of the cluster lens SDSS J1004+4112 with the Subaru telescope. A secure detection of an emission line of the faint blue stellar object (component E) near the center of the brightest cluster galaxy (G1) confirms that it is the central fifth image of the lensed quasar system. In addition, we measure the stellar velocity dispersion...

We present the black hole mass–bulge velocity dispersion relation for a complete sample of 75 soft X-ray selected AGNs. We find that the AGNs with highest accretion rates relative to Eddington lie below the MBH–σ relation of broad line Seyfert 1s, confirming the Mathur et al. (2001) result. The statistical result is robust and not due to any systematic measurement error. This has important cons...

We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topo...

The circumferential shear stress along the boundary of a traction-free circular hole in an infinite isotropic solid under antiplane shear is twice the circumferential shear stress along the corresponding circle in an infinite solid without a hole, under the same loading conditions. This result, originally derived by Lin et al. (Yielding, damage, and failure of anisotropic solids. EGF Publicatio...