Inertial Oscillations in Geostrophic Flow: Is the Inertial Frequency Shifted by ζ/2 or by ζ?

The short answer to the question posed in the title is that it depends on the frame of reference chosen to describe the motions. In the inertial limit, the frequency in a rotating frame of reference corresponds to the rotation rate of the inertial current vectors relative to that frame. When described in a reference frame rotating with a geostrophic flow having a relative vertical vorticity ζ, inertial oscillations have a frequency f + ζ, equal to twice the fluid’s rotation rate around the local vertical axis. From a nonrotating frame of reference, one would measure only half this frequency; the other half arises from describing inertial motions in a reference frame rotating with the background flow. However, when described in a reference frame rotating with Earth, hence rotating at −ζ/2 relative to the geostrophic frame, inertial oscillations have a frequency reduced to f + ζ/2.

BLACK HOLE AS A SUPERCOLLIDER

Recently, it was found that in the vicinity of the black hole horizon of a rotating black hole two particles can collide in such a way that the energy in their centre of mass frame becomes infinite (so-called BSW effect). I give a brief review of basic features of this effect and show that this is a generic property of rotating black holes. In addition, there exists its counterpart for radial motion of charged particles in the charged black hole background. Simple kinematic explanation is suggested that is based on observation that all massive particles fall in two classes. In the first case (by definition, "usual particles"), the velocity approaches that of light on the horizon in the locally-nonrotating frame due to special relationship between the energy and the angular momentum. In the second case, it tends to some value less than speed of light. As a result, the relative velocity also tends to the speed of light with infinitely growing Lorentz factor.

BLACK HOLE AS A SUPERCOLLIDER

Recently, it was found that in the vicinity of the black hole horizon of a rotating black hole two particles can collide in such a way that the energy in their centre of mass frame becomes infinite (so-called BSW effect). I give a brief review of basic features of this effect and show that this is a generic property of rotating black holes. In addition, there exists its counterpart for radial motion of charged particles in the charged black hole background. Simple kinematic explanation is suggested that is based on observation that all massive particles fall in two classes. In the first case (by definition, "usual particles"), the velocity approaches that of light on the horizon in the locally-nonrotating frame due to special relationship between the energy and the angular momentum. In the second case, it tends to some value less than speed of light. As a result, the relative velocity also tends to the speed of light with infinitely growing Lorentz factor.

Improved Secular Stability Limits for Rotating White Dwarfs

In the special case of the Maclaurin spheroids, it has been known for some time that the m = 2 barlike modes become secularly unstable for t ≡ T/IWI ≥ 0.1376 where T is the total rotational kinetic energy and W is the total gravitational energy of the spheroid. “Secular” here means that the instability depends on dissipative processes and grows on a long dissipative time scale. In particular, the Dedekind-like bar mode, which has zero eigenfrequency at t = 0.1376 as viewed in the nonrotating frame, is unstable due to gravitational radiation (Chandrasekhar 1970).