The inequality between mass and angular momentum for axially symmetric black holes

In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture on the physical implications of this characterization for the non linear stability problem for black holes.Comment: 8 pages, Honorable Mention in the Gravity Research Foundation Essay Competition 200

Knot theory of R-covered Anosov flows: homotopy versus isotopy of closed orbits

In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the universal cover are unknotted. When the manifold is atoroidal, we deduce some finer properties regarding the existence of embedded cylinders connecting two given homotopic orbits.Comment: 20 pages, 9 figure

Laboratory simulations of fluid/gas induced micro-earthquakes:application to volcano seismology

Understanding different seismic signals recorded in active volcanic regions allows geoscientists to derive insight into the processes that generate them. A key type is known as Low Frequency or Long Period (LP) event, generally understood to be generated by different fluid types resonating in cracks and faults. The physical mechanisms of these signals have been linked to either resonance/turbulence within fluids, or as a result of fluids ‘sloshing’ due to a mixture of gas and fluid being present in the system. Less well understood, however, is the effect of the fluid type (phase) on the measured signal. To explore this, we designed an experiment in which we generated a precisely controlled liquid to gas transition in a closed system by inducing rapid decompression of fluid-filled fault zones in a sample of basalt from Mt. Etna Volcano, Italy. We find that fluid phase transition is accompanied by a marked frequency shift in the accompanying microseismic dataset that can be compared to volcano seismic data. Moreover, our induced seismic activity occurs at pressure conditions equivalent to hydrostatic depths of 200 to 750 meters. This is consistent with recently measured dominant frequencies of LP events and with numerous models