The Jang Equation and the Positive Mass Theorem in the Asymptotically Hyperbolic Setting

We solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

Dwindling impact of large volcanic eruptions on global glacier changes in the Anthropocene

<p>Large volcanic eruptions impact climate through the injection of ash and sulfur gas into the atmosphere. While the ash particles fall out rapidly, the gas is converted to sulfate aerosols, which reflect solar radiation in the stratosphere and cause a cooling of the global mean surface temperature. Earlier studies suggested that major volcanic eruptions resulted in positive mass balances and advances of glaciers. Here we perform a multivariate analysis to decompose global glacier mass changes from 1961 to 2005 into components associated with anthropogenic influences, volcanic and solar activity, and El Niño Southern Oscillation (ENSO). We find that the global glacier mass loss was mainly driven by the anthropogenic forcing, interrupted by a few years of intermittent mass gains following large volcanic eruptions. The relative impact of volcanic eruptions is dwindling due to strongly increasing greenhouse gas concentrations since the mid of the 20<sup>th</sup> century. Furthermore, our study indicates that solar activity and ENSO have limited impacts on climate conditions at glacier locations and that volcanic eruptions alone can hardly explain decadal periods of glacier advances documented since the 16<sup>th</sup> century.</p>

Initial Data Rigidity Results

We prove several rigidity results related to the spacetime positive mass theorem. A key step is to show that certain marginally outer trapped surfaces are weakly outermost. As a special case, our results include a rigidity result for Riemannian manifolds with a lower bound on their scalar curvature.

Two Types of Space in the Hydrogen Atom not Predictable with Quantum Mechanics

Einstein’s energy-momentum relationship is not applicable to the electron in a hydrogen atom. Therefore, the author has previously derived an energy-momentum relationship applicable to the electron inside the hydrogen atom where potential energy exists. However, the initially-derived relationship did not incorporate the discontinuities in energy which are characteristic of quantum mechanics. Therefore, the author derived a new quantum condition to take the place of Bohr’s quantum condition, i.e., , and that was used to incorporate discontinuity into the relationship derived by the author. When that relationship is solved, it is evident that, in addition to the existing energy levels, there are also ultra-low energy levels where the electron mass becomes negative. A previously unknown state of the hydrogen atom exists, formed from an electron with negative mass and a proton with positive mass. The electron with negative mass exists near the proton. The author predicts that this unknown matter is the true nature of dark matter, an unknown source of gravity whose true nature is currently unknown.

Non-singular vortices with positive mass in 2+1-dimensional Einstein gravity with AdS3 and Minkowski background

In previous work, black hole vortex solutions in Einstein gravity with AdS3 background were found where the scalar matter profile had a singularity at the origin r = 0. In this paper, we find numerically static vortex solutions where the scalar and gauge fields have a non-singular profile under Einstein gravity in an AdS3 background. Vortices with different winding numbers n, VEV v and cosmological constant Λ are obtained. These vortices have positive mass and are not BTZ black holes as they have no event horizon. The mass is determined in two ways: by subtracting the numerical values of two separate asymptotic metrics and via an integral that is purely over the matter fields. The mass of the vortex increases as the cosmological constant becomes more negative and this coincides with the core of the vortex becoming smaller (compressed). We then consider the vortex with gravity in asymptotically flat spacetime for different values of the coupling α = 1/(16πG). At the origin, the spacetime has its highest curvature and there is no singularity. It transitions to an asymptotic conical spacetime with angular deficit that increases significantly as α decreases. For comparison, we also consider the vortex without gravity in flat spacetime. For this case, one cannot obtain the mass by the first method (subtracting two metrics) but remarkably, via a limiting procedure, one can obtain an integral mass formula. In the absence of gauge fields, there is a well-known logarithmic divergence in the energy of the vortex. With gravity, we present this divergence in a new light. We show that the metric acquires a logarithmic term which is the 2 + 1 dimensional realization of the Newtonian gravitational potential when General Relativity is supplemented with a scalar field. This opens up novel possibilities which we discuss in the conclusion.