Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

Resonant scattering of light in a near-black-hole metric

We show that low-energy photon scattering from a body with radius R slightly larger than its Schwarzschild radius rs resembles black-hole absorption. This absorption occurs via capture resulting in one of the many long-lived, densely packed resonances that populate the continuum. The lifetimes and density of these meta-stable states tend to infinity in the limit rs → R. We determine the energy-averaged cross section for particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus a non-singular static metric may trap photons for arbitrarily long times, making it appear completely 'black' before the actual formation of a black hole. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica

Different Flavors of Nonadiabatic Molecular Dynamics

The Born‐Oppenheimer approximation constitutes a cornerstone of our understanding of molecules and their reactivity, partly because it introduces a somewhat simplified representation of the molecular wavefunction. However, when a molecule absorbs light containing enough energy to trigger an electronic transition, the simplistic nature of the molecular wavefunction offered by the Born‐Oppenheimer approximation breaks down as a result of the now non‐negligible coupling between nuclear and electronic motion, often coined nonadiabatic couplings. Hence, the description of nonadiabatic processes implies a change in our representation of the molecular wavefunction, leading eventually to the design of new theoretical tools to describe the fate of an electronically‐excited molecule. This Overview focuses on this quantity—the total molecular wavefunction—and the different approaches proposed to describe theoretically this complicated object in non‐Born‐Oppenheimer conditions, namely the Born‐Huang and Exact‐Factorization representations. The way each representation depicts the appearance of nonadiabatic effects is then revealed by using a model of a coupled proton–electron transfer reaction. Applying approximations to the formally exact equations of motion obtained within each representation leads to the derivation, or proposition, of different strategies to simulate the nonadiabatic dynamics of molecules. Approaches like quantum dynamics with fixed and time‐dependent grids, traveling basis functions, or mixed quantum/classical like surface hopping, Ehrenfest dynamics, or coupled‐trajectory schemes are described in this Overview