Felix Finster

Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordstrom black hole background

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner–Nordstrom black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

Nonexistence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry

We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhars separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast with the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity.

Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry

Abstract: The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in

Particle-Like Solutions of the Einstein-Dirac-Maxwell Equations

L^infty_{mbox{scriptsize{loc}}}

Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system

at least at the rate t−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].

The interaction of Dirac particles with non-abelian gauge fields and gravity – bound states

Abstract We consider the coupled Einstein–Dirac–Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

The coupling of gravity to spin and electromagnetism

Abstract:We consider for j=½, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field.The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordström solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-½-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

The interaction of Dirac particles with non-abelian gauge fields and gravity---black holes.

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang–Mills field. The corresponding Einstein–Dirac–Yang–Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

Hypersurfaces of prescribed Gauß curvature in exterior domains

The coupled Einstein–Dirac–Maxwell equations are considered for a static, spherically symmetric system of two fermions in a singlet spinor state. Stable soliton-like solutions are shown to exist, and we discuss the regularizing effect of gravity from a Feynman diagram point of view.

Some recent progress in classical general relativity

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding EinsteinDirac-Yang/Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.