Quantizing gravitational instantons

Gravitational instantons are complete non-singular positive definite metrics satisfying the Einstein equations with or without cosmological constant. We treat quantum fluctuations about such solutions and introduce a useful decomposition of the space of gravitational degrees of freedom in terms of which the one-loop corrections take an especially simple form. We treat in detail the question of zero modes, and the fluctuations about de Sitter space.     

Twistor spinors and gravitational instantons

We construct a complete Riemannian metric on the four-dimensional vector space ⁴ which carries a two-dimensional space of twistor spinor with common zero point. This metric is half-conformally flat but not conformally flat. The construction uses a conformal completion at infinity of theEguchi-Hanson metric on the exterior of a closed ball in ⁴.     

One-sided type-D gravitational instantons

It is shown that for every one-sided type-D gravitational instanton, Einstein's vacuum equations can be reduced locally to a single second-order, nonlinear differential equation of second degree of one real function.     

Extended supersymmetry and gravitational instantons

Methods of extended supersymmetry are used to construct explicitly an instanton solution of the Euclidian Einstein equations in empty space.Translated fromIzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–21, June, 1989.     

Black holes on gravitational instantons

In this paper, we classify and construct five-dimensional black holes on gravitational instantons in vacuum Einstein gravity, with R×U(1)×U(1)$\mathbb{R}\times U(1)\times U(1)$ isometry. These black holes have spatial backgrounds which are Ricci-flat gravitational instantons with U(1)×U(1)$U(1)\times U(1)$ isometry, and are completely regular space–times outside the event horizon. Most of the known exact five-dimensional vacuum black-hole solutions can be classified within this scheme. Amongst the new space–times presented are static black holes on the Euclidean Kerr and Taub-bolt instantons. We also present a rotating black hole on the Eguchi–Hanson instanton.     

A Newman-Penrose formalism for gravitational instantons

A Euclidean version of the Newman-Penrose formalism is developed for the study of gravitational instantons. The formalism is explicitly based on theSU(2)×SU(2) spin structure of positive definite metrics. A Geroch-Held-Penrose formulation is also presented. The Euclidean analogues of several fundamental results in relativity are proved, including the Petrov classification and the Ehlers-Sachs, Goldberg-Sachs, and Mariot-Robinson theorems. In addition, the connection between Petrov type and the admissibility of complex structures is elucidated.     

Index theorem boundary terms for gravitational instantons

We compute the boundary correction terms for the Atiyah-Singer index theorem for spin $\text{1}\text{2}$, 1 and $\text{3}\text{2}$ in asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) metrics. In the case of the explicitly known self-dual multi-instanton (ALE) and multi-Taub-NUT (ALF) metrics we find complete agreement with previous work. We also find the corrections to be consistent for an extended class of ALE's which are not explicitly known but which have been constructed implicitly by Hitchin.     

The geodesic motion on generalized Taub-NUT gravitational instantons

A class of generalized Taub-NUT gravitational instantons is reported in five-dimensional Einstein gravity coupled to a non-linear sigma model. The geodesic dynamics of a spinless particle of unit mass on these static gravitational instantons is studied. This is accomplished by finding a generalized Runge-Lenz vector. Unlike the Kepler problem, or, the dynamics of a spinless particle on the familiar Taub-NUT gravitational instantons, the orbits are not conic sections.     

Spontaneous breaking of local supersymmetry by gravitational instantons

We study the gravitino condensate 〈(D_μΨ_ν − D_μΨ_ν)(D^μΨ^ν − D^νΨ^μ)〉 in the one-loop approximation around a nontrivial background metric. It turns out that, among the known regular solutions of the euclidean Einstein equations, the Eguchi-Hanson metric is the unique relevant configuration. The standard functional integration gives a finite answer for the gravitino condensate. Due to the presence of an anomalous supersymmetry transformation law, this implies that local supersymmetry is broken spontaneously in all supergravity models with scalar multiplets.     

The topology of asymptotically locally flat gravitational instantons

In this Letter we demonstrate that the intersection form of the Hausel–Hunsicker–Mazzeo compactification of a four-dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kähler forms of the hyper-Kähler gravitational instanton metric is exact. This leads to their topological classification.     

Information transfer during the universal gravitational decoherence

Recently Pikovski et al. (Nat Phys 11:668, 2015) have proposed in an intriguing universal decoherence mechanism, suggesting that gravitation may play a conceptually important role in the quantum-to-classical transition, albeit vanishingly small in everyday situations. Here we analyze information transfer induced by this mechanism. We show that generically on short time-scales, gravitational decoherence leads to a redundant information encoding, which results in a form of objectivization of the center-of-mass position in the gravitational field. We derive the relevant time-scales of this process, given in terms of energy dispersion and quantum Fisher information. As an example we study thermal coherent states and show certain robustness of the effect with the temperature. Finally, we draw an analogy between our objectivization mechanism and the fundamental problem of point individuation in General Relativity as emphasized by the Einstein’s Hole argument.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.     

SU(2) instantons with boundary jumps and spin tunneling in magnetic molecules

Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., boundary points lying outside classical phase space. Inclusion of these instantons is shown to resolve the "missing quench paradox" in the magnetic molecule Fe8, i.e., the fact that the tunneling between the ground Zeeman states of this molecule is quenched at only four magnetic field values, instead of the ten that would be expected from the topological Berry phase between interfering instantons. An approximate formula is found for the location of the four remaining quenches.     

Binary-black-hole encounters, gravitational bursts, and maximum final spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the "residual" orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole, and the gravitational bursts in a sequence of equal mass encounters. The initial orbital configurations range from those producing an almost direct infall to others leading to numerous orbits before infall, with multiple bursts of radiation. Our sequence consists of orbits with fixed impact parameter. What varies is the initial linear momentum of the black holes. For this sequence, the final black hole of mass M_{h} gets a maximum spin parameter a/M_{h} approximately 0.823, with this maximum occurring for initial orbital angular momentum L/M_{h};{2} approximately 1.176.     

Scattering induced spin orientation and spin currents in gyrotropic structures

It is shown that additional contributions both to current-induced spin orientation and to the spin Hall effect arise in quantum wells due to the gyrotropy of the structures. Microscopically, they are related to the basic properties of gyrotropic systems, namely, to linearity in the wave vector terms in the matrix element of electron scattering and in the energy spectrum. Calculation shows that, in high-mobility structures, the contribution to the spin Hall current considered here can exceed the term originating from the Mott skew scattering. The text was submitted by the author in English.