Gábor Etesi

Non-Turing Computations Via Malament-Hogarth Space-Times

We investigate the Church–Kalmár–Kreisel–Turing theses theoretical concerning (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turing-type theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory, then the above-mentioned limitations (predicted by these theses) become no more necessary, hence certain forms of the Church–Turing thesis cease to be valid (in general relativity). (For other choices of the background theory the answer might be different.) We also look at various “obstacles” to computing a nonrecursive function (by relying on relativistic phenomena) published in the literature and show that they can be avoided (by improving the “design” of our future computer). We also ask ourselves, how all this reflects on the arithmetical hierarchy and the analytical hierarchy of uncomputable functions.

Geometric interpretation of Schwarzschild instantons

Abstract We address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic 2-forms on the space. Gibbons found a non-topological L2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manifold and find a non-topological self-dual L2 harmonic 2-form on it. We show how this gives rise to Abelian instantons and identify them with SU(2)-instantons of Pontryagin number 2n2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we also calculate the full L2 harmonic space for the Euclidean Schwarzschild manifold.

Geometric construction of new Yang–Mills instantons over Taub-NUT space

Abstract In this Letter we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang–Mills instanton corresponding to the Eguchi–Hanson–Gibbons L2 harmonic 2-form, while at an inner point we recover the Pope–Yuille instanton constructed as a projection of the Levi-Civita connection onto the positive su (2) + ⊂ so (4) subalgebra. Our method imitates the Jackiw–Nohl–Rebbi construction originally designed for flat R 4 . That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civita connection onto the other negative su (2) − ⊂ so (4) part. Our solutions will possess the full U(2) symmetry, and thus provide more solutions to the recently proposed U(2) symmetric ansatz of Kim and Yoon.

The topology of asymptotically locally flat gravitational instantons

Abstract 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 Kahler forms of the hyper-Kahler gravitational instanton metric is exact. This leads to their topological classification. The proof exploits the relationship between L 2 cohomology and U ( 1 ) anti-instantons over gravitational instantons recognized by Hitchin. We then interprete these as reducible points in a singular SU ( 2 ) anti-instanton moduli space over the compactification leading to the identification of its intersection form. This observation on the intersection form might be a useful tool in the full geometric classification of various asymptotically locally flat gravitational instantons.

Spontaneous symmetry breaking in the SO(3) gauge theory to discrete subgroups

In this paper we give a systematical description of the possible symmetry breakings in the SO(3)‐gauge theory and show an algorithmical method to construct SU(2)‐ or SO(3)‐invariant Higgs potentials in an arbitrary irreducible representation using regular graphs. We close our paper with the explicit construction of the Lagrangian of the simplest SO(3)→A4 theory.

Harmonic Functions and Instanton Moduli Spaces on the Multi-Taub–NUT Space

Explicit construction of the basic SU(2) anti-instantons over the multi-Taub–NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unit energy anti-instantons have trivial holonomy at infinity.We also fully describe their unframed moduli space and find that it is a five dimensional space admitting a singular disk-fibration over

Note on a reformulation of the strong cosmic censor conjecture based on computability

{\mathbb{R}^3}

S-duality in Abelian gauge theory revisited

.On the way, we work out in detail the twistor space of the multi-Taub–NUT geometry together with its real structure and transform our anti-instantons into holomorphic vector bundles over the twistor space. In this picture we are able to demonstrate that our construction is complete in the sense that we have constructed a full connected component of the moduli space of solutions of the above type.We also prove that anti-instantons with arbitrary high integer energy exist on the multi-Taub–NUT space.