Perturbations of gravitational instantons

Journal Article · Fri Jun 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.3620· OSTI ID:6739141

Torre, C G ^[1]

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1. Center for Space Science Research, Space Research Institute, Florida Institute of Technology, Melbourne, FL (USA)

Ashtekar's spinorial formulation of general relativity is used to study perturbations of gravitational instantons corresponding to finite-action solutions of the Euclidean Einstein equations (with a nonzero cosmological constant) possessing an anti-self-dual Weyl curvature tensor. It is shown that, with an appropriate on-shell'' form of infinitesimal gauge transformations, the space of solutions to the linearized instanton equation can be described in terms of an elliptic complex; the cohomology of the complex defines gauge-inequivalent perturbations. Using this elliptic complex we prove that there are no nontrivial solutions to the linearized instanton equation on conformally anti-self-dual Einstein spaces with a positive cosmological constant. Thus, the space of gravitational instantons is discrete when the cosmological constant is positive; i.e., the dimension of the gravitational moduli space in this case is zero. We discuss the issue of linearization stability as well as the feasibility of using the Atiyah-Singer index theorem to compute the dimension of the gravitational moduli space when the cosmological constant is negative.

• OSTI ID: 6739141
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:12; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
INSTANTONS
INVARIANCE PRINCIPLES
LIE GROUPS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUASI PARTICLES
SPACE-TIME
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS