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Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions

Elşen Veli Veliev, Sergiu I. Vacaru

Abstract

We develop and apply the Batalin-Fradkin-Vilkovisky (BFV) formalism for quantizing off-diagonal solutions of the Einstein equations in general relativity. In the quasi-classical limit of quantum gravity, such solutions possess specific nonlinear symmetries and encode Hořava - Lifshitz (HL) configurations with anisotropic scaling and effective cosmological constants. The geometric constructions are performed on Lorentz manifolds enabled with nonholonomic 2+2 and 3+1 fibration structures.

Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions

Abstract

We develop and apply the Batalin-Fradkin-Vilkovisky (BFV) formalism for quantizing off-diagonal solutions of the Einstein equations in general relativity. In the quasi-classical limit of quantum gravity, such solutions possess specific nonlinear symmetries and encode Hořava - Lifshitz (HL) configurations with anisotropic scaling and effective cosmological constants. The geometric constructions are performed on Lorentz manifolds enabled with nonholonomic 2+2 and 3+1 fibration structures.
Paper Structure (32 sections, 101 equations)

This paper contains 32 sections, 101 equations.

Table of Contents

  1. Introduction, motivations and objectives
  2. Nonholonomic 2+2 and 3+1 fibrations on Lorentz manifolds
  3. N-adapted metrics, distortion of connections and geometric d-objects
  4. Nonholonomic Lorentz manifolds and N-adapted frames
  5. Metric structures adapted to double fibrations
  6. Distinguished connections and fundamental geometric objects
  7. The (modified) Einstein equations in canonical dyadic variables
  8. The canonical d-connection
  9. The Einstein d-tensor in canonical dyadic variables
  10. Effective sources and generating sources
  11. Nonholonomic Einstein equations and the LC conditions
  12. General ansatz and generating data for off-diagonal solutions in GR
  13. Decoupling properties in canonical nonholonomic variables
  14. Off-diagonal transforms and gravitational polarizations of prime metrics
  15. Modelling HL-configurations on noholonomic Lorentz manifolds
  16. ...and 17 more sections