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Generalized Ernst Potentials for arbitrary Dilatonic Theories

Leonel Bixano, Tonatiuh Matos

Abstract

In this work, we generalize Ernst potentials to the Einstein-Maxwell-Dilaton case and explicitly write the corresponding potential space metric. Since this metric is five-dimensional in potential space, we generalize the corresponding Newman-Penrose coefficients for this metric and compare this formalism with previous approaches to show that this formulation is very convenient for analyzing these spacetimes and finding new exact solutions. We show how to obtain old exact solutions and some new ones with very interesting properties.

Generalized Ernst Potentials for arbitrary Dilatonic Theories

Abstract

In this work, we generalize Ernst potentials to the Einstein-Maxwell-Dilaton case and explicitly write the corresponding potential space metric. Since this metric is five-dimensional in potential space, we generalize the corresponding Newman-Penrose coefficients for this metric and compare this formalism with previous approaches to show that this formulation is very convenient for analyzing these spacetimes and finding new exact solutions. We show how to obtain old exact solutions and some new ones with very interesting properties.
Paper Structure (27 sections, 1 theorem, 130 equations)

This paper contains 27 sections, 1 theorem, 130 equations.

Table of Contents

  1. Introduction
  2. Potentials method
  3. Definition of the potentials
  4. Matos Anzat
  5. Relations with Ernst formulation
  6. Interpretations of the variables A,B
  7. Generalized Ernst equations within extended reformulation
  8. Generalized Ernst equation for $\Phi$
  9. Generalized Ernst equations for $\varepsilon$
  10. Covariant form the field equations
  11. Carateristics of the general subspace
  12. Extended field equations
  13. Second Anzat
  14. Real scalar field existence.
  15. Known solution
  16. ...and 12 more sections

Key Result

Theorem 1

In the non-flat $(\xi,\overline{\xi})$-space $\sigma \neq 0$ and using the anzat AnzatABC and within Einstein–Maxwell theory (with $\alpha_0 = 0$), no solutions exist that correspond to configurations with a real scalar field $\phi$ coupled to the electromagnetic field, nor do such solutions arise i

Theorems & Definitions (2)

  • Theorem 1
  • proof