Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 1, Issue 1, August 2017, pp 42-55

The type III vacuum spacetime does not accept embedding into E6

V. Barrera-Figueroa11, J. López-Bonilla2, R. López-Vázquez 2

1 Instituto Politécnico Nacional, Posgrado en Tecnología Avanzada, Av. IPN 2580, Col. Barrio la Laguna 07340, CDMX, México.
2 ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México.

Abstract

We show the non-existence class two empty of Petrov type III without assuming that the second fundamental forms commute.

Keywords

Spacetime of embedding class two, Gauss-Codazzi-Ricci equations.

Subject classification: 83Cxx, 15A66, 83C60.

Preview

Reference

1. Stephani H, Kramer D, MacCallum M, Hoenselaers C, Herlt E. Exact Solutions of Einstein’s Field Equations, Cambridge: Cambridge University Press, 2003.

2. Yakupov M Sh. Einstein spaces of the second embedding class. Sov Phys Dokl 1968; 13: 585-587.

3. Hodgkinson D E. Empty spacetimes of embedding class two. Gen Rel Grav 1984; 16: 569-587.

4. Barrera-Figueroa V, López-Bonilla J, López-Bonilla R, Vidal-Beltrán S. Algebraic classification of the Weyl tensor. Prespacetime J 2016; 7: 445-455.

5. López-Bonilla J, López-Vázquez R, Morales J, Ovando G. Petrov types and their canonical tetrads. Prespacetime J 2016; 7: 1176-1186.

6. Lam-Estrada P, López-Bonilla J, López-Vázquez R, Rathie A K. Newman-Penrose equations, Bianchi identities and Weyl-Lanczos relations. Prespacetime J 2015; 6: 684-696.

7. López-Bonilla J, López-Vázquez R, Morales J, Ovando G. Spin coefficients formalism. Prespacetime J 2015; 6: 697-709.

8. Hernández-Aguilar C, Domínguez-Pacheco A, López-Bonilla J, Vidal-Beltrán S. Gauss-Codazzi equations in the Newman-Penrose formalism. Prespacetime J 2017; 8: 537-541.

9. Yakupov M Sh. Einstein spaces of class two. Grav i Teor Otnos Univ Kazan 1973; 9: 109-114.

10. Barnes. Vacuum spacetimes of embedding class two. J Phys: Conf. Series 2011; 314: 012091.

11. Van den Bergh N. Lorentz-and hyperrotation-invariant classification of symmetric tensors and the embedding class-2 problem. Class Quantum Grav 1996; 13: 2817-2838.

mail to asiamathematika@gmail.com for subscribtion

  
Visitors count