A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of such boundary terms in complex general relativity, where spacedme is a four-complex-dimensional complex-Riemannian manifold. A complex Ricci-flat spacetime is recovered providing some boundary conditions are imposed on two-complex-dimensional surfaces. One then finds that the holomorphic multimomenta should vanish on an arbitrary three-complex-dimensional surface, to avoid having restrictions at this surface on the spinor fields which express the invariance of the theory under holomorphic coordinate transformations. The Hamiltonian constraint of real general relativity is then replaced by a geometric structure linear in the holomorphic multimomenta, and a link with twistor theory is found. Moreover, a deep relation emerges between complex spacetimes which are not anti-self-dual and two-complex-dimensional surfaces which are not totally null.
Boundary terms in complex general relativity / Esposito, G; Stornaiolo, C. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - 12:7(1995), pp. 1733-1738. [10.1088/0264-9381/12/7/015]
Boundary terms in complex general relativity
ESPOSITO GPrimo
;
1995
Abstract
A recent analysis of real general relativity based on multisymplectic techniques has shown that boundary terms may occur in the constraint equations, unless some boundary conditions are imposed. This paper studies the corresponding form of such boundary terms in complex general relativity, where spacedme is a four-complex-dimensional complex-Riemannian manifold. A complex Ricci-flat spacetime is recovered providing some boundary conditions are imposed on two-complex-dimensional surfaces. One then finds that the holomorphic multimomenta should vanish on an arbitrary three-complex-dimensional surface, to avoid having restrictions at this surface on the spinor fields which express the invariance of the theory under holomorphic coordinate transformations. The Hamiltonian constraint of real general relativity is then replaced by a geometric structure linear in the holomorphic multimomenta, and a link with twistor theory is found. Moreover, a deep relation emerges between complex spacetimes which are not anti-self-dual and two-complex-dimensional surfaces which are not totally null.File | Dimensione | Formato | |
---|---|---|---|
CQGRD,12,1733.pdf
non disponibili
Dimensione
293.51 kB
Formato
Adobe PDF
|
293.51 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.