Abstract
In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the approach of Ref. [1]. Moreover, it is found that at first order in the gauge parameters, the Hamiltonian action is (on shell) fully gauge-invariant under the gauge symmetry generated by the first class constraints in the case when spacetime \(\mathcal{M}\) has the topology % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFZestcqWFaCFpcqGH% 9aqpcaWGsbGaey41aq7exLMBbXgBd9gzLbvyNv2CaeXbbjxAHXgiv5% wAJ9gzLbsttbacgaGaa43Odaaa!52EB!\[\mathcal{M} = R \times \Sigma \] = R × Σ and Σ has no boundary. Thus, the statement that the constraints linear in the momenta do not contribute to the boundary terms is right, but only in the case when Σ has no boundary.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Montesinos, M., Vergara, J.D. LETTER: Gauge Invariance of Complex General Relativity. General Relativity and Gravitation 33, 921–929 (2001). https://doi.org/10.1023/A:1010268110661
Issue Date:
DOI: https://doi.org/10.1023/A:1010268110661