Abstract
We compare the metric and the Palatini formalism to obtain the Einstein equations in thepresence of higher-order curvature corrections that consist of contractions of the Riemanntensor, but not of its derivatives. We find that there is a class of theories for which the twoformalisms are equivalent. This class contains the Palatini version of Lovelock theory, butalso more Lagrangians that are not Lovelock, but respect certain symmetries.For the general case, we find that imposing the Levi-Civita connection as anansatz, the Palatini formalism is contained within the metric formalism, in thesense that any solution of the former also appears as a solution of the latter,but not necessarily the other way around. Finally we give the conditions thesolutions of the metric equations should satisfy in order to solve the Palatiniequations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
