On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation

An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a \emph{criteria} in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in \emph{isolation}. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff's trace anomaly relation, which in \emph{four}-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any} dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.Comment: 30 pages, added reference

Decisions with Endogenous Frames (Replaces CentER DP 2010-21)

This paper contrasts the normative implications of a model of decision- making with endogenous frames to those of choice theoretic models of Bernheim and Rangel (2007, 2009) and Rubinstein and Salant (2008) in which observed choices are determined by exogenous frames or ancillary conditions. We argue that frames, though exogenous to the individual at the point when choices are made, matter for welfare purposes.Decisions;choice;frames;standard;behavioral;welfare

Black Hole Entropy and Quantum Gravity

An elementary introduction is given to the problem of black hole entropy as formulated by Bekenstein and Hawking. The information theoretic basis of Bekenstein's formulation is briefly reviewed and compared with Hawking's approach. The issue of calculating the entropy by actual counting of microstates is taken up next within two currently popular approaches to quantum gravity, viz., string theory and canonical quantum gravity. The treatment of the former assay is confined to a few remarks, mainly of a critical nature, while some of the computational techniques of the latter approach are elaborated. We conclude by trying to find commonalities between these two rather disparate directions of work.Comment: 13 pages, Revtex, 5 eps figures. Invited talk at National Symposium on Trends and Perspectives in Theoretical Physics, IACS, Calcutta, India, April, 1998. One reference adde