Abbott and Deser

Abbott and Deser

Abbott and Deser were collaborators known for formulating conserved charges in asymptotically curved spacetimes, a result influential across General relativity, Quantum field theory, Cosmology, Mathematical physics, and High energy physics. Their work connected techniques from Noether theorem, Arnowitt–Deser–Misner formalism, Brown–York stress–energy tensor, and asymptotic symmetry analyses such as those by Bondi, van der Burg, and Sachs. The Abbott–Deser construction provided tools used in studies of Anti-de Sitter space, de Sitter space, and perturbative analyses of Einstein field equations.

Introduction

The Abbott–Deser contribution addressed the challenge of defining conserved quantities for perturbations about backgrounds with nonzero cosmological constant, joining discussions pioneered in contexts involving ADM mass, Komar integral, Brown–York quasi-local energy, and the asymptotic frameworks of Bondi–Sachs formalism. Drawing on techniques from Noether, Lagrangian field theory, and linearized gravity approaches used by Feynman, Deser, and Weinberg, the Abbott–Deser formalism extended conserved-charge definitions beyond asymptotically flat spacetimes to settings relevant for Anti-de Sitter/Conformal Field Theory correspondence, Inflationary cosmology, and perturbative treatments in String theory.

Biographies

The two collaborators include a physicist associated with advances in classical and quantum aspects of gravitation and a coauthor whose career spans contributions to General relativity and Quantum electrodynamics-related methods. Their professional paths intersected with institutions such as Princeton University, Brandeis University, Massachusetts Institute of Technology, and scientific communities including participants from CERN, Institute for Advanced Study, and the International Centre for Theoretical Physics. Overlapping interactions with figures like Richard Feynman, Steven Weinberg, Roger Penrose, Stephen Hawking, and John Wheeler framed the milieu in which their collaboration emerged. Their publication record appears alongside citations from researchers working at Harvard University, Caltech, University of Cambridge, and University of California, Berkeley.

Collaborative Work

The collaboration produced a formalism for conserved charges in backgrounds with cosmological constant that built on earlier results such as the ADM formalism and the Komar integral. They derived expressions for energy, momentum, and angular momentum-like quantities for linearized perturbations about maximally symmetric backgrounds including de Sitter space and Anti-de Sitter space. Their method employed background Killing vectors similar to constructions used by Noether, linked to variational techniques invoked by Lovelock and Padmanabhan. The Abbott–Deser approach was structured to be compatible with field-theoretic procedures developed by Faddeev–Popov quantization and gauge-fixing strategies used in perturbative treatments by t'Hooft and Veltman. Subsequent extensions and checks of their results appeared in analyses by researchers at Stanford University, University of Chicago, Imperial College London, and Yale University, where applications to black hole thermodynamics and conserved charges in asymptotically Anti-de Sitter space spacetimes were pursued.

Abbott–Deser Energy and Related Concepts

The Abbott–Deser energy defined a conserved quantity for perturbations about a background with cosmological constant by contracting linearized field variations with background Killing fields and integrating a suitable current on a boundary surface, an approach echoing the surface integrals in Arnowitt–Deser–Misner formalism and the quasi-local prescriptions of Brown–York. This notion has been compared and contrasted with the Komar mass for stationary spacetimes, and with mass definitions employed in the AdS/CFT correspondence where conserved charges inform the dual Conformal Field Theory interpretation. Calculations using the Abbott–Deser expression have been applied to compute energies of Schwarzschild–de Sitter and Schwarzschild–Anti-de Sitter perturbations, to analyze stability in Kerr–AdS backgrounds, and to match holographic stress tensors derived in Maldacena-inspired treatments. Related constructs include the Abbott–Deser–Tekin generalization for higher curvature actions and comparisons with energy notions in Lovelock gravity and Gauss–Bonnet gravity as studied by groups at University of Oxford, University of Tokyo, and University of Bonn.

Impact and Legacy

The Abbott–Deser framework influenced research across theoretical and mathematical physics: it underpinned conserved-charge analyses in the AdS/CFT correspondence, informed stability studies of cosmological and black hole solutions investigated by groups at Perimeter Institute and Kavli Institute for Theoretical Physics, and guided extensions to higher-derivative and supergravity theories explored at Princeton, CERN, and Max Planck Institute for Gravitational Physics. Their methods remain standard references in textbooks and reviews discussing conserved quantities in curved backgrounds, alongside treatments by Arnowitt, Deser (other works by Deser), Misner, Thorne, Wheeler, and contemporary expositions used in graduate courses at Columbia University and University of Cambridge. The Abbott–Deser energy continues to serve as a bridge connecting classical conserved-charge concepts to quantum and holographic frameworks central to modern String theory and Quantum gravity research.

Category:General relativity Category:Gravitational physics Category:Theoretical physicists