de Sitter

de Sitter
Name	Willem de Sitter
Birth date	6 May 1872
Death date	20 November 1934
Nationality	Dutch
Fields	Astronomy, Mathematics, Cosmology
Institutions	Leiden Observatory, University of Leiden, Royal Netherlands Academy of Arts and Sciences
Known for	de Sitter spacetime, work on cosmology, stellar dynamics

de Sitter de Sitter is a term primarily associated with the Dutch mathematician and astronomer Willem de Sitter and a family of solutions and models in relativistic cosmology. It denotes an exact solution of Einstein's field equations and related cosmological concepts that influenced research by figures such as Albert Einstein, Arthur Eddington, Georges Lemaître, and Edwin Hubble. The name appears across theoretical physics, differential geometry, observational astronomy, and the history of science.

Overview

The term connects to a set of mathematical and physical constructs developed in the early twentieth century amid debates involving Albert Einstein, Arthur Eddington, Hendrik Lorentz, Paul Ehrenfest, and Erwin Schrödinger about cosmological models, the Cosmological constant, and observational programs by Edwin Hubble, Vesto Slipher, Harlow Shapley, Fritz Zwicky, and institutions like Mount Wilson Observatory and Leiden Observatory. It serves as both an eponym for Willem de Sitter and a label for spacetime geometries invoked in work by Alexander Friedmann, Georges Lemaître, Subrahmanyan Chandrasekhar, George Gamow, and later researchers at institutions including Princeton University, Cambridge University, and University of Leiden.

History and Eponym

The name originated with Willem de Sitter, whose writings and correspondence with Albert Einstein, Arthur Eddington, and Erwin Freundlich during the 1910s and 1920s shaped debates at meetings like those of the Royal Astronomical Society and the International Astronomical Union. His contributions intersected with theoretical advances by Karl Schwarzschild, Alexander Friedmann, and observational discoveries by Edwin Hubble and Vesto Slipher, and influenced discussions involving Hendrik Lorentz, Paul Ehrenfest, and Felix Klein. Later historians and biographers such as Abraham Pais, George Gamow, and Allan Sandage examined de Sitter's role alongside developments at Mount Wilson Observatory, Leiden Observatory, and academies like the Royal Netherlands Academy of Arts and Sciences.

de Sitter Spacetime

The de Sitter spacetime solution appears as a maximally symmetric vacuum solution with positive curvature of Einstein's field equations, discussed in tandem with solutions by Karl Schwarzschild, Alexander Friedmann, and Georges Lemaître. Mathematically it relates to symmetric spaces studied by Élie Cartan, Hermann Weyl, and Marcel Grossmann, and it provides a background for quantum field theory calculations by researchers such as Stephen Hawking, Gerard 't Hooft, Leonard Susskind, and Alexander Polyakov. The geometry admits coordinate charts used by authors like Arthur Eddington, Howard Percy Robertson, and A. G. Walker and connects to concepts in work by Satyendra Nath Bose, Paul Dirac, and Richard Feynman when quantizing fields on curved backgrounds.

de Sitter Universe in Cosmology

As a cosmological model the de Sitter universe was central to exchanges among Albert Einstein, Willem de Sitter, Alexander Friedmann, Georges Lemaître, and observers such as Edwin Hubble and Vesto Slipher, and was compared to matter-dominated models used by Fritz Zwicky and Harlow Shapley. It underpins inflationary scenarios developed by Alan Guth, Andrei Linde, Alexei Starobinsky, and Paul Steinhardt, and it provides the asymptotic future for dark-energy dominated models constrained by observations from collaborations like Planck Collaboration, Supernova Cosmology Project, High-Z Supernova Search Team, and surveys by Sloan Digital Sky Survey and Dark Energy Survey.

Mathematical Properties

The solution is a maximally symmetric Lorentzian manifold with constant positive scalar curvature, related to work by Bernhard Riemann, Élie Cartan, Hermann Weyl, and Ludwig Schläfli. Its group of isometries is the de Sitter group, which is isomorphic to the Lorentz group in one higher dimension as studied by Eugene Wigner, H. Weyl, and Marcel Grossmann. Coordinate representations used in the literature include static coordinates employed in analyses by Karl Schwarzschild and Howard Percy Robertson, global coordinates used by Stephen Hawking and Gary Gibbons, and flat slicing used in inflationary calculations by Alan Guth and Andrei Linde. Related mathematical tools were further developed by John Wheeler, Roger Penrose, Kip Thorne, and Robert Wald in discussions of horizons, causal structure, and quantum fields on curved backgrounds.

Physical Implications and Observational Evidence

Physically, de Sitter geometries predict cosmological horizons and thermal attributes analogous to Hawking radiation studied by Stephen Hawking and Gary Gibbons, and they inform particle-creation effects considered by Leonard Parker and Yakov Zel'dovich. Observationally, the late-time approach to a de Sitter–like expansion is tested by measurements by Planck Collaboration, Wilkinson Microwave Anisotropy Probe, Supernova Cosmology Project, High-Z Supernova Search Team, Sloan Digital Sky Survey, and instruments at Mount Wilson Observatory and Palomar Observatory. The model's role in inflation links it to baryogenesis scenarios by Andrei Sakharov and nucleosynthesis work by George Gamow and Ralph Alpher, while contemporary constraints involve collaborations like BICEP2 and projects led by Max Tegmark and Sean Carroll.

Extensions and Related Models

Extensions include anti-de Sitter space central to the AdS/CFT correspondence developed by Juan Maldacena, and quasi–de Sitter backgrounds in slow-roll inflation by Alan Guth, Andrei Linde, and Andrei Starobinsky. Alternative proposals and perturbative analyses involve researchers such as Steven Weinberg, Leonard Susskind, Gerard 't Hooft, Raphael Bousso, and Thomas Hertog. Related exact solutions and matched cosmologies involve the Schwarzschild–de Sitter and Reissner–Nordström–de Sitter metrics used in studies by Karl Schwarzschild, Hermann Weyl, and Roy Kerr, and modern numerical and observational investigations are conducted by groups at Princeton University, Harvard University, California Institute of Technology, and collaborations like Planck Collaboration and Dark Energy Survey.

Category:Relativity Category:Cosmology Category:Willem de Sitter