Rainer Kurt "Ray" Sachs (June 13, 1932 - April 16, 2024) was a German-American mathematical physicist, with interests in general relativistic cosmology and astrophysics, as well as a computational radiation biologist. He was professor emeritus of Mathematics and Physics at the University of California, Berkeley, and adjunct professor at Tufts Medical School. [1]
Sachs was born in Frankfurt am Main in 1932, a son of the German Jewish metallurgist George Sachs. In 1937 the family left Germany to flee from Nazi persecution, and settled in the United States, so Rainer Sachs is generally considered an American scientist. He received his bachelor's degree in mathematics from MIT in 1953 and his PhD in theoretical physics from Syracuse University in 1959. [1]
In 1962 Joshua N. Goldberg and he proved the Goldberg–Sachs theorem. Later that year, he gave the first exposition of the asymptotically flat spacetime symmetry group, which he called the "generalized Bondi-Metzner group" and is now known as the Bondi–Metzner–Sachs group. [2]
In 1966 he and Ronald Kantowski were responsible for the Kantowski–Sachs dust solutions to the Einstein field equation. [3] These are widely used family of anisotropic cosmological models.
In 1967, he and Arthur M. Wolfe were the authors of the Sachs–Wolfe effect, which concerns a property of the Cosmic microwave background radiation. [4] The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and R. Sachs, shows that if, in a given universe, there exists a reference frame at each event such that the cosmic background radiation is isotropic, then under certain conditions that universe is an isotropic and homogeneous FLRW spacetime.
From 1969 to 1993, he was Professor of Math and Physics at the University of California, Berkeley (UCB), and from 1993 he has been Professor Emeritus at UCB. In 1994, he was appointed Research Professor of Mathematics UCB, and since 2005 he has been an adjunct professor at the Tufts medical school.
Until 1985, he worked on general relativistic cosmology and astrophysics. With Hung-Hsi Wu he co-wrote the books General Relativity and Cosmology in 1971 [5] and General Relativity for Mathematicians in 1977. [6] From 1985, he has worked in mathematical and computational biology, especially radiation biology. His work in radiobiology has included research on radiation and cancer. [7]
Sachs died on April 16, 2024.
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
The following is a timeline of gravitational physics and general relativity.
The Friedmann–Lemaître–Robertson–Walker metric is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term.
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure. Dust solutions are an important special case of fluid solutions in general relativity.
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand, one would like to account for a universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties ; on the other hand, there is the deep question on the origin of the second law of thermodynamics.
In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.
Wolfgang Rindler was a physicist working in the field of general relativity where he is known for introducing the term "event horizon", Rindler coordinates, and for the use of spinors in general relativity. An honorary member of the Austrian Academy of Sciences and foreign member of the Accademia delle Scienze di Torino, he was also a prolific textbook author.
The concept of mass in general relativity (GR) is more subtle to define than the concept of mass in special relativity. In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions that are applicable under different circumstances. Under some circumstances, the mass of a system in general relativity may not even be defined.
General Relativity is a graduate textbook and reference on Albert Einstein's general theory of relativity written by the gravitational physicist Robert Wald.
An inhomogeneous cosmology is a physical cosmological theory which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces enough to skew our view of the Universe. When the universe began, matter was distributed homogeneously, but over billions of years, galaxies, clusters of galaxies, and superclusters have coalesced, and must, according to Einstein's theory of general relativity, warp the space-time around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies claimed in 1998-1999 that high redshift supernovae were further away than our calculations showed they should be, it was suggested that the expansion of the universe is accelerating, and dark energy, a repulsive energy inherent in space, was proposed to explain the acceleration. Dark energy has since become widely accepted, but it remains unexplained. Accordingly, some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.
Robert Geroch is an American theoretical physicist and professor at the University of Chicago. He has worked prominently on general relativity and mathematical physics and has promoted the use of category theory in mathematics and physics. He was the Ph.D. supervisor for Abhay Ashtekar, Basilis Xanthopoulos and Gary Horowitz. He also proved an important theorem in spin geometry.
Jürgen Ehlers was a German physicist who contributed to the understanding of Albert Einstein's theory of general relativity. From graduate and postgraduate work in Pascual Jordan's relativity research group at Hamburg University, he held various posts as a lecturer and, later, as a professor before joining the Max Planck Institute for Astrophysics in Munich as a director. In 1995, he became the founding director of the newly created Max Planck Institute for Gravitational Physics in Potsdam, Germany.
The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and Rainer K. Sachs, shows that if, in a given universe, all freely falling observers measure the cosmic background radiation to have exactly the same properties in all directions, then that universe is an isotropic and homogeneous FLRW spacetime, if the one uses a kinetic picture and the collision term vanishes, i.e. in the so-called Vlasov case or if there is a so-called detailed balance. This result was later extended to the full Boltzmann case by R. Treciokas and G.F.R. Ellis.
Ivor Robinson was a British-American mathematical physicist, born and educated in England, noted for his important contributions to the theory of relativity. He was a principal organizer of the Texas Symposium on Relativistic Astrophysics.
In gravitational theory, the Bondi–Metzner–Sachs (BMS) group, or the Bondi–van der Burg–Metzner–Sachs group, is an asymptotic symmetry group of asymptotically flat, Lorentzian spacetimes at null infinity. It was originally formulated in 1962 by Hermann Bondi, M. G. van der Burg, A. W. Metzner and Rainer K. Sachs in order to investigate the flow of energy at infinity due to propagating gravitational waves. Half a century later, this work of Bondi, van der Burg, Metzner, and Sachs is considered pioneering and seminal. In his autobiography, Bondi considered the 1962 work as his "best scientific work".
In theoretical physics, null infinity is a region at the boundary of asymptotically flat spacetimes. In general relativity, straight paths in spacetime, called geodesics, may be space-like, time-like, or light-like. The distinction between these paths stems from whether the spacetime interval of the path is positive, negative, or zero. Light-like paths physically correspond to physical phenomena which propagate through space at the speed of light, such as electromagnetic radiation and gravitational radiation. The boundary of a flat spacetime is known as conformal infinity, and can be thought of as the end points of all geodesics as they go off to infinity. The region of null infinity corresponds to the terminus of all null geodesics in a flat Minkowski space. The different regions of conformal infinity are most often visualized on a Penrose diagram, where they make up the boundary of the diagram. There are two distinct region of null infinity, called past and future null infinity, which can be denoted using a script 'I' as and . These two regions are often referred to as 'scri-plus' and 'scri-minus' respectively. Geometrically, each of these regions actually has the structure of a topologically cylindrical three dimensional region.
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