Einstein field equations, the Glossary
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.[1]
Table of Contents
88 relations: Accelerating expansion of the universe, Albert Einstein, Annalen der Physik, Astronomy, Black hole, Cambridge University Press, Charge (physics), Classical limit, Conformastatic spacetimes, Cosmological constant, Covariant derivative, Curvature, Curvature form, Degrees of freedom (physics and chemistry), Differential form, Divergence, Dynamical system, Edwin Hubble, Einstein manifold, Einstein tensor, Einstein–Hilbert action, Electric current, Electric field, Electromagnetic field, Electromagnetic stress–energy tensor, Electromagnetism, Equivalence principle, Exact solutions in general relativity, Expansion of the universe, Exterior derivative, Free fall, Gauge fixing, General relativity, Geodesic, Geodesics in general relativity, George Gamow, Gravitation (book), Gravitational constant, Gravitational field, Gravitational wave, Hamilton–Jacobi–Einstein equation, History of general relativity, Inertia, International Journal of Theoretical Physics, Kerr metric, Levi-Civita symbol, Linearized gravity, Magnetic field, Manifold, Massachusetts Institute of Technology, ... Expand index (38 more) »
Accelerating expansion of the universe
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time.
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Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".
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Annalen der Physik
Annalen der Physik (English: Annals of Physics) is one of the oldest scientific journals on physics; it has been published since 1799.
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Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos.
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Black hole
A black hole is a region of spacetime where gravity is so strong that nothing, not even light and other electromagnetic waves, is capable of possessing enough energy to escape it.
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Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
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Charge (physics)
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics.
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Classical limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters.
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Conformastatic spacetimes
Conformastatic spacetimes refer to a special class of static solutions to Einstein's equation in general relativity. Einstein field equations and Conformastatic spacetimes are general relativity.
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Cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. Einstein field equations and cosmological constant are Albert Einstein and general relativity.
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Covariant derivative
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.
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Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
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Curvature form
In differential geometry, the curvature form describes curvature of a connection on a principal bundle.
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Degrees of freedom (physics and chemistry)
In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system.
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Differential form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.
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Divergence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.
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Edwin Hubble
Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer.
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Einstein manifold
In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. Einstein field equations and Einstein manifold are Albert Einstein.
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Einstein tensor
In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. Einstein field equations and Einstein tensor are Albert Einstein.
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Einstein–Hilbert action
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. Einstein field equations and Einstein–Hilbert action are Albert Einstein and general relativity.
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Electric current
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space.
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Electric field
An electric field (sometimes called E-field) is the physical field that surrounds electrically charged particles.
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Electromagnetic field
An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges.
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Electromagnetic stress–energy tensor
In relativistic physics, the electromagnetic stress–energy tensor is the contribution to the stress–energy tensor due to the electromagnetic field.
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Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields.
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Equivalence principle
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. Einstein field equations and equivalence principle are Albert Einstein and general relativity.
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Exact solutions in general relativity
In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Einstein field equations and exact solutions in general relativity are general relativity.
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Expansion of the universe
The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. Einstein field equations and expansion of the universe are general relativity.
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Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
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Free fall
In classical mechanics, free fall is any motion of a body where gravity is the only force acting upon it.
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Gauge fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables.
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General relativity
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. Einstein field equations and general relativity are Albert Einstein.
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Geodesic
In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.
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Geodesics in general relativity
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Einstein field equations and geodesics in general relativity are general relativity.
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George Gamow
George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; Георгий Антонович Гамов; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist.
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Gravitation (book)
Gravitation is a widely adopted textbook on Albert Einstein's general theory of relativity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. Einstein field equations and Gravitation (book) are general relativity.
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Gravitational constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.
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Gravitational field
In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. Einstein field equations and gravitational field are general relativity.
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Gravitational wave
Gravitational waves are waves of the intensity of gravity that are generated by the accelerated masses of binary stars and other motions of gravitating masses, and propagate as waves outward from their source at the speed of light.
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Hamilton–Jacobi–Einstein equation
In general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation of geometrodynamics in superspace, cast in the "geometrodynamics era" around the 1960s, by Asher Peres in 1962 and others. Einstein field equations and Hamilton–Jacobi–Einstein equation are general relativity.
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History of general relativity
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. Einstein field equations and History of general relativity are Albert Einstein and general relativity.
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Inertia
Inertia is the tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes its speed or direction to change.
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International Journal of Theoretical Physics
The International Journal of Theoretical Physics is a peer-reviewed scientific journal of physics published by Springer Science+Business Media since 1968.
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Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.
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Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
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Linearized gravity
In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. Einstein field equations and linearized gravity are general relativity.
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Magnetic field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts.
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Mathematics of general relativity
When studying and formulating Albert Einstein's theory of general relativity, various mathematical structures and techniques are utilized.
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Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. Einstein field equations and Maxwell's equations are equations of physics and partial differential equations.
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Metric tensor (general relativity)
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.
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Minkowski space
In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation. Einstein field equations and Minkowski space are equations of physics.
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Momentum
In Newtonian mechanics, momentum (momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object.
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Nature (journal)
Nature is a British weekly scientific journal founded and based in London, England.
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Newton's law of universal gravitation
Newton's law of universal gravitation says that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
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Numerical relativity
Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. Einstein field equations and partial differential equation are partial differential equations.
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Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
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Physical cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models.
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Poincaré lemma
In mathematics, the Poincaré lemma gives a sufficient condition for a closed differential form to be exact (while an exact form is necessarily closed).
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Post-Newtonian expansion
In general relativity, post-Newtonian expansions (PN expansions) are used for finding an approximate solution of Einstein field equations for the metric tensor. Einstein field equations and post-Newtonian expansion are general relativity.
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Quantum mechanics
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.
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Quantum vacuum state
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy.
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Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection.
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Ricci curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold.
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Ricci-flat manifold
In the mathematical field of differential geometry, Ricci-flatness is a condition on the curvature of a Riemannian manifold.
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Rotating black hole
A rotating black hole is a black hole that possesses angular momentum.
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Scalar curvature
In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold.
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Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Einstein field equations and Schrödinger equation are partial differential equations.
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Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.
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Sign convention
In physics, a sign convention is a choice of the physical significance of signs (plus or minus) for a set of quantities, in a case where the choice of sign is arbitrary.
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Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Spacetime symmetries
Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry.
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Speed of light
The speed of light in vacuum, commonly denoted, is a universal physical constant that is exactly equal to). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.
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Static universe
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Einstein field equations and static universe are Albert Einstein.
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Stress–energy tensor
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.
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Suzanne Imber
Suzanne Mary Imber (born May 1983) is a British planetary scientist specialising in space weather at the University of Leicester.
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Symmetric tensor
In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies The space of symmetric tensors of order r on a finite-dimensional vector space V is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V.
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Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.
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Universe
The universe is all of space and time and their contents.
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Vacuum
A vacuum (vacuums or vacua) is space devoid of matter.
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Vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire universe.
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Vacuum solution (general relativity)
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.
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Viking Press
Viking Press (formally Viking Penguin, also listed as Viking Books) is an American publishing company owned by Penguin Random House.
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W. H. Freeman and Company
W.
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Wave function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system.
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References
[1] https://en.wikipedia.org/wiki/Einstein_field_equations
Also known as Albert Einstein's equation, Albert Einstein's field equations, Einstein Equations, Einstein Field Equations (EFE), Einstein equation, Einstein field equation, Einstein gravitational constant, Einstein's equation, Einstein's equations, Einstein's equations of gravity, Einstein's field equation, Einstein's field equations, Einstein-Maxwell equations, Einstein/Maxwell field equations, Mass-energy tensor, Vacuum field equations.
, Mathematics of general relativity, Maxwell's equations, Metric tensor (general relativity), Minkowski space, Momentum, Nature (journal), Newton's law of universal gravitation, Numerical relativity, Partial differential equation, PDF, Physical cosmology, Poincaré lemma, Post-Newtonian expansion, Quantum mechanics, Quantum vacuum state, Ricci calculus, Ricci curvature, Ricci-flat manifold, Rotating black hole, Scalar curvature, Schrödinger equation, Schwarzschild metric, Sign convention, Spacetime, Spacetime symmetries, Speed of light, Static universe, Stress–energy tensor, Suzanne Imber, Symmetric tensor, Tensor, Universe, Vacuum, Vacuum energy, Vacuum solution (general relativity), Viking Press, W. H. Freeman and Company, Wave function.