Special relativity

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

• Foundational issues
  • principle of relativity
    Principle of relativity
    In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
    
    
  • speed of light
    Speed of light
    The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
    
    
  • faster than light
• four-vector
  Four-vector
  In the theory of relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the four-vector name tacitly assumes that its components refer to a standard basis...
  
  
  • four-acceleration
    Four-acceleration
    In special relativity, four-acceleration is a four-vector and is defined as the change in four-velocity over the particle's proper time:whereandand \gamma_u is the Lorentz factor for the speed u...
    
    
  • four-force
  • four-momentum
    Four-momentum
    In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime...
    
    
  • four-velocity
    Four-velocity
    In physics, in particular in special relativity and general relativity, the four-velocity of an object is a four-vector that replaces classicalvelocity...
    
    
• light-like
• Lorentz covariance
  Lorentz covariance
  In standard physics, Lorentz symmetry is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space"...
  
  
• Lorentz group
  Lorentz group
  In physics , the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting for all physical phenomena...
  
  
• Lorentz transformation
  Lorentz transformation
  In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
  
  
• Lorentz-Fitzgerald contraction hypothesis
• Minkowski space
  Minkowski space
  In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
  
  
• Poincaré group
  Poincaré group
  In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.-Simple explanation:...
  
  
• proper length
  Proper length
  In relativistic physics, proper length is an invariant measure of the distance between two spacelike-separated events, or of the length of a spacelike path within a spacetime....
  
  
• relativistic wave equations
  Relativistic wave equations
  Before the creation of quantum field theory, physicists attempted to formulate versions of the Schrödinger equation which were compatible with special relativity...
  
  
• relativistic mass
• world line
  World line
  In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein...
  
  

General relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

• black hole
  Black hole
  A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
  
  s
  • no hair theorem
    No hair theorem
    The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum...
    
    
  • Hawking radiation
    Hawking radiation
    Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
    
    
  • Hawking temperature
  • Black hole entropy
  • charged black hole
    Charged black hole
    A charged black hole is a black hole that possesses electric charge. Since the electromagnetic repulsion in compressing an electrically charged mass is dramatically greater than the gravitational attraction , it is not expected that black holes with a significant electric charge will be formed in...
    
    
  • rotating black hole
    Rotating black hole
    A rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...
    
    
  • micro black hole
    Micro black hole
    Micro black holes are tiny black holes, also called quantum mechanical black holes or mini black holes, for which quantum mechanical effects play an important role....
    
    
  • Schwarzschild black hole
  • Schwarzschild metric
    Schwarzschild metric
    In Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
    
    
  • Schwarzschild radius
    Schwarzschild radius
    The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
    
    
  • Reissner-Nordström black hole
  • Immirzi parameter
    Immirzi parameter
    The Immirzi parameter is a numerical coefficient appearing in loop quantum gravity, a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units...
    
    
• closed timelike curve
  Closed timelike curve
  In mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...
  
  
• cosmic censorship hypothesis
  Cosmic censorship hypothesis
  The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....
  
  
• chronology protection conjecture
  Chronology protection conjecture
  The chronology protection conjecture is a conjecture by the physicist Professor Stephen Hawking that the laws of physics are such as to prevent time travel on all but sub-microscopic scales. Mathematically, the permissibility of time travel is represented by the existence of closed timelike curves...
  
  
• Einstein-Cartan theory
• Einstein's field equation
• geodesic
  Geodesic
  In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...
  
  
• gravitational redshift
  Gravitational redshift
  In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...
  
  
• Penrose-Hawking singularity theorems
  Penrose-Hawking singularity theorems
  The Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.A singularity in solutions of the Einstein field equations is one of two things:...
  
  
• stress-energy tensor
  Stress-energy tensor
  The stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...
  
  
• worm hole

Cosmology

Physical cosmology

Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

• anti de Sitter space
  Anti de Sitter space
  In mathematics and physics, n-dimensional anti de Sitter space, sometimes written AdS_n, is a maximally symmetric Lorentzian manifold with constant negative scalar curvature...
  
  
• Ashtekar variables
  Ashtekar variables
  In theoretical physics, Ashtekar variables represent an unusual way to rewrite the metric on the three-dimensional spatial slices in terms of a SU gauge field and its complementary variable...
  
  
• Batalin-Vilkovisky
• big bang
  Big Bang
  The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
  
  
• Cauchy horizon
  Cauchy horizon
  In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...
  
  
• cosmic inflation
  Cosmic inflation
  In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
  
  
• cosmic microwave background
• cosmic variance
  Cosmic variance
  Cosmic variance is the statistical uncertainty inherent in observations of the universe at extreme distances. It is based on the idea that it is only possible to observe part of the universe at one particular time, so it is difficult to make statistical statements about cosmology on the scale of...
  
  
• cosmological constant
  Cosmological constant
  In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
  
  
• dark energy
  Dark energy
  In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
  
  
• dark matter
  Dark matter
  In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
  
  
• de Sitter space
  De Sitter space
  In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space , denoted dS_n, is the Lorentzian manifold analog of an n-sphere ; it is maximally symmetric, has constant positive curvature,...
  
  
• Friedmann-Lemaître-Robertson-Walker
• horizon problem
  Horizon problem
  The horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s. It points out that different regions of the universe have not "contacted" each other because of the great distances between them, but nevertheless they have the same temperature...
  
  
• large-scale structure of the cosmos
• Randall-Sundrum model
  Randall-Sundrum model
  In physics, Randall–Sundrum models imagine that the real world is a higher-dimensional Universe described by warped geometry...
  
  
• warped geometry
• Weyl curvature hypothesis
  Weyl curvature hypothesis
  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 Sir Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the...