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Energy Condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathematical formulation. There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory. The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions. Energy conditions are not physical constraints , but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive". Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well-known to violate the strong energy condition. In general relativity, energy conditions are often used (and required) in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Relativity
The theory of relativity usually encompasses two interrelated 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 theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence (general Relativity)
In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation. Types of congruences Congruences generated by nowhere vanishing timelike, null, or spacelike vector fields are called ''timelike'', ''null'', or ''spacelike'' respectively. A congruence is called a ''geodesic congruence'' if it admits a tangent vector field \vec with vanishing covariant derivative, \nabla_ \vec = 0. Relation with vector fields The integral curves of the vector field are a family of ''non-intersecting'' parameterized curves which fill up the spacetime. The congruence consists of the curves themselves, without reference to a particular parameterization. Many distinct vector fields can give rise to the ''same'' congrue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Solution
In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid. In astrophysics, fluid solutions are often employed as stellar models. (It might help to think of a perfect gas as a special case of a perfect fluid.) In cosmology, fluid solutions are often used as cosmological models. Mathematical definition The stress–energy tensor of a relativistic fluid can be written in the form :T^ = \mu \, u^a \, u^b + p \, h^ + \left( u^a \, q^b + q^a \, u^b \right) + \pi^ Here * the world lines of the fluid elements are the integral curves of the velocity vector u^a, * the projection tensor h_ = g_ + u_a \, u_b projects other tensors onto hyperplane elements orthogonal to u^a, * the matter density is given by the scalar function \mu, * the pressure is given by the scalar function p, * the heat flux vector is given by q^a, * the viscous shear tensor is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy. Einstein originally introduced the constant in 1917 to counterbalance the effect of gravity and achieve a static universe, a notion that was the accepted view at the time. Einstein's cosmological constant was abandoned after Edwin Hubble's confirmation that the universe was expanding. From the 1930s until the late 1990s, most physicists agreed with Einstein's choice of setting the cosmological constant to zero. That changed with the discovery in 1998 that the expansion of the universe is accelerating, im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Casimir Effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948. In the same year, Casimir together with Dirk Polder described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface which is referred to as the Casimir–Polder force. Their result is a generalization of the London–van der Waals force and includes retardation due to the finite speed of light. Since the fundamental principles leading to the London–van der Waals force, the Casimir and the Casimir–Polder force, respectively, can be formulated on the same footing, the distinction in nomenclature nowadays serves a historical purpose mostly and usually refers to the different physical setups. It was not until 1997 that a direct experiment by S. Lamor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech) until 2009 and is one of the world's leading experts on the astrophysical implications of Einstein's general theory of relativity. He continues to do scientific research and scientific consulting, most notably for the Christopher Nolan film '' Interstellar''. Thorne was awarded the 2017 Nobel Prize in Physics along with Rainer Weiss and Barry C. Barish "for decisive contributions to the LIGO detector and the observation of gravitational waves". Life and career Thorne was born on June 1, 1940, in Logan, Utah. His father, D. Wynne Thorne (1908–1979), was a professor of soil chemistry at Utah State University, and his mother, Alison (née Comish; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raychaudhuri's Equation
In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter. The equation is important as a fundamental lemma for the Penrose–Hawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation of our intuitive expectation that gravitation should be a universal attractive force between any two bits of mass-energy in general relativity, as it is in Newton's theory of gravitation. The equation was discovered independently by the Indian physicist Amal Kumar Raychaudhuri and the Soviet physicist Lev Landau.'' The large scale structure of space-time'' by Stephen W. Hawking and G. F. R. Ellis, Cambridge University Press, 1973, p. 84, . Mathematical statement Given a timelike unit vector field \vec (which can be interpreted as a family or congruence of nonintersecting world lines via th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tidal Tensor
{{disambiguation ...
Tidal is the adjectival form of tide. Tidal may also refer to: * ''Tidal'' (album), a 1996 album by Fiona Apple * Tidal (king), a king involved in the Battle of the Vale of Siddim * TidalCycles, a live coding environment for music * Tidal (service), a music streaming service * Tidal, Manitoba, Canada ** Tidal station, Tidal, Manitoba See also * Tidal flow (traffic), the flow of traffic thought of as an analogy with the flow of tides * Tidal force, a secondary effect of the force of gravity and is responsible for the tides * Tide (other) A tide is the rise and fall of a sea level caused by the Moon's gravity and other factors. Tide may also refer to: Media * ''The Tide'' (Nigeria), a newspaper * ''Tide'' (TV series), 2019 Irish/Welsh/Scottish documentary series * WTKN, a radio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trace (linear Algebra)
In linear algebra, the trace of a square matrix , denoted , is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of . The trace is only defined for a square matrix (). It can be proved that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proved that for any two matrices and . This implies that similar matrices have the same trace. As a consequence one can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to a basis are similar. The trace is related to the derivative of the determinant (see Jacobi's formula). Definition The trace of an square matrix is defined as \operatorname(\mathbf) = \sum_^n a_ = a_ + a_ + \dots + a_ where denotes the entry on the th row and th column of . The entries of can be real numbers or (more generally) complex numbers. The trace is not def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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