This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

The Einstein – Cartan – Sciama – Kibble theory of gravity extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.

Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.

There is no definite or clear way to define the total energy of the universe due to the most widely accepted theory of gravity, general relativity.

Under the special theory of relativity, a particle ( that has rest mass ) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times ( tachyons ).

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

In special relativity, mass turns out to be part of a more general quantity called the energy – momentum tensor, which includes both energy and momentum densities as well as stress ( that is, pressure and shear ).

In special relativity, conservation of energy – momentum corresponds to the statement that the energy – momentum tensor is divergence-free.

Special relativity shows that rest mass ( or invariant mass ) and rest energy are essentially equivalent, via the well-known relationship E = mc < sup > 2 </ sup >.

Einstein ’ s theory of relativity explained that when protons and neutrons come together to form an atomic nucleus, some of the mass of the nucleus is released in the form of binding energy.

File: Albert Einstein ( Nobel ). png | Albert Einstein ( 1879-1955 ): revolutionized physics due to his theories of special and general relativity, described Brownian motion, awarded the Nobel Prize in Physics in 1921 for his work on the photoelectric effect, formulated mass – energy equivalence formula E = mc < sup > 2 </ sup >, published more than 300 scientific papers and over 150 non-scientific works, considered the " Father of Modern Physics "

However, certain physical phenomena, such as singularities, are " very small " spatially yet are " very large " from a mass or energy perspective ; such objects cannot be understood with current theories of quantum mechanics or general relativity, thus motivating the search for a quantum theory of gravity.

) Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass – energy equivalence formula E = mc < sup > 2 </ sup >, where c is the speed of light in vacuum.

The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in a vacuum c = 299, 792, 458 meters per second, approximately 1079 million kilometers per hour ( 671, 000, 000 mph ).

In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it ; but it is also possible to run the Einstein field equations in the other direction, first specifying a metric and then finding the energy-momentum tensor associated with it, and this is what Alcubierre did in building his metric.

* General relativity predicts that light should lose its energy when travelling away from the massive bodies.

In relativity, the momentum and the energy are the space and time parts of a space-time vector, the 4-momentum, and they are related by the relativistically invariant relation

Thus for example atomic processes that are observed as rates, will necessarily be adjusted in a way consistent with relativity, while those involving the measurement of energy and momentum, which themselves form a relativistic vector, will undergo parallel adjustment which preserves the relativistic covariance of the observed values.

According to special relativity, because photons are massless their energy ( E ) and momentum ( p ) are related by E = pc.

That is, according to relativity theory, mass is simply frozen energy, energy is simply liquid mass.

The Standard Model falls short of being a complete theory of fundamental interactions because it does not incorporate the full theory of gravitation as described by general relativity, or predict the accelerating expansion of the universe ( as possibly described by dark energy ).

His other contributions include a simplified proof of the positive energy theorem involving spinors in general relativity, his work relating supersymmetry and Morse theory, his introduction of topological quantum field theory and related work on mirror symmetry, knot theory, twistor theory and D-branes and their intersections.

The 1976 definition of the astronomical unit was incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and " vigorous debate " ensued until in August 2012 the International Astronomical Union adopted the current definition of 1 astronomical unit = 149597870700 meters.

According to the special theory of relativity, the aberration looks as a transform of the celestial sphere due to different frames of reference and is virtually a special case of velocity addition, namely one of the light beam and frames ' relative velocity v. The formula from relativistic aberration can be simplified to

Despite their embrace of the principle of rectilinear inertia and the recognition of the kinematical relativity of apparent motion ( which underlies whether the Ptolemaic or the Copernican system is correct ), natural philosophers of the seventeenth century continued to consider true motion and rest as physically separate descriptors of an individual body.

Physical cosmology, as it is now understood, began with the twentieth century development of Albert Einstein's general theory of relativity and better astronomical observations of extremely distant objects.

One consequence of this is that in standard general relativity, the universe began with a singularity, as demonstrated by Stephen Hawking and Roger Penrose in the 1960s.

* the equivalence principle, whether or not Einstein's general theory of relativity is the correct theory of gravitation, and if the fundamental laws of physics are the same everywhere in the universe.

While special relativity constrains objects in the universe from moving faster with respect to one another than the speed of light, there is no such constraint in general relativity.

But, according to Einstein's theory of special relativity, no information-bearing signal or entity can travel at or faster than the speed of light, which is finite.

Thus, it seems as if the Copenhagen interpretation is inconsistent with special relativity.

* The strong cosmic censorship hypothesis asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory.

A special case of this is a Lorentzian manifold, which is the mathematical basis of Einstein's general relativity theory of gravity.

An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only where the gravitational field is weak.

Einstein's theory of general relativity shows that the true geometry of spacetime is not Euclidean geometry.

It is possible to object to this interpretation of general relativity on the grounds that light rays might be improper physical models of Euclid's lines, or that relativity could be rephrased so as to avoid the geometrical interpretations.

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity.

The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole.

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass ( now called the Chandrasekhar limit at 1. 4 solar masses ) has no stable solutions.

In general relativity, the apsides of any orbit ( the point of the orbiting body's closest approach to the system's center of mass ) will precess — the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape ( see image ).

Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are equivalent ; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.

From the viewpoint of any single unaccelerated observer, mass can neither be created or destroyed, and special relativity does not change this understanding.

In special relativity, relativistic mass is a formalism which accounts for relativistic effects by having the mass increase with velocity.

The special and general theories of relativity give three types of corrections to the Newtonian precession, of a gyroscope near a large mass such as the earth, described above.

Since the particle speed < math > v < c </ math > for any particle that has mass ( according to special relativity ), the phase velocity of matter waves always exceeds c, i. e.

General relativity models gravity as a curvature within space-time that changes as a gravitational mass moves.

High-precision test of general relativity by the Cassini-Huygens | Cassini space probe ( artist's impression ): radio signals sent between the Earth and the probe ( green wave ) are Shapiro effect | delayed by the warping of space and time ( blue lines ) due to the Sun's mass.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole.

Symmetry between inertial and gravitational mass results in general relativity.