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Semiclassical gravity
 
 
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Semiclassical gravity is the approximation to the theory of quantum gravity
Quantum gravity

Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the Fundamental interaction , with general relativity, the theory of the fourth fundamental force: Gravitation....
 in which one treats matter fields as being quantum and the gravitational field
Gravitation

Gravitation is a natural phenomenon that gives weight to objects. In everyday life, attraction due to gravity is the result of the presence of relatively large bodies, such as the Earth and the Moon....
 as being classical.

In semiclassical gravity, matter is represented by quantum matter fields that propagate according to the theory of quantum fields in curved spacetime
Quantum field theory in curved spacetime

Quantum field theory in curved spacetime is an extension of standard quantum field theory to general relativity. A general prediction of this theory is that particles can be created by time dependent gravitational fields, or by time independent graviational fields that contain horizons....
. The spacetime in which the fields propagate is classical but dynamical. The curvature of the spacetime is given by the semiclassical Einstein equations, which relate the curvature of the spacetime, given by the Einstein tensor
Einstein tensor

The Einstein tensor expresses spacetime curvature in the Einstein field equations for gravitation in the theory of general relativity. It is sometimes called the trace-reversed Ricci tensor....
 , to the expectation value of the energy-momentum 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 of Newtonian physics....
 operator, , of the matter fields:

where G is Newton's constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 and indicates the quantum state of the matter fields.

Since the theory of quantum gravity is not yet known, it is difficult to say what is the regime of validity of semiclassical gravity.






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Semiclassical gravity is the approximation to the theory of quantum gravity
Quantum gravity

Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the Fundamental interaction , with general relativity, the theory of the fourth fundamental force: Gravitation....
 in which one treats matter fields as being quantum and the gravitational field
Gravitation

Gravitation is a natural phenomenon that gives weight to objects. In everyday life, attraction due to gravity is the result of the presence of relatively large bodies, such as the Earth and the Moon....
 as being classical.

In semiclassical gravity, matter is represented by quantum matter fields that propagate according to the theory of quantum fields in curved spacetime
Quantum field theory in curved spacetime

Quantum field theory in curved spacetime is an extension of standard quantum field theory to general relativity. A general prediction of this theory is that particles can be created by time dependent gravitational fields, or by time independent graviational fields that contain horizons....
. The spacetime in which the fields propagate is classical but dynamical. The curvature of the spacetime is given by the semiclassical Einstein equations, which relate the curvature of the spacetime, given by the Einstein tensor
Einstein tensor

The Einstein tensor expresses spacetime curvature in the Einstein field equations for gravitation in the theory of general relativity. It is sometimes called the trace-reversed Ricci tensor....
 , to the expectation value of the energy-momentum 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 of Newtonian physics....
 operator, , of the matter fields:

where G is Newton's constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 and indicates the quantum state of the matter fields.

Since the theory of quantum gravity is not yet known, it is difficult to say what is the regime of validity of semiclassical gravity. However, one can formally show that semiclassical gravity could be deduced from quantum gravity by considering N copies of the quantum matter fields, and taking the limit of N going to infinity while keeping the product GN constant. At diagrammatic level, semiclassical gravity corresponds to summing all Feynman diagram
Feynman diagram

In quantum field theory a Feynman diagram is an intuitive graphical representation of a contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory....
s which do not have loops of gravitons (but have an arbitrary number of matter loops). Semiclassical gravity can also be deduced from an axiomatic approach.

The most important applications of semiclassical gravity are to understand the Hawking radiation
Hawking radiation

Hawking radiation is a thermal radiation with a black body predicted to be emitted by black holes due to quantum physics effects. It is named after the physicist Stephen Hawking who provided the theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein who predicted that black holes should have a...
 of black holes
Black hole

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation , can escape its pull after having fallen past its event horizon....
 and the generation of random gaussian-distributed perturbations in the theory of cosmic inflation
Cosmic inflation

In physical cosmology, cosmic inflation is the hypothesis that the wiktionary:nascent universe passed through a phase of exponential growth metric expansion of space was driven by a negative pressure vacuum energy density....
, which is thought to occur at the very beginnings of the big bang
Big Bang

The Big Bang is the physical cosmology model of the initial conditions and subsequent development of the universe supported by the most comprehensive and accurate explanations from current scientific method and observation....
.

  • Birrell, N. D. and Davies, P. C. W., Quantum fields in curved space, (Cambridge University Press, Cambridge, UK, 1982).