Remarks on the thermofield double state in 4D black hole background

Anempodistov, P. A.

doi:10.1103/physrevd.103.105008

Cited by 9 publications

(3 citation statements)

References 18 publications

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“…This class of states includes the isometry invariant states for the canonical values of temperature. But, even though the states are thermal, we find a nontrivial result, similar to the one discovered in our previous papers [3,[14][15][16][17], which were devoted to the aspects of quantum fields physics in the background space-times with horizons. In those papers we mainly considered two-dimensional theories and studied the properties of the Wightman functions.…”

Section: Introductionsupporting

confidence: 82%

Notes on peculiarities of quantum fields in space–times with horizons

Bazarov¹

2022

Class. Quantum Grav.

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We consider a massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress--energy tensor operator for the thermal states with arbitrary temperatures. It turns out that the dependence of the expectation values on the temperature and tensor structure of the stress--energy tensor are different from the usual ones in the Minkowski space-time. Moreover, for non--canonical temperatures these expectation values are divergent on the horizons. We also show that the Wightman functions have additional infrared peculiarities near the horizons.

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Section: Introductionsupporting

confidence: 82%

Notes on peculiarities of quantum fields in space–times with horizons

Bazarov¹

2022

Class. Quantum Grav.

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“…In space-times with Killing horizons, one can also consider a thermal gas with the planckian density matrix with an arbitrary temperature, different from the canonical one. But if the temperature is different from the canonical one, then correlation functions do not posses Hadamard properties on Killing horizons and the back-reaction on the background geometry is strong (see, for example: [37][38][39][40][41][42][43][44][45]). Furthermore, the thermalization process in curved space-times, in general, is far from being well understood [46].…”

Section: Jhep04(2024)077mentioning

confidence: 99%

Is the Euclidean path integral always equal to the thermal partition function?

Diakonov

2024

J. High Energ. Phys.

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The Euclidean path integral is compared to the thermal (canonical) partition function in curved static space-times. It is shown that if spatial sections are non-compact and there is no Killing horizon, the logarithms of these two quantities differ only by a term proportional to the inverse temperature, that arises from the vacuum energy. When spatial sections are bordered by Killing horizons the Euclidean path integral is not equal to the thermal partition function. It is shown that the expression for the Euclidean path integral depends on which integral is taken first: over coordinates or over momenta. In the first case the Euclidean path integral depends on the scattering phase shift of the mode and it is UV diverge. In the second case it is the total derivative and diverge on the horizon. Furthermore we demonstrate that there are three different definitions of the energy, and the derivative with respect to the inverse temperature of the Euclidean path integral does not give the value of any of these three types of energy. We also propose the new method of computation of the Euclidean path integral that gives the correct equality between the Euclidean path integral and thermal partition function for non-compact spaces with and without Killing horizon.

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“…It should be noted that there are already papers (see, for example, recent papers [11][12][13]), in which the quantum scalar field is considered only outside the event horizon of the Schwarzschild black hole. Nevertheless, despite the fact that, in some rigorous methods for constructing quantum theory in the gravitational field of a black hole, it is not necessary to take into account the internal regions of black and white holes, the question remains whether it is possible to construct a consistent quantum field theory in the Schwarzschild spacetime only above the horizon.…”

Section: Introductionmentioning

confidence: 99%

Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation

Egorov,

Smolyakov,

Volobuev

2024

Class. Quantum Grav.

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We discuss the problem of canonical quantization of a free massive spinor ﬁeld in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the ﬁeld can be carried out without taking into account the internal region of the black hole, the canonical commutation relations in the resulting theory hold exactly and the Hamiltonian has the standard form. Spin sums are obtained for solutions of the Dirac equation in the Schwarzschild spacetime.

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Remarks on the thermofield double state in 4D black hole background

Cited by 9 publications

References 18 publications

Notes on peculiarities of quantum fields in space–times with horizons

Notes on peculiarities of quantum fields in space–times with horizons

Is the Euclidean path integral always equal to the thermal partition function?

Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation

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