scholarly journals ON GRAVITATIONAL FLUCTUATIONS AND THE SEMICLASSICAL LIMIT IN MINISUPERSPACE MODELS

2000 ◽  
Vol 09 (05) ◽  
pp. 511-529 ◽  
Author(s):  
ROBERTO CASADIO
Keyword(s):  
Wave Function ◽  
Gravitational Collapse ◽  
Classical Theory ◽  
Semiclassical Approximation ◽  
Semiclassical Limit ◽  
Compact Objects ◽  
Back Reaction

An attempt is made to go beyond the semiclassical approximation for gravity in the Born–Oppenheimer decomposition of the wave-function in minisuperspace. New terms are included which correspond to quantum gravitational fluctuations on the background metric. They induce a back-reaction on the semiclassical background and can lead to the avoidance of the singularities the classical theory predicts in cosmology and in the gravitational collapse of compact objects.

scholarly journals Quantum collapse of a charged n-dimensional BTZ-like domain wall

2017 ◽  
Vol 26 (04) ◽  
pp. 1750028 ◽  
Author(s):  
Eric Greenwood
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Domain Wall ◽  
Gravitational Collapse ◽  
Particle Production ◽  
Proper Time ◽  
Back Reaction ◽  
Finite Amount ◽  
Classical Singularity ◽  
Asymptotic Observer

We investigate both the classical and quantum gravitational collapse of a massive, charged, nonrotating [Formula: see text]-dimensional Bañados–Teitelboim–Zanelli (BTZ)-like domain wall in AdS space. In the classical picture, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present in the domain wall; that is, if the domain wall is extremal, nonextremal or overcharged. In both the extremal and nonextremal cases, the collapse takes an infinite amount of observer time to complete. However, in the over-charged case, the collapse never actually occurs, instead one finds an oscillatory solution which prevents the formation of a naked singularity. As far as the infalling observer is concerned, in the nonextremal case, the collapse is completed within a finite amount of proper time. Thus, the gravitational collapse follows that of the typical formation of a black hole via gravitational collapse.Quantum mechanically, we take the absence of induced quasi-particle production and fluctuations of the metric geometry; that is, we ignore the effect of radiation and back-reaction. For the asymptotic observer, we find that, near the horizon, quantization of the domain wall does not allow the formation of the black hole in a finite amount of observer time. For the infalling observer, we are primarily interested in the quantum mechanical effect as the domain wall approaches the classical singularity. In this region, the main result is that the wave function exhibits nonlocal effects, demonstrated by the fact that the Hamiltonian depends on an infinite number of derivatives that cannot be truncated after a finite number of terms. Furthermore, in the large energy density limit, the wave function vanishes at the classical singularity implying that quantization does not rid the black hole of its singularity.

QUANTIZATION OF SECOND-ORDER CONSTRAINED LAGRANGIAN SYSTEMS USING THE WKB APPROXIMATION

2005 ◽  
Vol 02 (03) ◽  
pp. 485-504 ◽  
Author(s):  
EQAB M. RABEI ◽  
EYAD H. HASSAN ◽  
HUMAM B. GHASSIB ◽  
S. MUSLIH
Keyword(s):  
Wave Function ◽  
General Theory ◽  
Semiclassical Limit ◽  
Second Order ◽  
Constrained Systems ◽  
Wkb Approximation ◽  
Lagrangian Systems

A general theory is given for quantizing both constrained and unconstrained systems with second-order Lagrangian, using the WKB approximation. In constrained systems, the constraints become conditions on the wave function to be satisfied in the semiclassical limit. This is illustrated with two examples.

ON THE RELATION BETWEEN QUANTUM HYDRODYNAMICS AND CONVENTIONAL QUANTUM FIELD THEORY

1954 ◽  
Vol 32 (8) ◽  
pp. 530-537
Author(s):  
F. A. Kaempffer
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Classical Theory ◽  
Quantum Field ◽  
Quantum Hydrodynamics ◽  
Quantization Procedure ◽  
Nonrelativistic Theory ◽  
Hydrodynamical Description ◽  
Charged Medium

The conditions are examined under which the procedure of quantum hydrodynamics would be a consequence of the conventional quantization procedure, and vice versa. Using the classical nonrelativistic theory of a charged medium as an example, it is shown that the commutation rules of the two procedures differ by a factor 2, if in accordance with an idea by Geilikman the wave function of the classical theory is expanded as ψ = ψ0 + ψ1, with ψ0 a constant and [Formula: see text], and if terms of higher than second order in ψ1 are neglected in the hydrodynamical description of the theory.

scholarly journals Validity of the semiclassical approximation and back reaction

1996 ◽  
Vol 53 (12) ◽  
pp. 7089-7093 ◽  
Author(s):  
Sukanta Bose ◽  
Leonard Parker ◽  
Yoav Peleg
Keyword(s):  
Semiclassical Approximation ◽  
Back Reaction

Transport of neutrinos, radiation and energetic particles in accretion flows

1982 ◽  
Vol 383 (1785) ◽  
pp. 409-437 ◽  
Keyword(s):  
Cosmic Rays ◽  
Electromagnetic Radiation ◽  
Gravitational Collapse ◽  
Charged Particles ◽  
Energetic Particles ◽  
Compact Objects ◽  
Red Giants ◽  
X Ray ◽  
Accretion Flows

The equations describing the transport of suprathermal charged particles, electromagnetic radiation and neutrinos across accretion flows onto compact objects are solved analytically, the effects of shocks in the flow being included. These solutions are used in discussing three illustrative astrophysical examples: acceleration of cosmic rays, generation of spectral continua in quasars and the effect of neutrinos during the collapse of supernova precursors. The main results are: ( а ) Accretion flows with shocks accelerate cosmic rays very efficiently up to the highest energies. ( b ) The emergent spectra of electromagnetic radiation from such flows reproduce the observed spectra of quasars from infrared to the hard X-ray region. ( c ) The neutrinos in the collapsing cores of red giants develop a very hard non-thermal tail in their distribution facilitating the rebound of the gravitational collapse leading to the supernovae.

GRAVITATIONAL COLLAPSE OF MASSIVE STARS AS A PROBE INTO HOT DENSE MATTER

2008 ◽  
Vol 23 (27n30) ◽  
pp. 2443-2450 ◽  
Author(s):  
SHOICHI YAMADA
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Nuclear Physics ◽  
Massive Stars ◽  
Dense Matter ◽  
High Energy ◽  
Compact Objects ◽  
Core Collapse ◽  
Accretion Shock ◽  
Very High

Nuclear physics is an indispensable input for the investigation of high energy astrophysical phenomena involving compact objects. In this paper I take a gravitational collapse of massive stars as an example and show how the macroscopic dynamics is influenced by the properties of nuclei and nuclear matter. I will discuss two topics that are rather independent of each other. The first one is the interplay of neutrino-nuclei inelastic scatterings and the standing accretion shock instability in the core of core collapse supernovae and the second is concerning the neutrino emissions from black hole formations and their dependence on the equation of state at very high densities. In the latter, I will also demonstrate that future astronomical observations might provide us with valuable information on the equation of state of hot dense matter.

Gibbons–Hawking temperature corrected by quantum cosmology

2017 ◽  
Vol 26 (10) ◽  
pp. 1750116 ◽  
Author(s):  
Je-An Gu ◽  
Sang Pyo Kim ◽  
Che-Min Shen
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Quantum Correction ◽  
Planck Scale ◽  
Friedmann Equation ◽  
Back Reaction ◽  
De Sitter ◽  
Pure Gravity ◽  
The Universe ◽  
Spacetime Fluctuations

We explore a quantum cosmology description of the de Sitter (dS) radiation and its back-reaction to a dS space, inherent in the wave function of the Wheeler–DeWitt equation for pure gravity with a cosmological constant. We first investigate the quantum Friedmann–Lemaitre–Robertson–Walker cosmological model and then consider the possible effects of inhomogeneities of the universe on the dS radiation. In both the cases we obtain the modified Friedmann equation, including the back-reaction from spacetime fluctuations, and the quantum-corrected Gibbons–Hawking (GH) temperature. It is shown that the quantum correction increases the GH temperature with the increment characterized by the ratio of the dS scale to the Planck scale.

scholarly journals The Maslov correction in the semiclassical Feynman integral

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Peter. Horváthy
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Semiclassical Approximation ◽  
Feynman Integral ◽  
Second Variation ◽  
The Second Variation

AbstractThe Maslov correction to the wave function is the jump of $$ \left( { - \frac{\pi } {2}} \right) $$ in the phase when the system passes through a caustic. This can be explained by studying the second variation and the geometry of paths, as conveniently seen in Feynman’s path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.

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