scholarly journals Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

2021 ◽  
Author(s):  
◽  
Finnian Gray
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Hawking Temperature ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Wick Rotation ◽  
Radiation Process ◽  
Black Hole Radiation ◽  
Euclidean Quantum Field Theory

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process.  The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

scholarly journals Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

2021 ◽  
Author(s):  
◽  
Finnian Gray
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Hawking Temperature ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Wick Rotation ◽  
Radiation Process ◽  
Black Hole Radiation ◽  
Euclidean Quantum Field Theory

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process.  The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

scholarly journals Examining a covariant and renormalizable quantum field theory in de Sitter space by studying “black hole radiation”

2016 ◽  
Vol 31 (11) ◽  
pp. 1650052 ◽  
Author(s):  
Hamed Pejhan ◽  
Surena Rahbardehghan
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
De Sitter ◽  
Black Hole Radiation

Respecting that any consistent quantum field theory in curved space–time must include black hole radiation, in this paper, we examine the Krein–Gupta–Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman–Gärding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy–momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field to vanish. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy–momentum tensor. On this basis, by evaluating the Casimir energy–momentum tensor for a conformally coupled massless scalar field in the vicinity of a nonrotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals INTERACTION MEASURES ON THE SPACE OF DISTRIBUTIONS OVER THE FIELD OF p-ADIC NUMBERS

2003 ◽  
Vol 06 (03) ◽  
pp. 389-411 ◽  
Author(s):  
ANATOLY N. KOCHUBEI ◽  
MUSTAFA R. SAIT-AMETOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operator ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Quantum Field ◽  
Pseudo Differential Operator ◽  
Schwartz Distributions ◽  
Space Of Distributions ◽  
Euclidean Quantum Field Theory

We construct measures on the space [Formula: see text], n≤4, of Bruhat–Schwartz distributions over the field of p-adic numbers, corresponding to finite volume polynomial interactions in a p-adic analog of the Euclidean quantum field theory. In contrast to earlier results in this direction, our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudo-differential operator over [Formula: see text]. Analogs of the Euclidean P(φ)-theories with free and half-Dirichlet boundary conditions are considered.

scholarly journals A self-consistency check for unitary propagation of Hawking quanta

2017 ◽  
Vol 32 (33) ◽  
pp. 1750198 ◽  
Author(s):  
Daniel Baker ◽  
Darsh Kodwani ◽  
Ue-Li Pen ◽  
I-Sheng Yang
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Negative Answer ◽  
Space Time ◽  
Quantum Field ◽  
Consistency Check ◽  
Curved Space ◽  
Self Consistency ◽  
Double Slit

The black hole information paradox presumes that quantum field theory in curved space–time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space–time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.

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