Questions tagged [qft-in-curved-spacetime]
Quantum field theory in curved spacetime (QFTCS) is a field of study that focuses on problems that arise when considering a quantum field on a fixed, curved spacetime. It allows the study of quantum effects in strong gravitational fields, and has led to many interesting conclusions, such as the Unruh effect and the Hawking effect.
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Boundary conditions and field quantization in AdS
While studying the AdS/CFT correspondence, one encounters very early the example of a scalar field in AdS. The general solution to the Klein-Gordon equation in the limit $z\rightarrow 0$ may be ...
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Cosmological horizon and Hawking/Unruh radiation? [closed]
I have two questions about cosmological horizons and their emission of radiation
The first one is:
There are some authors that propose that dark energy or the accelerated expansion of the universe ...
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Spectrum of Klein-Gordon operator in AdS Black Hole
I'm working on obtaining the spectrum of the Klein-Gordon operator in $AdS_2$ for black hole coordinates. To accomplish that, I first consider the problem in hyperbolic space $H_2$ and then Wick ...
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Trace of stress-energy tensor for a scalar field
I'm trying to reproduce a calculation done in Birrell & Davies' book Quantum Fields in Curved Space (page 191). Given Klein-Gordon's equation $$(\Box + m^2 + R\xi)\phi = 0$$ and
$$T_{\mu \nu} = (1 ...
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The Electromagnetic Energy and Momentum Conservation in curved space-time
Can someone please show me the formalisms of the energy and the momentum conservation in the curved space-time for electromagnetic?
I know it's going to be two equations.
but I couldn't find them ...
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Solution to the Klein-Gordon equation in a generic metric
Is there a way to solve the Klein-Gordon equation in a generic spacetime for a massless scalar field?
\begin{equation}
\frac{1}{\sqrt{-g}}\partial_{\mu}(\sqrt{-g}g^{\mu\nu}\partial_{\nu}\phi)=0.
\end{...
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Why negative energy particles not created near a black hole? [duplicate]
If you take empty space right next to a black hole once in awhile, you will get a positive particle being admitted in the opposite direction of the black hole. In the creation of the photon this ...
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Canonical quantization of gauge field under the Schwarzschild background
I have read some papers (e.g.0803.2001, PhysRevD.24.297, especially section 4 in 1809.03467 ) to find the mode expansion of gauge field under the Schwarzschild background.
In paper PhysRevD.24.297, ...
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Curved spacetime generalization of Bethe-Salpeter equation
I am interested in the problem of bound states in QFT in curved spacetime. I was wondering if the generalization of the Bethe-Salpeter equation is as simple as replacing the Green’s functions in the ...
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Energy-momentum tensor of Majorana field
The Majorana field action in curved spacetime, in general, is usually written as (see this answer on Physics SE)
$$\mathcal{A}_M = \displaystyle\int_\mathcal{M} d^4x ~ e \left\{\dfrac{1}{2} \bar{\psi}\...
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Majorana field Lagrangian in curved spacetime
In this paper(An Exact Cosmological Solution of the Coupled
Einstein-Majorana Fermion-Scalar Field Equations), the Majorana field Lagrangian has been stated as
$\mathcal{L}_M = i \bar{\psi} \left(\...
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What vacuum should be defined for a observer in Kerr spacetime?
A scalar field in Kerr spacetime can have two kinds of modes, one labeled by "in", and the other by "up". The "in" modes originate from the past null infinity, while the &...
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Making background curvature variable in QFT on curved spacetime
In QFT on curved spacetime one may start with a Klein-Gordon like equation
$$(\square_g - m^2 j) \phi = j,$$
where $\square_g := g^{\mu \nu} \nabla_\mu \nabla_\mu$ is the D'Alembertian operator, and $...
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No hair theorem and Klein-Gordon equation
The no-hair theorem states that we can't detect scalar fields outside a black hole, meaning that the solution for the KG equation is trivial, but in fact, we can solve it (for instance for a ...
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Energy and momenta of a field on a curved manifold
In a curved spacetime with metric $g$, let us have a complex scalar field $\Phi$. The stress energy momentum tensor of the field is defined as,
$$T_{ab} := \frac{-2}{\sqrt{-g}} \frac{\delta S_\Phi}{\...
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Spin field on curved space: meaning of coupling with spin connection
I'm studying qft on curved space and i'm a bit confused as the teacher made the example of covariant electromagnetism when obtained the covariant derivative of a spin vector (with spin connection). So ...
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Spin connection for a vector field
Using Birrel & Davies convention, the covariant derivative for a field of arbitrary spin in curved spacetime is given by
$$\nabla_\mu=\partial_\mu+\Omega_\mu,\tag{1}$$
with
$$\Omega_\mu=\frac{1}{2}...
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Particles, strings, and field theories
I work in quantum field theory in curved spacetime. Within QFTCS, we have a bunch of phenomena showing that the notion of "particle" is quite subtle. For example, the Unruh effect let's us ...
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Would this experiment potentially work for detecting whether gravitons exist?
Take a primordial black hole and measure the Hawking radiation over a large amount of time by gamma-ray detectors, as well as a Large neutrino detector.
Using theoretical calculations about the ...
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How we know that Dirac equation in curved spacetime is the correct one?
Dirac equation in curved spacetime is given by
$$\left(i \gamma^\mu D_\mu-m\right) \Psi=0$$
How does we know that this is the correct equations to describe spinors in curved space time?
Is there any ...
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Reasoning about spin coupling on curved space
In the course of QFT i learnt that the gauge field emerges from the need of a gauge invariance in the action, as we use the covariant derivative in minimal coupling. Now i'm studying how spin fields ...
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Can someone help me understand backreaction?
I was reading a paper on black-hole information loss and it mentioned backreaction. I had never heard the word before so I googled it and was surprised to find no cohesive definition that I could ...
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Where from Hawking radiation actually arise?
Where from Hawking radiation actually arise? I would like to connect the answer with the technical derivation along the lines of the original calculation by Hawking (a modern account of which is given ...
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Will Hawking radiation violate baryon number conservation around gravitating bodies other than black holes?
Numberous articles discussing a recent research paper suggest that even stars and planets will eventually radiate away their mass like hawking radiation. My question is will this violate baryon ...
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Are non-virtual particles of QFT real?
Perhaps the question may seem a bit provocative, but it refers to several mathematical and, presently physical facts, pointed out a long time ago:
The Unruh effect suggests that an accelerated ...
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Bogolubov coefficients calculation
I'm studing the Hawking effect in a two dimensional Schwarzchild spacetime.
I have the modes:
$
\phi(t,r^*) = \int_\mathbb{R} \frac{d k}{(2 \pi)^{1/2}} \frac{1}{\sqrt{2 \Omega}}\left[ e^{-i(\Omega t - ...
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Is Hawking radiation possible for all massive objects (based on new research)? [duplicate]
So a few years ago, looking at the answer to this question the answer was no and that there needed to be an event horizon for hawking radiation to arise and that it is not purely curvature that causes ...
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Annihilation and creation operators time-dependence in curved spacetime (Again)
Let me ask this question again to hopefully get an answer.
Consider a free scalar field $\phi$ on a curved spacetime.
The way we define the vacuum is by decomposing the field in terms of mode ...
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Realistic model for the stress-energy tensor for the Casimir effect
According to Visser M. in the book "Lorentzian Wormholes: from Einstein to Hawking", a realistic model for the stress-energy tensor of the Casimir effect is presented in equation (12.31):
$$ ...
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Stationary spacetimes and metric tensor [duplicate]
A stationary spacetime is defined to be one for which there exists a timelike Killing vector field such that the Lie derivative of the metric wrt this vector field vanishes,
i.e.
$\mathcal{L}_X g_{\mu\...
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Klein-Gordon in Schwarzschild Curved Spacetime [closed]
Given such a Schwarzschild metric, the covariant Klein-Gordon equation for a mass $m$ takes the form
$$\left[\frac{1}{g_{00}} \frac{\partial^2}{\partial t^2 }-\frac{1}{r^2} \frac{\partial}{\partial r}...
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Negative energy particle effect on observable object
A recent paper "Gravitational Pair Production and Black Hole Evaporation" (discussed in short here) says that any spacetime curvature would produce Hawking radiation, no need for event ...
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Euclidean Black hole diagram
I am trying to understand how the Euclidean "cigar" is built. I understand how and why the time is periodic, as for the radius of the cigar I am confused, it should be constant far from the ...
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Is a conformally coupled scalar always massive?
Maybe this is trivial, but the action of a conformally coupled scalar is
$$ S = \frac{1}{2} \int d^Dx \sqrt{g} (g^{ab} \partial_a \phi \partial_b \phi + \xi R \phi^2),$$
where $\xi = (D-1)/4D$. Does ...
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Writing Einstein-Hilbert and Gravity-matter Hamiltonian in terms of creation/annihilation operators
I am trying to understand how to write the gravity-matter and gravity-gravity hamiltonians in terms of daggered/undaggered operators. Is there any pedagogic review paper on writing such hamiltonians ...
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Generalizing the expression for $T_{\mu\nu}$ for fermions, from Minkowski to curved spacetime
Background to my question: the flat case
I am interested in the following (part of a) Lagrangian involving spinors in a general curved spacetime:
$$L=\frac{1}{2}\overline{\psi}\left(i\gamma^{\alpha}\...
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How do electrons interact with a graviton?
The spin of graviton is 2 and spin of electron is $\frac{1}{2}$. Of course, since electrons have mass, they pull each other in respect to gravitational force.
Whenever i tried to draw Feynman diagram ...
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Fulling–Davies–Unruh effect with non-uniform acceleration
Can there be some version of the Fulling–Davies–Unruh effect, in which the accelerating observer is moving with a non-uniform acceleration? Can someone refer some papers to read?
If there can not be ...
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Physical interpretation of the spin connection field for the Dirac equation in curved spacetime [duplicate]
When dealing with the Dirac equation in curved spacetime one has to replace the partial derivative with the following covariant derivative:
${\partial_{\mu}}-\frac{i}{4}\omega_{\mu}^{\alpha\beta}\...
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Covariant derivative of gauge theory in curved space
I am reading Witten's article and have a basic question about gauge theory in curved space.
In ordinary flat space (Euclidean space or Minkowski spacetime), covariant derivative of a gauge field $A_{\...
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Properties of analytic continuation of two point/ Wightman function
In this paper, the author considers Wightman functions calculated on an accelerating detector for a massless scalar field, namely
$$G_+^R = {}_M \langle 0 | \phi(x) \phi^{\dagger}(x') | 0 \rangle_M$$
$...
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Questions about the details of deriving Hartle-Hawking state
I'm studying Hartman's "Black holes and Quantum Information" lesson(I'm a chinese so maybe I have some syntax error),and I'm confused about the Hartle-Hawking state. He says we start from ...
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Was Stephen Hawking's explanation of Hawking Radiation in "A Brief History of Time" not entirely accurate?
I've been looking into black holes and Hawking radiation recently (just on the surface level) and was reading "A Brief History in Time" by Stephen Hawking to understand the basics of ...
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Interior Hawking radiation
The Hawking effect is induced by the causal horizon of a black hole, which separates the interior and exterior modes such that asymptotic observers at infinity see thermal radiation flux. What can we ...
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Gravitational backreaction in AdS/CFT
When we add a scalar field into AdS space time, under which limit can we ignore the gravitational back reaction? In the case of massless scalar, can we totally ignore the backreation to the background ...
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Assumptions in the bound on chaos
In the paper A bound on chaos, by Maldacena, Shenker and Stanford. They mention two assumptions to prove that the Lyapunov exponent in the OTOCs must be smaller than or equal to $2\pi T$.
One of the ...
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Deriving the equation for a particle in curved spacetime [closed]
When Dirac derived his equation he started from the non relativistic time dependent Schrodinger equation and then treated the partial derivative of time as the partial derivative of position and then ...
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How to derive form of reflecting waves from black holes?
Consider a collapsing sphere that becomes a black hole. The interior schwartzchild lightcone coordinate $U$ can be written as $U$ = $\tau - r + R_{0}$ where $R_{0}$ is the radius of the sphere before ...
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Derivation of out-vacuum in terms of in-vacuum
Say that spacetime undergoes an expansion, and the quantum field is in the state $\phi_{in}$ at $t \rightarrow -\infty$ and $\phi_{out}$ at $t \rightarrow \infty$. The annihilation operators can be ...
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Does Hawking radiation have a statistical physics origin like the usual derivation of Boltzmann factors?
According to Andrew Steane's Thermodynamics chapter 19 on Thermal radiation:
"The total emission from a physical object can usefully be separated in two parts: the thermal radiation and the rest. ...
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