We present the interior solution for a static, spherically symmetric perfect fluid star backreacted by QFT in four dimensions invoking no arbitrary parameters. It corresponds to a constant energy density star and is fully non-perturbative. The space of solutions includes ultra-compact configurations that have neither singularities nor light rings inside the star and can exist arbitrarily close to the Schwarzschild limit, showing that the classical paradigm of astrophysics does not hold once QFT in curved space is taken into account.
In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important…
We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $λϕ^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.
In the present paper we study the Hawking radiation as a quantum tunneling effect of spin-$1$ particles from a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (5D EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results in a set of five differential equations, and reproduces in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the …
It has been proposed recently to consider in the framework of cosmology an extension of the semiclassical Einstein's equations in which the Einstein tensor is considered as a random function. This paradigm yields a hierarchy of equations between the $n$-point functions of the quantum, normal ordered, stress energy-tensor and those associated to the stochastic Einstein tensor. Assuming that the matter content is a conformally coupled massive scalar field on de Sitter spacetime, this framework has been applied to compute the power spectrum of the quantum fluctuations and to show that it is almos…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributi…
University of Colorado, Boulder（科罗拉多大学博尔德分校）；University of Maryland, College Park（马里兰大学帕克分校）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechani…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be …
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get a state for the quantum field which gives finite expectation values for the stress-energy tensor. Furthermore, it is possible to control this expectation value by means of a global estimate on regular cosmological spacetimes. The obtained estimates permit to write a theorem about the existence and uniqueness of the local solutions encompassing both the space…
We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown. Different from previous work on this subject, we do not restrict to the conformally coupled scalar field and we admit the full renormalization freedom. Based on a regularization procedure, which utilizes homogeneous distributions and is equivalent to Hadamard point-splitting, we obtain a reformulation of the evolution of the quantum state as an infinite-dimensional dynamical system with mathematical features that are distinct from the standa…
In this paper we shall discuss the backreaction of a massive quantum scalar field on the curvature, the latter treated as a classical field. Furthermore, we shall deal with this problem in the realm of cosmological spacetimes by analyzing the Einstein equations in a semiclassical fashion. More precisely, we shall show that, at least on small intervals of time, solutions for this interacting system exist. This result will be achieved providing an iteration scheme and showing that the series, obtained starting from the massless solution, converges in the appropriate Banach space. The quantum sta…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard singular structure can be characterised explicitly, which allows one to in principle give initial data for the Wightman function that has correct distributional singularities, such that the expectation value of the renormalised stress-energy tensor of the solution can be defined, and that hence the semiclassical Einstein equations make sense. Assuming a "positi…
This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity, based on a lattice regularization of the quantum-gravitational path integral. It is shown that inside the, so-called, de Sitter phase one recovers a four-dimensional semiclassical universe, where behaviour of the scale factor is consistent with classical solutions of Einstein's field equations and fluctuations of the scale factor are very accurately described b…
The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory turns out to be a non-commutative field theory on configuration space and a group field theory on momentum space. Using basic non-commutative Fourier transform tools we introduce the notion of non-commutative heat-kernel associated with the Laplacian on the non-commutative configuration space. We show that the spectral dimension associated to the non-commutati…
This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress-energy tensor of a quantum field with classical gravity. Here we consider a free massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale…
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.
We present an extension of the semiclassical Einstein equations which couples n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the cal…
We employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H <…
We propose to formulate a theory for Classical Stochastic Gravity for certain applications in Astrophysics and Cosmology.This involves the Langevin approach in curved spacetime, which is introduced here, in the form of a classical Einstein-Langevin equation.The domain of applications of such an approach and possible outcomes of this formulation which are quite different than its semiclassical counterpart (which is an active area of research), are discussed.This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Sem…
The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski Spacetime
University of York（约克大学）；Università di Trento（特伦托大学）；GNFM-INdAM（意大利数学国家研究委员会几何与函数论全国小组）；TIFPA-INFN（意大利国家核物理研究所特伦托前沿物理与分析中心）；Università di Genova（热那亚大学）；INFN（意大利国家核物理研究所）；Universität Regensburg（雷根斯堡大学）
