Semiclassical backreaction around a nearly spinning cosmic string
Vitorio A. De Lorenci, Edisom S. Moreira
备注：
6 pages, no figures, REVTeX4 file. This version provides a clearer discussion stressing that the ergoregion is a coordinate independent effect. Misleading sentences regarding this matter are amended
This paper investigates semiclassical backreaction of a conformally coupled massless scalar field on the geometrical background of a nearly spinning cosmic string - the spin density is smaller than, but arbitrarily close to, the dislocation parameter. As the spin density approaches the dislocation parameter, it is shown that an "ergoregion" spreads indefinitely around the cosmic string, boosting along the string axis the once static observers. Considering that the geometrical background contains closed timelike curves when the spin density exceeds the dislocation parameter, it is argued that the appearance of the "ergoregion" may be part of a chronology protection mechanism that takes place in related non stationary geometries.
Analytic semiclassical backreaction of a Schwarzschild black hole in a finite cavity: horizon shift, temperature renormalization, and canonical stability in the Hartle-Hawking State
Centre for Theoretical Physics, The British University（英国大学理论物理中心）；Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊马姆穆罕默德·本·沙特伊斯兰大学数学与统计系）；Faculty of Physics, Babeş-Bolyai University（巴比什-博雅依大学物理学院）；Astronomical Observatory（天文台）
We examine backreaction of quantum massive fields on multiply-degenerate (ultraextremal) horizons. It is shown that, under influence of the quantum backreaction, the horizon of such a kind moves to a new position, near which the metric does not change its asymptotics, so the ultraextremal black holes and cosmological spacetimes do exist as self-consistent solutions of the semiclassical field equations.
The evolution under radiation backreaction of a binary system consisting of a black hole and a companion is studied in the limiting case when the spin of the companion is negligible compared with the spin S of the black hole. To first order in the spin, the motion of the reduced-mass particle excluding radiation effects, is characterized by three constants: the energy E, the magnitude L of the angular momentum and the projection L_S of the angular momentum along the spin S. This motion is quasiperiodic with a period determined by r_{min} and r_{max}. We introduce a new parametrization, making …
In this review, we investigate the question of backreaction in different approaches to cosmological perturbation theory, and with a special focus on quantum theoretical aspects. By backreaction, we refer here to the effects of matter field or cosmological inhomogeneities on the homogeneous dynamical background degrees of freedom of cosmology. We begin with an overview of classical cosmological backreaction which is ideally suited for physical situations in the late time Universe. We then proceed backwards in time, considering semiclassical approaches such as semiclassical or stochastic (semicl…
The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of …
The semiclassical approximation has frequently been used to describe the initial stage of particle production, often called preheating, which occurs after the inflationary epoch in chaotic models of inflation. During this phase backreaction effects from the produced particles on the inflaton field are significant, and one might be concerned about the validity of the semiclassical approximation, even though large backreaction effects are allowed if the inflaton field is coupled to a large number of quantum fields. A criterion is presented for the validity of the semiclassical approximation in t…
Using the influence functional formalism we show how to derive a generalized Einstein equation in the form of a Langevin equation for the description of the backreaction of quantum fields and their fluctuations on the dynamics of curved spacetimes. We show how a functional expansion on the influence functional gives the cumulants of the stochastic source, and how these cumulants enter in the equations of motion as noise sources. We derive an expression for the influence functional in terms of the Bogolubov coefficients governing the creation and annihilation operators of the Fock spaces at dif…
We consider the effect of backreaction of quantized massive fields on the metric of extreme black holes (EBH). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum backreaction is consistent with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass M_{tot} and charge Q we show that for all cases of physical interest M_{tot}…
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.
From previous work arXiv:2010.09811, the semiclassical backreaction equation in 1+1 dimensions was solved and a criterion was implemented to assess the validity of the semiclassical approximation in this case. The criterion involves the behavior of solutions to the linear response equation which describes perturbations about solutions to the semiclassical backreaction equation. The linear response equation involves a time integral over a two-point correlation function for the current induced by the quantum field and it is expected that significant growth in this two-point function (and therefo…
The expected stress-energy tensor <T_{ab}> of quantum fields generically violates the local positive energy conditions of general relativity. However, <T_{ab}> may satisfy some nonlocal conditions such as the averaged null energy condition (ANEC), which would rule out traversable wormholes. Although ANEC holds in Minkowski spacetime, it can be violated in curved spacetimes if one is allowed to choose the spacetime and quantum state arbitrarily, without imposition of the semiclassical Einstein equation G_{ab} = 8 π<T_{ab}>. In this paper we investigate whether ANEC holds for solutions to this e…
We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass $M$ which collapses to a radius close to $r=2M$ will emit approximately thermal radiation for a period of time. In particular, a shell which collapses …
In this work we analyse the backreaction of a quantum field on a spherically symmetric black hole geometry with an inner horizon, i.e. an internal boundary of the trapped region. We start with a black hole background with an inner horizon which remains static after its formation. We quantise a massless scalar field on it and calculate its renormalised stress-energy tensor in the Polyakov approximation. We use this tensor as a source of perturbation on top of the background spacetime. We find that the inner horizon has a tendency to evaporate outward much more quickly than the outer one evapora…
The predictions of the semiclassical description of particle creation based on QFT in classical backgrounds may be significantly modified when the source of the classical background is also quantized and backreaction is taken into account. In the cases of a stable charged particle, expanding empty (Milne) universe, and de Sitter universe with a true cosmological constant, the semiclassical particle creation is completely blocked up.
In the context of the vacuum polarization effect, we consider the backreaction of the energy-momentum tensor of a charged scalar field on the background metric of a cosmic string carrying a magnetic flux $Φ$. Working within the semiclassical approach to the Einstein eqs. we find the first-order (in $\hbar$) metric associated to the magnetic flux cosmic string. We show that the contribution to the vacuum polarization effect coming from the Aharonov-Bohm interaction is larger than the one coming from the non-trivial gravitational interaction.
We compute the Renormalized Stress-Energy Tensor (RSET) of a massless minimally coupled scalar field in the Regularized Polyakov approximation, as well as its backreaction, on the classical Reissner-Nordström spacetime. The complete set of solutions of the semiclassical self-consistent equations is obtained and compared with the classical counterparts. The semiclassical Reissner-Nordström family involves three kinds of geometries that depend on the charge-to-mass ratio of the spacetime. In the under-charged regime, the geometry has its external horizon replaced by a wormhole neck that leads to…
We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole ($a=0.99$) and the dominant $m=1$ azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-energy tensor and, hence, spacetime. We find that in excess of $9\%$ of the black hole's mass can be transferred into the field. In all cases studied, …
Zero temperature black hole solutions to the semiclassical backreaction equations are investigated. Evidence is provided that certain components of the stress-energy tensors for free quantum fields at the horizon only depend on the local geometry near the horizon. This allows the semiclassical backreaction equations to be solved near the horizon. It is found that macroscopic uncharged zero temperature black hole solutions to the equations may exist if the coefficient of one of the higher derivative terms in the gravitational Lagrangian is large enough and of the right sign for Starobinsky infl…
We continue our earlier investigation of the backreaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional (IF) method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the backreaction problem, such as particle creation, decoherence and dissipation. We show how noise and fluctuation arise naturally from the CTP fo…
Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space
Stellenbosch University（斯泰伦博斯大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）；Ramakrishna Mission Vivekananda Educational and Research Institute（罗摩克里希纳传教士维韦卡南达教育与研究机构）
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…
Hybrid quantum-classical simulations of semiclassical gravity
Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学-西班牙国家研究委员会理论物理研究所）；Departamento de Física Fundamental, Universidad de Salamanca（萨拉曼卡大学基础物理系）；Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca（萨拉曼卡大学基础物理与数学大学研究所）
We consider the backreaction of the vacuum polarization effect for a massive charged scalar field in the presence of a singular magnetic massless string on the background metric. Using semiclassical approach, we find the first-order (in $\hbar$ units) metric modifications and the corresponding gravitational potential and deficit angle. It is shown that, in certain region of values of coupling constant and magnetic flux, the gravitational potential and deficit angle can be positive as well as negative over all distances from the string and can even change its sign. Unlike the case of massless s…
We investigate the scattering of a spinning test particle by a Kerr black hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The particle's spin and orbital angular momentum are taken to be aligned with the black hole's spin. Both the particle's mass and spin length are assumed to be small in comparison with the characteristic length scale of the background curvature, in order to avoid backreaction effects. We analytically compute the modifications due to the particle's spin to the scattering angle, the periastron shift, and the condition for capture by the black hole, e…
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background…
We describe the procedure for obtaining Hamiltonian equations on a manifold with $so(k, m)$ Lie-Poisson bracket from a variational problem. This implies identification of the manifold with base of a properly constructed fiber bundle embedded as a surface into the phase space with canonical Poisson bracket. Our geometric construction underlies the formalism used for construction of spinning particles in [24-27], and gives precise mathematical formulation of the oldest idea about spin as the "inner angular momentum".
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat bot…
We study the quantum backreaction from inflationary fluctuations of a very light, non-minimally coupled spectator scalar and show that it is a viable candiate for dark energy. The problem is solved by suitably adapting the formalism of stochastic inflation. This allows us to self-consistently account for the backreaction on the background expansion rate of the Universe where its effects are large. This framework is equivalent to that of semiclassical gravity in which matter vacuum fluctuations are included at the one loop level, but purely quantum gravitational fluctuations are neglected. Our …
It is well-known that some physical effects may arise in the spacetime of a straigth cosmic string due to its global conic properties. Among these effects, the vacuum polarization effect has been extensively studied in the litterature. In papers of reference [4] a more general situation has been considered in which the cosmic string carries a magnetic flux $Φ$ and interacts with a charged scalar field. In this case, the vacuum polarization arises both via non-trivial gravitational interaction (i.e, the conical structure) and via Aharonov-Bohm interaction. In papers [4] the non vanishing VEV of…
Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Post-geodesic effects include the gravitational self force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for …
