We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we study the behavior of these different complementary properties of massive spin-$1/2$ particles in the Schwarzschild spacetime. For geodetic circular orbits, we find that the spin state of one particle oscillates between a separable and an entangled state. For non-geodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit gets nearer to the Schwarzschild radius $r_s$.
We prove that conformal curved spacetime can be encoded into the initial wave function and that curved propagation can be simulated on a two-dimensional regular lattice with a finite set of homogeneous unitary operators. We generalize recent results shown in [1], where the author transforms flat-spacetime in curved static spacetime via non-unitary rotations. In particular, encoding the metric in the initial quantum state via unitary local rotations, can naturally be useful for quantum simulators due to the efficiency and simplicity of the implementation scheme. We validate our model proving th…
We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a par…
Generalizing to relativistic exponential scaling and using the theory of noise from quantum fluctuations, it has been shown that one vacuum (Rindler, Hartle-Hawking, or Gibbons-Hawking for the cases of the uniformly accelerated detector, black hole, and de-Sitter universe, respectively) can be understood as resulting from the scaling of quantum noise in another vacuum. We explore this idea more generally to establish a flat spacetime and curved spacetime analogy. For this purpose, we start by examining noise kernels for free fields in some well-known curved spacetimes, e.g., the spacetime of a…
A boundary undergoing relativistic motion can create particles from quantum vacuum fluctuations in a phenomenon known as the dynamical Casimir effect. We examine the creation of particles, and more generally the transformation of quantum field states, due to boundary motion in curved spacetime. We provide a novel method enabling the calculation of the effect for a wide range of trajectories and spacetimes. We apply this to the experimental scenario used to detect the dynamical Casimir effect, now adopting the Schwarzschild metric, and find novel resonances in particle creation as a result of t…
We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.
We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.
It is pointed out that in curved spacetime, one cannot define the sum of energy-momemtum 4-vector over a space-like hypersurface. The difficulty in finding satisfactory gravitational energy-momentum complex stems from misunderstanding of this question. The law of conservation of energy-momentum holds valid only approximately when spacetime is not seriously curved.
Quasi-classical picture of motion of spin 1/2 massive particle in a curved spacetime is built on base of simple Lagrangian model. The one is constructed due to analogy with Lagrangian of massive vector particle. Equations of motion and spin propagation coincide with Papapetrou equations describing dynamic of classical spinning particle in a curved spacetime.
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
Quasi-classical picture of motion of spin 1/2 massless particle in a curved spacetime is built on base of simple Lagrangian model. The one is constructed due to analogy with Lagrangian of massive spin 1/2 particle. Equations of motion and spin propagation coincide with Papapetrou equations describing dynamic of photon in a curved spacetime.
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple manipulations of the optical setup. Examples presented here contain two-dimensional spaces of positive and negative curvature as well as homogeneous cosmological models and metric waves. Most of them are extendable to three spatial dimensions. We mention some interesting phenomena of quantum field theory in curved spacetimes which might be simulated in such opt…
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of Poincare symmetry, positivity of total energy, and the existence of a unique, Poincare invariant vacuum state. These and other key features of quantum field theory do not generalize straightforwardly to curved spacetime. We discuss the conceptual obstacles to formulating quantum field theory in curved spacetime and how they can be overcome
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the stability of relativistic bubbles in curved spacetimes.
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
Bargmann-Wigner equations and their solutions are studied in (3+1)-dimensional curved spacetime. Fermion-Boson correspondence for bi-spinor case is studied through the Bargmann-Wigner equations and solutions over curved spacetime. As an application to scattering phenomena of massive Fermions and Bosons on the rotating black holes, the superradiance with negative energy $(ω<0)$ and positive effective energy in co-rotating coordinate system near horizon $(ω-mΩ_{H}>0)$ is possible to occur as stable physical states in Kerr spacetime.
Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts can be trivially extended to field theories in curved spacetime if all the representations of canonical commutation or anticommutation relations are unitarily equivalent. We show that both concepts can be applied even when there is no such unitary equivalence.
Localising the galileon symmetry along with Poincare symmetry we have found a version of galileon model coupled with curved spacetime which retains the internal galileon symmetry in covariant form. Also, the model has second order equations of motion.
Some recent (1997-1998) theoretical results concerning the $ζ$-function regularization procedure used to renormalize, at one-loop, the effective Lagrangian, the field fluctuations and the stress-tensor in curved spacetime are reviewed.
The late time behavior of waves propagating on a general curved spacetime is studied. The late time tail is not necessarily an inverse power of time. Our work extends, places in context, and provides understanding for the known results for the Schwarzschild spacetime. Analytic and numerical results are in excellent agreement.
A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.
We use the brick wall model to calculate the free energy of quantum scalar field in a curved spacetime (D +1) dimensions. We find the thermodynamics properties of quantum scalar field in several scenaries: Minkowski spacetime, Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the thermodynamical properties of quantum scalar field is exactly with the reported. It was found that the entropy of the gas is proportional to the horizon area in a gravity field strong, which is consistent with the holographic principle.
The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the pro…
We propose a fully covariant model for smeared particle detectors in quantum field theory in curved spacetimes. We show how effects related to accelerated motion of the detector and the curvature of spacetime influence the way different observers assign an interaction Hamiltonian between the detector and the field. The fully covariant formulation explicitly leaves the physical predictions of the theory invariant under general coordinate transformations, hence providing a description of particle detector models (e.g., Unruh-DeWitt detectors, models for the light-matter interaction, etc) that is…
This is a status report about the ongoing work on the realization of quantum field theory on curved graphene spacetimes that uses Weyl symmetry. The programme is actively pursued from many different perspectives. Here we point to what has been done, and to what needs to be done.
The success of the S-matrix in quantum field theory in Minkowski spacetime naturally demands the extension of the construction of the S-matrix in a general curved spacetime in a covariant manner. However, it is well-known that a global description of the S-matrix may not exist in an arbitrary curved spacetime. Here, we give a local construction of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinates which mimics the methods, generally used in Minkowski spacetime. Using this construction, the scattering amplitudes and cross-sections of some scattering processes …
We generalize our previous thick shell formalism to incorporate any codimension-1 thick wall with a peculiar velocity and proper thickness bounded by arbitrary spacetimes. Within this new formulation we obtain the equation of motion of a spherically symmetric dust thick shell immersed in vacuum as well as in Friedmann-Robertson-Walker spacetimes.
We propose to develop the Kalb-Ramond theory in four-dimensional spacetime at the level of a classical field theory by following the same formal development steps as in Maxwell theory of standard electrodynamics. Solutions of Kalb-Ramond theory in the presence of static sources in various curved spacetimes are then analyzed. A question that we address here is that of a possible Kalb-Ramond polarization in curved spacetimes, like one can encounter a dielectric polarization in ordinary Maxwell electrodynamics in certain types of spacetimes.
In this article we investigated the influence of the gravity induced higher dimensional operators on the issue of vacuum stability in a model containing two interacting scalar fields. As a framework we used the curved spacetime Effective Field Theory (cEFT) applied to the aforementioned system in which one of the scalars is heavy. After integrating out the heavy scalar we used the standard Euclidean approach to the obtained cEFT. Apart from analyzing the influence of standard operators like the non-minimal coupling to gravity and the dimension six contribution to the scalar field potential, we…
Stereoscopic visualization adds an additional dimension to the viewer's experience, giving them a sense of distance. In a general relativistic visualization, distance can be measured in a variety of ways. We argue that the affine distance, which matches the usual notion of distance in flat spacetime, is a natural distance to use in curved spacetime. As an example, we apply affine distance to the visualization of the interior of a black hole. Affine distance is not the distance perceived with normal binocular vision in curved spacetime. However, the failure of binocular vision is simply a limit…
We adopt the Dirac-Detweiler-Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric dependent term.
We present a new formulation to deal with the consistency problem of a massive spin-2 field in a curved spacetime. Using Fierz variables to represent the spin-2 field, we show how to avoid the arbitrariness and inconsistency that exists in the standard formulation of spin-2 field coupled to gravity. The superiority of the Fierz frame appears explicitly in the combined set of equations for spin-2 field and gravity: it preserves the standard Einstein equations of motion.
We revisit the invariance of the curved spacetime Maxwell equations under conformal transformations. Contrary to standard literature, we include the discussion of the four-current, the wave equations for the four-potential and the field, and the behaviour of gauge conditions under the conformal transformation.
A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime and introduces a framework for studing in a precise manner membranes behavior near the black hole horizon and on the other hand, introduces a more general framework for examining the stability of topological defects in curved spacetimes.
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the same generality as in flat spacetime and it holds only if the system satisfies certain constraints. We derive these constraints and the basic equations of duality and discuss the implications in the quantum theory.
We derive a new regularization method for the calculation of the (massless) scalar self force in curved spacetime. In this method, the scalar self force is expressed in terms of the difference between two retarded scalar fields: the massless scalar field, and an auxiliary massive scalar field. This field difference combined with a certain limiting process gives the expression for the scalar self-force. This expression provides a new self force calculation method.
From the curved spacetime Lagrangian the first approximation scalar particle quantum equation was obtained following the canonical formalism. The roots of this equation in Schwarzschild's pseudo flat space were found. As it was shown in a more general curved spacetime it is tedious to find equation's roots. The massless particle limiting case was considered. The Maxwell set of equations generalized to Schwarzschild's space was reproduced.
The ideal MHD theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime. The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime. Nevertheless, it is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a $3+1$ foliation of spacetime.
We analyze the classical approximations made in "The general relativistic effects to the magnetic moment in the Earth's gravity", originally published as "Post-Newtonian effects of Dirac particle in curved spacetime - I : magnetic moment in curved spacetime", and work out precisely where in the argument the mistakes are made. We show explicitly that any difference vanishes when properly distinguishing between coordinate and physical distance. In doing this, we illustrate some of the pitfalls in using GR to make predictions.
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.
In this paper we will investigate how one can create emergent curved spacetimes by locally tuning the coupling constants of condensed matter systems. In the continuum limit we thus obtain continuous effective quantum fields living on curved spacetimes. In particular, using Stingnet condensates we can obtain effective electromagnetism. We will show for example how we obtain quantum electromagnetism (U(1)-Yang-Mills) in a black hole (Schwarzschild) spacetime.
In General Relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving geodesic equations of a general spacetime manifold. Furthermore, knowing all possible conserved quantities of a system tells about the hidden symmetries of that system since, conserved quantities are deeply connected with the symmetries of the system, which are very important in their own right. Conserved quantities are also useful to capture certain features of space…
The discontinuities of electromagnetic test fields generated by general layers of electric and magnetic monopoles and dipoles are investigated in general curved spacetimes. The equivalence of electric currents and magnetic dipoles is discussed. The results are used to describe exact "Schwarzschild disk" solutions endowed with such sources. The resulting distributions of charge and dipole densities on the disks are corroborated using the membrane paradigm.
Earlier we obtained quasi-classical equations of motion of spin 1/2 massless particle in a curved spacetime on base of simple Lagrangian model \cite{al2}. Now we suggest an approach to derive the equations in framework of field theory. Noether theorem formulated in terms of Cartan' formalism of orthonormal frames gives equations for current of spin of the field and tensor of stress-energy. It is shown that under eikonal approximation the above mentioned equations can be reduced to equations for worldline of the particle and equation of spin of the particle along the worldline. This way conform…
In this paper we will investigate how one can create emergent curved spacetimes by locally tuning the coupling constants of condensed matter systems. In the continuum limit we thus obtain continuous effective quantum fields living on curved spacetimes. In particular, using Stingnet condensates we can obtain effective electromagnetism. We will show for example how we obtain quantum electrodynamics in a blackhole (Schwarzschild) spacetime.
We offer a novel derivation of the electromagnetic self-force acting on a charged particle moving in an arbitrary curved spacetime. Our derivation is based on a generalization from flat spacetime to curved spacetime of the extended-body approach of Ori and Rosenthal. In this approach the charged particle is first modeled as a body of finite extension s, the net force acting on the extended body is computed, and the limit s -> 0 is taken at the end of the calculation. Concretely our extended body is a dumbbell that consists of two point charges that are maintained at a constant spacelike separa…
In this work, we derive two formulas encoding the polarization direction and luminosity of synchrotron radiations from the moving electrons in curved spacetime under the geometric optics approximation. As an application, we further study the polarized images of synchrotron radiations from electron sources in Schwarzschild black hole spacetime with a vertical and uniform magnetic field. In particular, by focusing on the circular orbits of electrons on the equatorial plane, we show the polarized images of the synchrotron radiations from these orbits for different observational angles and discuss…
The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this (non-perturbative) property of the Schwinger-DeWitt series has a natural and equivalent counterpart in the adiabatic (Parker-Fulling) series expansion of the scalar modes in an homogeneous cosmological spacetime. The equivalence between both R-summed adiabatic expansions can be further extended when a background scalar field is also present.
Moeller's energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a "generalized Schwarzschild" geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.
We establish a global existence theory for the equation governing the evolution of a relativistic membrane in a (possibly curved) Lorentzian manifold, when the spacetime metric is a perturbation of the Minkowski metric. Relying on the Hyperboloidal Foliation Method introduced by LeFloch and Ma in 2014, we revisit a theorem established earlier by Lindblad (who treated membranes in the flat Minkowski spacetime) and we provide a simpler proof of existence, which is also valid in a curved spacetime and, most importantly, leads to the important property that the total energy of the membrane is glob…
The Schrodinger picture description of vacuum states in curved spacetime is further developed. General solutions for the vacuum wave functional are given for both static and dynamic (Bianchi type I) spacetimes and for conformally static spacetimes of Robertson-Walker type. The formalism is illustrated for simple cosmological models with time-dependent metrics and the phenomenon of particle creation is related to a special form of the kernel in the vacuum wave functional.
