Donato Bini, Christian Cherubini, Andrea Geralico, Robert T. Jantzen
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
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We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gra…
We consider the static vacuum C metric that represents the gravitational field of a black hole of mass $m$ undergoing uniform translational acceleration $A$ such that $mA<1/(3\sqrt{3})$. The influence of the inertial acceleration on the exterior perturbations of this background are investigated. In particular, we find no evidence for a direct spin-acceleration coupling.
Optical reference geometry and related concept of inertial forces are investigated in Kerr-de Sitter spacetimes. Properties of the inertial forces are summarized and their typical behaviour is illustrated. The intuitive 'Newtonian' application of the forces in the relativistic dynamics is demonstrated in the case of the test particle circular motion, static equilibrium positions and perfect fluid toroidal configurations. Features of the optical geometry are illustrated by the embedding diagrams of its equatorial plane. The embedding diagrams do not cover whole the stationary regions of the spa…
By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of ma…
A coordinate system is set up for a general accelerating observer and is used to determine the particle content of the Dirac vacuum for that observer. Equations are obtained for the spatial distribution and total number of particles for massless fermions as seen by this observer, generalising previous work.
Quasinormal modes of accelerating spacetime
本文精确计算纯加速时空中无质量扰动的准正则频率，证明其与自旋无关且源于纯加速时空，黑洞会使其频谱形变，并验证了方法的有效性。
We have investigated the motion of timelike particles along geodesic in the background of accelerating and rotating black hole spacetime. We confirmed that the chaos exists in the geodesic motion of the particles by Poincaré sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram. Moreover, we probe the effects of the acceleration and rotation parameters on the chaotic behavior of a timelike geodesic particle in the black hole spacetime. Our results show that the acceleration brings richer physics for the geodesic motion of particles.
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion near the limiting energy density. It is shown that cosmological models are regular not only with respect to the Hubble parameter and the energy density but also with respect to the torsion and curvature tensors.
Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial …
We apply the theory of non-inertial frames in Minkowski space-time, developed in the previous paper, to various relevant physical systems. We give the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics.
The mass contained in an arbitrary spacetime in general relativity is not well defined. However, for asymptotically flat spacetimes various definitions of mass have been proposed. In this paper I consider eight masses and show that some of them correspond to the active gravitational mass while the others correspond to the inertial mass. For example, the ADM mass corresponds to the inertial mass while the M$ø$ller mass corresponds to the active gravitational mass. In general the inertial and active gravitational masses are not equal. If the spacetime is vacuum at large $r$ the Einstein equation…
It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for $ΛCDM$-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for $ΛCDM$-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.
Given, in an arbitrary spacetime, a 2-dimensional timelike submanifold (worldsheet) and an observer field on this worldsheet, we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline in the worldsheet with respect to the observer field. We prove that centrifugal and Coriolis forces vanish, for all particle worldlines with respect to any observer field, if and only if the worldsheet is a photon 2-surface, i.e., generated by two families of lightlike geodesics. We further demonstrate that a photon 2-surface can be characterized in terms of gyroscope transport a…
Homogeneous isotropic cosmological models built in the framework of the Poincaré gauge theory of gravity based on general expression of gravitational Lagrangian with indefinite parameters are analyzed. Special points of cosmological solutions for flat cosmological models at asymptotics and conditions of their stability in dependence of indefinite parameters are found. Procedure of numerical integration of the system of gravitational equations at asymptotics is considered. Numerical solution for accelerating Universe without dark energy is obtained.
Talk at the 25th Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey", Firenze September 2001.
We consider an explicit example of a process, where the entropy carried by radiation through an accelerating two-plane is proportional to the decrease in the area of that two-plane even when the two-plane is not a part of any horizon of spacetime. Our results seem to support the view that entropy proportional to area is possessed not only by horizons but by all spacelike two-surfaces of spacetime.
The spinning C-metric was discovered by Plebanski and Demianski as a generalization of the standard C-metric which is known to represent uniformly accelerated non-rotating black holes. We first transform the spinning C-metric into Weyl coordinates and analyze some of its properties as Killing vectors and curvature invariants. A transformation is then found which brings the metric into the canonical form of the radiative spacetimes with the boost-rotation symmetry. By analytically continuing the metric across "acceleration horizons", two new regions of the spacetime arise in which both Killing …
Quantum Cosmology in Accelerating Spacetimes
本文研究了加速时空中的量子宇宙学，通过简化引力方程并探讨局部膨胀率可观测量，提出所有阶次重新求和的微扰主导对数项的理论框架。
The response of the Unruh-DeWitt type monopole detectors which were coupled to the quantum field only for a finite proper time interval is studied for inertial and accelerated trajectories, in the Minkowski vacuum in (3+1) dimensions. Such a detector will respond even while on an inertial trajctory due to the transient effects. Further the response will also depend on the manner in which the detector is switched on and off. We consider the response in the case of smooth as well as abrupt switching of the detector. The former case is achieved with the aid of smooth window functions whose width,…
Quasi-local energies for constantly accelerating observers in Bañados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.
We prove that spacetime is locally inertial at points of shock wave collision in General Relativity. The result applies for collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. We give a constructive proof that there exist coordinate transformations which raise the regularity of the gravitational metric tensor from $C^{0,1}$ to $C^{1,1}$ in a neighborhood of such points of shock wave interaction, and a $C^{1,1}$ metric regularity suffices for locally inertial frames to exist. This result corrects an error in our earlier RSPA-publica…
We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr spacetime and the Gödel spacetime, wherein the inertial frame dragging has an important role. As it shows similar behaviour for both co and counter rotating particles, it may indeed be an indication of the influence of the faraway universe on local physics and thus Machian.
An exact solution of $(2+1)$-dimensional Einstein gravity with cosmological constant is studied. The corresponding spacetime is interpreted as an accelerating BTZ spacetime. The proper acceleration, horizon structure, temperature and entropy are presented in detail. The metric being studied is very similar to the one studied by Astorino in arXiv:1101.2616, but the range of parameters is different which results in significant changes in the causal structures.
The C-metric is a solution to Einstein's vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and the resulting lensing features in this metric. We first solve the lightlike geodesic equation using elliptic integrals and Jacobi elliptic functions. Then we fix a static observer in the region of outer communication of the C-metric and introduce an orthonormal tetrad to parameterise the directions of the light rays ending at the position of the observer using latitude-longitude coordinates on the observer's celestial sphere. In th…
The influence functional is derived for a massive scalar field in the ground state, coupled to a uniformly accelerating DeWitt monopole detector in $D+1$ dimensional Minkowski space. This confirms the local nature of the Unruh effect, and provides an exact solution to the problem of the accelerating detector without invoking a non-standard quantization. A directional detector is presented which is efficiently decohered by the scalar field vacuum, and which illustrates an important difference between the quantum mechanics of inertial and non-inertial frames. From the results of these calculatio…
The Berry phase of mixed states, as neutrino oscillations, is calculated in a accelerating and rotating reference frame. It turns out to be depending on the vacuum mixing angle, the mass--squared difference and on the coupling between the momentum of the neutrino and the spinorial connection. Berry's phase for solar neutrinos and its geometrical aspects are also discussed.
The nature of superluminal photon propagation in the gravitational field describing radiation from a time-dependent, isolated source (the Bondi-Sachs metric) is considered in an effective theory which includes interactions which violate the strong equivalence principle. Such interactions are, for example, generated by vacuum polarisation in conventional QED in curved spacetime. The relation of the resulting light-cone modifications to the Peeling Theorem for the Bondi-Sachs spacetime is explained.
Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the accelerating cosmological expansion and the origin of the torsion of the spacetime. These solutions can be divided into two classes. The solutions in the first class define the critical points of a dynamical system representing an asymptotically stable de Sitter spacetime. The solutions in the second class have exact analytic expressions which have never been found …
We show the index 0 Fredholm property of the spectral family of the azimuthal harmonics of the charged Klein-Gordon operator on general cosmological slowly accelerating and rotating charged black hole type spacetimes, including the De Sitter-Kerr-Newman family, using a parametrix construction for abstract totally characteristic operators. We then present a numerical scheme to compute the meromorphic poles of the inverse of the spectral family and provide an explicit estimate of the numerical error.
We revisit the old question of what distinguishes the formulation of spacetime geometry in terms of a Lorentzian metric physically from more general geometric structures. Our approach to this question is operational and leads us to also revisit the notion of local inertial frames, arising in operational formulations of the equivalence and Mach's principle, both of which can be interpreted in generalized geometries. We extend the notion of inertial laboratory frames by taking serious that all matter inside the lab is fundamentally quantum and considering how it may couple to the quantum gravita…
Conditions for separability in multiqubit systems with an accelerating qubit using a conditional entropy
本文利用Abe-Rajagopal q-条件熵研究含加速量子比特的多量子比特GHZ态和W态的可分性，发现纯态始终不可分，而引入全局噪声的混合态在参数q渐近极限下可获得以加速度、噪声和量子比特数表示的更强可分性必要条件。
We calculate the total energy of an exact spherically symmetric solutions, i.e., Schwarzschild and Reissner Nordstr$\ddot{o}$m, using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical! Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.
In axistationary asymptotically flat spacetimes zero angular momentum observers (ZAMOs) define an absolute standard of non--rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein's equations for an approximate thin shell model where we keep a degree of freedom by relaxing the natural assumption of vanishing rotation at asymptotic infinity at the outset of the analysis. The solution reveals tha…
The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall for gravitation by demanding inextendibility of spacetime beyond the Cauchy horizon. For asymptotically flat spacetimes, the predominance of the blueshift instability and the subsequent formation of a mass-inflation singularity at the Cauchy horizon have, so far, substantiated the conjecture. Accelerating black holes, described by the $C-$metric, are exact sol…
The somewhat fragmented body of current literature analyzing the properties of test particle motion in static and stationary spacetimes and in general spacetimes is pulled together and clarified using the framework of gravitoelectromagnetism.
Quantum Cosmology in Accelerating Spacetimes II
本文进一步分析适用于加速宇宙时空的量子引力方程，研究其对原初张量功率谱和测试源引力的影响。
Using the known result that the nucleation of baby universes in correlated pairs is equivalent to spacetime squeezing, we show in this letter that there exists a T-duality symmetry between two-dimensional warp drives, which are physically expressible as localized de Sitter little universes, and two dimensional Tolman-Hawking and Gidding-Strominger baby universes respectively correlated in pairs, so that the creation of warp drives is also equivalent to spacetime squeezing. Perhaps more importantly, it has been also seen that the nucleation of warp drives entails a violation of the Bell's inequ…
Thermodynamic relation of accelerating black holes in anti-de Sitter spacetime
本文研究四维反德西特时空中的加速黑洞，验证了Goon和Penco普适极端性关系对其成立，并指出需在微扰参数与锥形缺陷/弦张力参数间建立匹配条件，其行为类似弱引力猜想。
In this paper we scrutinize the concept of locally inertial reference frames (LIRF) in Lorentzian and Riemann-Cartan spacetime structures. We present rigorous mathematical definitions for those objects, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally adapted coordinate functions to a given reference frame and which properties may characterize an inertial reference frame (if any) in the Lorentzian and Riemann-Cartan structures. We hope to have clarified some eventual obscure issues associated to the concept of LIRF…
It has been argued that the spacetime of our universe can be accurately described by a perturbed conformal Newtonian metric, and hence even large density inhomogeneities in a dust universe can not change the observables predicted by the homogeneous dust model. In this paper we study a spherically symmetric dust model and illustrate conditions under which large spatial variations in the expansion rate can invalidate the argument.
We analyze the response of a detector with a uniform acceleration $α$ in $κ-$Minkowski spacetime using the first order perturbation theory. The monopole detector is coupled to a massless complex scalar field in such a way that it is sensitive to the Lorentz violation due to the noncommutativity of spacetime present in the $κ-$deformation. The response function deviates from the thermal distribution of Unruh temperature at the order of $1/κ$ and vanishes exponentially as the proper time of the detector exceeds a certain critical time, a logarithmic function of $κ$. This suggests that the Unruh …
Accelerating Kerr solution in SU(1,1)/U(1)-sigma model
在SU(1,1)/U(1)-σ模型中，通过反散射技术构造了加速Kerr解的三种孤子形式，并证明其等价性。
Principle of Equivalence makes effects of classical gravity vanish in local inertial frames. What role does the Principle of Equivalence play as regards quantum gravitational effects in the local inertial frames? I address this question here from a specific perspective. At mesoscopic scales close to, but somewhat larger than, Planck length one could describe quantum spacetime and matter in terms of an effective geometry. The key feature of such an effective quantum geometry is the existence of a zero-point-length. When we proceed from quantum geometry to quantum matter, the zero-point-length w…
Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearin…
We study the interplay of non-locality and Lorentz invariance in a version of deformed or doubly special relativity (DSR) based on kappa-Minkowski spacetime. We find that Einstein's procedure for an inertial observer to assign coordinates to distant events becomes ambiguous for sufficiently distant events. The accuracy to which two clocks can be synchronized turns out to depend on the distance between them. These are consequences of the non-commutativity of space and time coordinates or a dependence of the speed of light on energy in relativistic theories. These ambiguities grow with distance …
Generalized Coulomb-type interaction embedded in a non-inertial cosmic string spacetime in a slow-rotation limit
研究非惯性宇宙弦时空中的广义库仑型相互作用，通过慢旋转极限下的近似精确解探讨标量玻色子行为，恢复普通库仑相互作用的解。
In a flat spacetime with one spatial dimension compactified, inertial reference frames are not all equivalent, but there are the preferred ones. This paper investigates the nonequivalence of inertial frames and also that of uniformly accelerated frames in connection with the response of the Unruh-DeWitt detector coupled to a massless scalar field. The detector's transition rates of both excitation and de-excitation are studied in depth for three different cases: (i) the detector moving at an arbitrary constant velocity, (ii) moving with a constant acceleration in the compact direction, and (ii…
It has been proposed that the scattering of electromagnetic zero-point radiation by accelerating objects results in a reaction force that may account, at least in part, for inertia [1,2,3]. This arises because of asymmetries in the electromagnetic zero-point field (ZPF) or electromagnetic quantum vacuum as perceived from an accelerating reference frame. In such a frame, the Poynting vector and momentum flux of the ZPF become non-zero. If one assumes that scattering of the ZPF radiation takes place at the level of quarks and electrons constituting matter, then it is possible for both Newton's e…
Building on the well-known Unruh-Davies effect, we examine the effects of projective measurements and quantum communications between accelerated and stationary observers. We find that the projective measurement by a uniformly accelerated observer can excite real particles from the vacuum in the inertial frame, even if no additional particles are created by the measurement process in the accelerating frame. Furthermore, we show that the particles created by this accelerating measurement can be highly entangled in the inertial frame, and it is also possible to use this process to generate even m…
Making two particle detectors in flat spacetime communicate quantumly
本文提出一种在(3+1)维平坦时空中利用粒子探测器进行量子通信的协议，发现探测器间的相对加速度能产生非零量子容量，从而在匀加速发送者和惯性接收者间实现可靠的量子通信。
The spacetimes for Vaidya's radiating stellar exterior and Kinnersley's photon rocket in a cosmological background are obtained by performing the same conformal transformation as is used to obtain the Robertson-Walker metric from Minkowski spacetime. In the case of the cosmological radiating stellar exterior, a two-fluid solution is found that obeys all of the energy conditions and consists of a null fluid and a perfect fluid that asymptotically falls off to the standard cosmological values for pressure and density at infinite radius. For the cosmological photon rocket, the massless case is fi…
To investigate the origin and nature of inertia, we introduce a new concept of hypothetical 2D, so-called, "master-space" (MS), subject to certain rules. The MS, embedded in the background 4D-spacetime, is an indispensable individual companion to the particle of interest, without relation to every other particle. We argue that a deformation/(distortion of local internal properties) of MS is the origin of inertia. With this perspective in sight, we construct the alternative relativistic theory of inertia (RTI), which allows to compute the relativistic inertial force acting on an arbitrary point…
Overcharging an accelerating Reissner-Nordström-Anti-de Sitter black hole with test field and particle
本文通过带电场散射和带电粒子吸收，研究加速RN-AdS黑洞的弱宇宙监督猜想，发现极端黑洞不可过度充电，近极端黑洞在特定条件下可被过度充电，并指出需考虑二阶效应。
Asymptotic behaviour of gravitational and electromagnetic fields of exact type D solutions from the large Plebanski-Demianski family of black hole spacetimes is analyzed. The amplitude and directional structure of radiation is evaluated in cases when the cosmological constant is non-vanishing, so that the conformal infinities have either de Sitter-like or anti-de Sitter-like character. In particular, explicit relations between the parameters that characterize the sources (that is their mass, electric and magnetic charges, NUT parameter, rotational parameter, and acceleration) and properties of…
Lecture at BOSS2011 on relativistic metrology, on clock synchronization, relativistic dynamics and non-inertial frames in Minkowski spacetime, on relativistic atomic physics, on ADM canonical tetrad gravity in asymptotically Minkowskian spacetimes, on the York canonical basis identifying the inertial (gauge) and tidal degrees of freedom of the gravitational field, on the Post-Minkowskian linearization in 3-orthogonal gauges, on the Post-Newtonian limit of matter Hamilton equations, on the possibility to interpret dark matter as a relativistic inertial effect connected with relativistic metrolo…
In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the un…
We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\to\infty$) observers, around $x\to\infty$ and $x\to-\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null in…
We consider an Unruh-DeWitt detector in inertial and circular motion in Minkowski spacetime of arbitrary dimension, coupled to a quantised scalar field with the Lorentz-violating dispersion relation $ω= |{\bf k}|\, f (|{\bf k}|/M_{\star})$, where $M_{\star}$ is the Lorentz-breaking scale. Assuming that $f$ dips below unity somewhere, we show that an inertial detector experiences large low energy Lorentz violations in all spacetime dimensions greater than two, generalising previous results in four dimensions. For a detector in circular motion, we show that a similar low energy Lorentz violation…
Some aspects of QFT in non-inertial frames
本文研究闵可夫斯基时空非惯性系中的量子场论，确认视界与正能量解修改并非普遍现象，表明非惯性系与弯曲时空在定义粒子方面相似。
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one and vice versa, but its acceleration $g$ undergoes the transformation $g \rightarrow 1/b^{2}g$, where $b$ is a constant. A nongeodesic congruence of a static observer has a scalar expansion which grows linearly with time but the acceleration is proportional to $r$, as for the classical rotation.
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