The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves solutions of the Maxwell equation which are eigenfunctions of the energy operator. Such particular solutions complete the theory in which only the solutions of given momentum were considered so far. The energy eigenfunctions can be obtained thanks to our new time-evolution picture proposed previously for the scalar and Dirac fields. Considering both these types of modes, it is shown that the second quantization of the free electromagnetic potential in the Coulomb gauge can be done in a canonical manner as in special relativity. The principal conserved one-particle operators associated to Killing vectors are derived, concentrating on the energy, momentum and total angular momentum operators.
In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de Sitter invariant two-points function which is very simple. Our method relies on the one hand on a geometrical point of view which uses the realization of Minkowski, de Sitter and anti-de Sitter spaces as intersections of the null cone in $\setR^6$ and a moving plane, and on the other hand on a canonical quantization scheme of the Gupta-Bleuler type.
Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499]. Here we discuss the time dilation (of the twin paradox) and the Lorentz contraction on the de Sitter expanding portions, pointing out the dependence of these effects on the position and moment in which the time and lengths are measured.
The propagators of the Dirac fermions are studied in the configuration representation on the expanding portion of the $(1+3)$-dimensional de Sitter spacetime considering a fixed vacuum of Bunch-Davies type. In this representation the method of Koksma and Prokopec [J. F. Koksma and T. Prokopec, Class. Quant. Grav. {\bf 26}, 125003 (2009)] is applied recovering thus the form of the propagators in the massive case but obtaining a new result for the left-handed massless fermions (neutrinos).
A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorenzian isometries of our new de Sitter relativity [I. I. Cot\u aescu, {Eur. Phys. J. C} {\bf 77} (2017) 485]. This formula combines in a non-trivial manner the well-known cosmological contribution given by Lama\' itre's law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagati…
We study the theory of interaction between charged scalar field and Maxwell field in de Sitter background. Solving the equation of interacting fields we define the in-out fields as asymptotic free fields and construct the reduction formalism for scalar field. Then we derive the perturbation expansion of the scattering operator. The first order transition amplitudes corresponding to particle production from de Sitter vacuum and pair production in an external field are analysed. We show that all these effects are important only in strong gravitational fields and vanish in the flat limit.
A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step functions of the Feynman propagators making possible for the first time the calculation of Feynman diagrams involving scalar particles on this background. In order to convince that, a simple example is given outlining the amplitudes in the second order of perturbations of the Compton effect in the de Sitter scalar quantum electrodynamics.
The propagators of the Dirac fermions on the expanding portion of the (1+3)-dimensional de Sitter spacetime are considered as mode sums in momentum representation with a fixed vacuum of Bunch-Davies type. The principal result reported here is a new integral representation of the Feynman propagators of the massive and left-handed massless Dirac fields which can be used for deriving the Feynman rules of the de Sitter QED in Coulomb gauge or of an extended QFT.
The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying a special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expectation values of the energies of the emitted and detected photons comply with the Lema\^ itre rule of Hubble's law. Moreover, the quantum corrections to the dispersions of the principal observables and new uncertainty relations are derived.
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat FLRW charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.
A new method is applied for deriving the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a co-moving remote observer. This method is manly algebraic focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole proper co-moving frame to observer's one. Hereby one extracts the general expressions of the redshifts and shadows of the black holes having peculiar velocities but their expressions are too extended to be written down here. Therefore, only some particular cases and intui…
We consider first order transition amplitudes in external fields in QED in the expanding de Sitter space and point out that they are gauge dependent quantities. We examine the gauge variations of the amplitudes assuming a decoupling of the interaction at large times, which allows to conclude that the source of the problem lies in the fact that the frequencies of the modes in the infinite future become independent of the comoving momenta. We show that a possibility to assure the gauge invariance of the external field amplitudes is to restrict to potentials which vanish sufficiently fast at infi…
We study the nonlinear evolution of the spherical symmetric black holes under a small neutral scalar field perturbation in Einstein-Maxwell-dilaton theory with coupling function $f(ϕ)=e^{-bϕ}$ in asymptotic anti-de Sitter spacetime. The non-minimal coupling between scalar and Maxwell fields allows the transmission of the energy from the Maxwell field to the scalar field, but also behaves as a repulsive force for the scalar. The scalar field oscillates with damping amplitude and converges to a final value by a power law. The irreducible mass of the black hole increases abruptly at initial times…
New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well-known from long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the background. One component of the vector field is expressed, in its radial part, through the solution of a fourth-order ordinary differential equation obeying given initial conditions. The other components of the vector field are then found by acting with lower-order differential operators on the solution of the fourth-order equation (while the transverse part is decou…
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart of conformal time. It is shown that the canonical quantization leads to new vector propagators which satisfy similar equations as the propagators derived by Tsamis and Woodard [{\em J.Math.Phys.} {\bf 48} (2007) 052306] but having a different structure. The one-particle operators are also written down pointing out that their properties are similar with those …
The phenomenon of spontaneous scalarization of charged black holes has attracted a lot of attention. In this work, we study the dynamical process of the spontaneous scalarization of charged black hole in asymptotically anti-de Sitter spacetimes in Einstein-Maxwell-scalar models. Including various non-minimal couplings between the scalar field and Maxwell field, we observe that an initial scalar-free configuration suffers tachyonic instability and both the scalar field and the black hole irreducible mass grow exponentially at early times and saturate exponentially at late times. For fractional …
It is shown that on the de Sitter space-time the global behavior of the free Dirac spinors in momentum representation is determined by several phases factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator whic…
We prove that there exists a phase space of canonical variables for the initial value problem for axially symmetric Maxwell fields propagating in Kerr-de Sitter black hole spacetimes such that their motion is restricted to the level sets of a positive-definite Hamiltonian, despite the ergo-region.
We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic field in the de Sitter space from given currents and initial data. It only uses the Green's function of the massless Minkowskian scalar field. This leads to drastic simplifications in practical calculations. We apply this formula to the classical problem of the two charges of opposite signs at rest at the North and South Poles of the de Sitter space.
It has been shown that the Christodoulou version of the Strong Cosmic Censorship (SCC) conjecture can be violated for a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the effects of higher derivative corrections to the Einstein-Hilbert action on the validity of SCC, by considering a neutral massless scalar perturbation in 5- and 6-dimensional Einstein-Maxwell-Gauss-Bonnet-de Sitter black holes. Our numerical results exhibit that the higher derivative term plays a different role in the d = 5 case than it does in the d = 6 case. For d = 5, …
We study the Maxwell quasinormal spectrum on asymptotically anti-de Sitter black holes with a set of two Robin type boundary conditions, by requiring the energy flux to vanish at asymptotic infinity. Focusing, for illustrative purposes, on Schwarzschild-anti-de Sitter black holes both without and with a global monopole, we unveil that, on the one hand, the Maxwell quasinormal spectrum bifurcates as the black hole radius increases for both boundary conditions, which is termed the mode split effect; while on the other hand, with an appropriate fixed black hole radius but increasing the monopole …
The $(1+3)$-dimensional Dirac equation of the fermions moving in ideal Aharonov-Bohm rings in the de Sitter expanding universe is used for deriving the exact expressions of the general relativistic partial currents and corresponding energies. In the de Sitter geometry, these quantities depend on time but these are related each other just as in the non-relativistic case or in special relativity. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. The total relativistic persistent current at $T=0$ takes over this property even t…
In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle-West like model action for five-dimensional space-time in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein's field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell-Mansouri like action that contains the Einstein…
We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existe…
In a recent study [NVdB2017] of algebraically special Einstein-Maxwell fields it was shown that, for non-zero cosmological constant, non-aligned solutions cannot have a geodesic and shearfree multiple Debever-Penrose vector k. When $Λ=0$ such solutions do exist and can be classified, after fixing the null-tetrad such that $Ψ_0 = Ψ_1 = Φ_1 = 0$ and $Φ_0 = 1$, according to whether the Newman-Penrose coefficient $π$ is 0 or not. The family $π= 0$ contains the Griffiths solutions (Griffiths 1986), with as sub-families the Cahen-Spelkens, Cahen-Leroy and Szekeres metrics. It was claimed in [Griffit…
We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a 1+1-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.
We discuss electrostatics in Anti-de-Sitter ($AdS$) spacetime, in global coordinates. We observe that the multipolar expansion has two crucial differences to that in Minkowski spacetime. First, there are everywhere regular solutions, with finite energy, for every multipole moment except for the monopole. Second, all multipole moments decay with the same inverse power of the areal radius, $1/r$, as spatial infinity is approached. The first observation suggests there may be regular, self-gravitating, Einstein-Maxwell solitons in $AdS$ spacetime. The second observation, renders a Lichnerowicz-typ…
The discrete symmetries of the Dirac field on the de Sitter manifold are studied taking into account that this has two portions that can play the role of physical space-times, namely the expanding and a collapsing universes. The proper discrete isometries which preserve the portion have a physical meaning in contrast to the improper ones which change the portion remaining thus of a mere mathematical interest. The discrete symmetries generated by the proper isometries and charge conjugation are studied in physical frames on the expanding portion shoving that all the discrete transformations rev…
We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner-Nordstrøm-de Sitter black bole spacetime. This is done using uniform energy decay results that we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.
The exact charged rotating solution of 2+1 Einstein-Maxwell equations with $Λ$ term is obtained and its properties outlined. It generalizes the Cataldo-Cruz-del Campo-Garc{\'ı}a relativistic charged massive black hole on the 2+1 anti-de Sitter cosmological background. We show that rotating solutions correspond to inhomogeneous field equations, thus presence of sources in 2+1 Maxwell's equations cannot be identified with existence of a charge distribution. Instead, these sources are related to the 2+1 Machian 2-form field, and the overall Lagrangian structure of the rotating system is reconstru…
The Maxwell field with a general gauge fixing (GF) term is nontrivial, not only the longitudinal and temporal modes are mixed up in the field equations, but also unwanted consequences might arise from the GF term. We derive the complete set of solutions in de Sitter space, and implement the covariant canonical quantization which restricts the residual gauge transformation down to a quantum residual gauge transformation. Then, in the Gupta-Bleuler (GB) physical state, we calculate the stress tensor which is amazingly independent of the gauge fixing constant and is also invariant under the quant…
We investigate the thermodynamics of the Einstein-non linear-Maxwell-Yukawa black hole solution in de-Sitter spacetime. After presenting the black hole solution and its horizons, we use different thermodynamics points of view to probe the phase structure of such a black hole, ranging from local, global thermodynamics to the effective thermodynamics formalism with two horizons. Our analysis shows that the black hole can undergo a thermal phase transition between an unstable phase and stable phase. These results are consolidated by our proposal of generalizing effective thermodynamics to three h…
We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.
In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in the Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner-Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a …
We study the black-box parameter estimation of expanding parameters and the dynamics of Gaussian interferometric power for the de Sitter space. We find that the state between separated open charts can be employed as probe state for the black-box quantum metrology. This is nontrivial because the open charts are causally disconnected and classical information can not be exchanged between them according to the general relativity. It is shown that the mass of the scalar field remarkably affects the accuracy of the black-box parameter estimation in the de Sitter space, which is quite different from…
In this work, we consider solutions of the Maxwell equations on the Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the static region bounded by black hole and cosmological horizons, solutions of the Maxwell equations decay to stationary Coulomb solutions at a super-polynomial rate, with decay measured according to ingoing and outgoing null coordinates. Our method employs a differential transformation of Maxwell tensor components to obtain higher-order quantities satisfying a Fackerell-Ipser equation, in the style of Chandrasekhar and the more recent work of Pasqualo…
Electrostatics on global Anti-de-Sitter (AdS) spacetime is sharply different from that on global Minkowski spacetime. It admits a multipolar expansion with everywhere regular, finite energy solutions, for every multipole moment except the monopole (arXiv:1507.04370). A similar statement holds for global AdS magnetostatics. We show that everywhere regular, finite energy, electric plus magnetic fields exist on AdS in three distinct classes: $(I)$ with non-vanishing total angular momentum $J$; $(II)$ with vanishing $J$ but non-zero angular momentum density, $T^t_φ$; $(III)$ with vanishing $J$ and…
Exact black hole solutions in the Einstein-Maxwell-scalar theory are constructed. They are the extensions of dilaton black holes in de Sitter or anti de Sitter universe. As a result, except for a scalar potential, a coupling function between the scalar field and the Maxwell invariant is present. Then the corresponding Smarr formula and the first law of thermodynamics are investigated.
Hawking evaporation of photons in a Vaidya-de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time. It is shown that Hawking radiation of photons exists only for the complex Maxwell scalar $ϕ_0$ in the advanced Eddington-Finkelstein coordinate system. This asymmetry of Hawking radiation for different components of Maxwell fields probably arises from the asymmetry of spacetime in the advanced Eddington-Finkelstein coordinate system. It is shown that the black body ra…
Circular massless cosmic strings which move with the speed of light in the de Sitter universe are described. Construction of the background geometry is based on parabolic isometries of the de Sitter spacetime. Microscopic circular cosmic strings may appear at the Planck epoch and then grow up to the Hubble size. We analyze: images of the strings, influence of strings on trajectories of matter, formation of overdensities, and shifts of energies of photons. These effects allow one to discriminate massless strings from their massive cousins. The present work extends our results on straight massle…
Since the Randall-Sundrum 1999 papers, braneworlds have been a favourite playground to test string inspired cosmological models. The subject has developped into two main directions : elaborating more complex models in order to strenghten the connection with string theories, and trying to confront them with observations, in particular the Cosmic Microwave Background anisotropies. We review here the latter and see that, even in the simple, "paradigmatic", case of a single expanding brane in a 5D anti-de Sitter bulk, there is still a missing link between the "view from the brane" and the "view fr…
We present arguments for the existence of charged, rotating black holes in $d=2N+1$ dimensions, with $d\geq 5$ with a positive cosmological constant. These solutions posses both, a regular horizon and a cosmological horizon of spherical topology and have $N$ equal-magnitude angular momenta. They approach asymptotically the de Sitter spacetime background. The counterpart equations for $d=2N+2$ are investigated, by assuming that the fields are independant of the extra dimension $y$, leading to black strings solutions. These solutions are regular at the event horizon. The asymptotic form of the m…
A class of exact solutions of the Einstein-Maxwell equations is presented which describes an accelerating and rotating charged black hole in an asymptotically de Sitter or anti-de Sitter universe. The metric is presented in a new and convenient form in which the meaning of the parameters is clearly identified, and from which the physical properties of the solution can readily be interpreted.
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1 dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the e…
In this paper we use Morawetz estimates with geometric energy estimates -the so-called vector field method- to prove decay results for the Maxwell field in the static exterior region of the Reissner-Nordstrøm-de Sitter black hole. We prove two types of decay: The first is a uniform decay of the energy of the Maxwell field on achronal hypersurfaces as the hypersurfaces approach timelike infinities. The second decay result is a pointwise decay in time with a rate of $t^{-1}$ which follows from local energy decay by Sobolev estimates. Both results are consequences of bounds on the conformal energ…
We study conformally-coupled massive scalar field theory with the mass term treated as a perturbation in the expanding half of de Sitter spacetime as a toy model for comparing various perturbative formalisms. We point out that the in-out perturbation theory breaks down due to infrared divergences coming from the infinite future. We then clarify the relation between the free-theory vacuum and the true vacuum using the Bogolubov transformation and show that the discrepancy between the free-theory out-vacuum and the true vacuum causes apparent pair creation of free-theory particles and makes the …
Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation appl…
