arXiv subjects

M. Nouri-Zonoz

Publications and source records attributed to M. Nouri-Zonoz.

At least 19 recordsLinked to original sources

arXiv2026

Conductors and superconductors in stationary spacetimes: generalized Schiff-Barnhill and Meissner effects

Previous studies on conductors and superconductors in curved spacetimes, and the gravitationally-induced electric and magnetic fields in them, are mostly restricted to the limit of weak fields and low velocities. Also the observer-dependence of these phenomena are not discussed in the literature. In this article, following London's phenomenological approach to superconductivity, we consider the electrodynamics of superconductors in stationary spacetimes without employing any weak field or low velocity limit. To this end, first we define the 3-force acting on charged particles in gravitational and electromagnetic fields, and derive its explicit form in a general spacetime decomposition formalism. Then, to highlight the role of observers, we apply the force equation to the free charges in superconductors in stationary spacetimes in the two well known threading and slicing decomposition formalisms. Applying the stationary condition in the superconducting state, we arrive at the generalized Schiff-Barnhill and Meissner effects, which compared to the low velocity and weak field limit include extra terms originating from the recently introduced gravitationally-induced constitutive equations. To show the consistency of our approach, we also derive the generalized Meissner effect from the second London equation in stationary spacetimes.

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arXiv2025

Electrodynamics in curved spacetime: Gravitationally-induced constitutive equations and the spacetime index of refraction

Previous studies on spacetime index of refraction are mostly restricted to the static spacetimes. In this study we fill this gap by introducing the refractive index for full stationary spacetimes, employing three different approaches. These include applying Fermat's principle, employing the classical definition of refractive index, and using gravitationally-induced constitutive equations. These calculations are carried out in both threading and slicing spacetime decomposition formalisms, and their equivalence is stablished. We discuss possible applications of the spacetime index of refraction, specially in the study of light trajectories and their characteristics in stationary spacetimes. More specifically we show that there is a gravitational analog of a toroidal moment, and discuss possible gravitational analog of nonreciprocal refraction in materials with a toroidal domain wall.

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arXiv2025

Photon rings in the metamaterial analog of a gravitomagnetic monopole

After studying null geodesics in the equatorial plane in NUT spacetime, we show that there are unstable photon rings in this plane. Next we transform the metric of this plane to the isotropic coordinates and introduce its equivalent two-parameter index of refraction. Utilizing the analog gravity concepts, we assign this index of refraction to a metamaterial analog of this plane, and by ray-tracing simulation find its photon rings. Furthermore, we extend our analysis to the charged NUT spacetime and employ wave optics to numerically solve Maxwell's equations for electromagnetic waves within an inhomogeneous medium assigned with this spacetime's three-parameter index of refraction. We investigate the optical properties of such metamaterial analogs for designing enhanced and fine-tuned optical devices.

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arXiv2024

Embedding diagrams in stationary spacetimes

We find the spatial and dynamic embedding diagrams in some stationary spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared by calculating their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes.

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arXiv2022

Metamaterial analog of a black hole shadow: An exact ray-tracing simulation based on the spacetime index of refraction

In this letter first we show that the equation of null geodesics in spherically symmetric spacetimes in isotropic coordinates is identical to the equation of light ray trajectories in isotropic media in flat spacetime. Based on this analogy we introduce an exact simulation of the light ray trajectories both in these spacetimes and in their metamaterial analogs in terms of the spacetime index of refraction. As unstable light trajectories, the photon spheres form in these metamaterial analogs at {\it exactly} the same radial distances as expected from the corresponding black hole geometries. Using the same ray-tracing simulation we find the analog of a simple black hole shadow formed by the metamaterial analog of a Schwarzschild black hole, eclipsing a line of light sources near its analog horizon.

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arXiv2021

Static and stationary dark fluid universes: A gravitoelectromagnetic perspective

We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields. The absence or presence of either or both of these fields could restrict the equations of state of the underlying perfect fluid sources. As the representative of each family of solutions, we consider those spaces that include the cosmological term as a dark fluid source with the equation of state $p=-ρ= constant$.

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arXiv2020

Stationary analogs of de Sitter and anti-de Sitter spacetimes: Evidence in favor of $Λ$ as a dark fluid

We introduce novel Einstein spaces which are the {\it stationary analogs of de Sitter and ani-de Sitter} spacetimes. Having $Λ$ as their only parameter, the inherent anisotropy in these solutions appears as a dilemma if we treat the cosmological term as a constant background curvature. Since the cosmological term is an inseparable element of the current cosmological models, further development of these models as well as resolution of the problems related to this term, including any quantum aspect will crucially depend on the true nature of this term. These solutions, which to the best of our knowledge appear here for the first time in the literature, not only open a new direction to study the cosmological term, but also provide strong evidence in favor of the cosmological term as a dark fluid, hence furnishing a resolution to the above mentioned dilemma.

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arXiv2020

Optical Aharonov-Bohm effect due to toroidal moment inspired by general relativity

We study the analogy between propagation of light rays in a stationary curved spacetime and in a toroidal (meta-)material. After introducing a novel gravitational analog of the index of refraction of a magneto-electric medium, it is argued that light rays not only feel a Lorentz-like force in a magneto-electric medium due to the non-vanishing curl of the toroidal moment, but also there exists an optical analog of Aharonov-Bohm effect for the rays traveling in a region with a curl-free toroidal moment. Experimental realization of this effect could utilize either a multiferroic material or a toroidal metamaterial.

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arXiv2019

General relativistic analogs of Poisson's equation and gravitational binding energy

Employing the quasi-Maxwell form of the Einstein field equations in the context of gravitoelectromagnetism, we introduce a general relativistic analog of Poisson's equation as a natural outcome of the corresponding spacetime decomposition formalism. The active density introduced in this formalism, apart from the matter-energy density and pressure, includes a third component which is the gravitoelectromagnetic energy density. This general relativistic analog of Poisson's equation is compared with another analog introduced by Ehlers et al. in [1]. Introduction of the cosmological constant and its effect on the active mass, are also discussed for both exterior and interior static spacetimes. In the stationary case, we consider the Kerr spacetime with a special choice for its interior metric.

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arXiv2017

A tale of two velocities: Threading vs Slicing

Two principal definitions of a 3-velocity assigned to a test particle following timelike trajectories in stationary spacetimes are introduced and analyzed systematically. These definitions are based on the $1+3$ (threading) and $3+1$ (slicing) spacetime decomposition formalisms and defined relative to two different sets of observers. After showing that Synge's definition of spatial distance and 3-velocity are equivalent to those defined in the $1+3$ (threading) formalism, we exemplify differences between the two definitions, by calculating them for particles in circular orbits in axially symmetric stationary spacetimes. Illustrating its geometric nature, the relative linear velocity between the corresponding observers is obtained in terms of the spacetime metric components. Circular particle orbits in the Kerr spacetime, as the prototype and the most well known of stationary spacetimes, are examined with respect to these definitions to highlight their observer-dependent nature. We also examine the Kerr-NUT spacetime in which the NUT parameter contributing to the off-diagonal terms in the metric is mainly interpreted not as a rotation parameter but as a gravitomagnetic monopole charge. Finally, in a specific astrophysical setup which includes rotating black holes, it is shown how these local definitions are related to the velocity measurements made by distant observers using spectral line shifts.

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arXiv2015

Papapetrou field as the gravitoelectromagnetic field tensor in stationary spacetimes

Introducing the well known Papapetrou field as the gravitoelectromagnetic field tensor, we express the Maxwell-type part of the 3-dimensional quasi-Maxwell form of the {\it vacuum} Einstein field equations in terms of differential forms, analogous to their electromagnetic counterparts in curved spacetimes. Using the same formalism we introduce the junction conditions on non-null hypersurfaces in terms of the introduced gravitoelectromagnetic 4-vector fields and apply them to the case of the Van Stockum interior and exterior solutions.

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arXiv2015

Dark fluid or cosmological constant : Why there are different de Sitter-type spacetimes

Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity and non-stationarity of these two different forms are traced back to the noncomoving and comoving nature of the corresponding coordinate systems. In this paper using the quasi-Maxwell form of the Einstein field equations and a definition of static spacetimes based upon them, we look at these two different forms of the same solution from a new perspective which classifies them as a special case in a general one-parameter family of solutions. Specifically it is proved that, {\it irrespective of the spacetime symmetry, a one-element perfect fluid in any frame noncomoving with the fluid could be the source of a static spacetime, only if its equation of state is that of a dark fluid namely $p = -ρ= const.$}. These static solutions, which include the well-known de Sitter spacetime, are called de Sitter-type spacetimes. To exemplify we consider static axially and cylindrically symmetric de Sitter-type spacetimes and their dynamic (cosmological) versions. It is shown how despite the seemingly natural expectation based on the presence of $Λ$ as their only parameter, the nonspherical expansions of these genuinely different solutions should be expected indeed. To the best of our knowledge the dynamic version of the cylindrically symmetric de Sitter-type spacetime is introduced here for the first time. Finally it is noted that the identification of the geometric term $Λg_{ij}$ with a perfect fluid with equation of state $p = -ρ= const.$, although mathematically consistent, obscures the crucial role of the (dark) fluid's velocity in defining a preferred (comoving) coordinate system in de Sitter-type spacetimes.

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arXiv2014

On Franklin's relativistic rotational transformation and its modification

Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high relative velocities, there seems to be no such a consensus in the case of coordinate transformation between inertial frames and uniformly rotating ones. There have been some attempts to generalize the Galilean rotational transformation to high rotational velocities. Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922. The modified version is shown to resolve some of the drawbacks of the Franklin transformation, specially with respect to the corresponding spacetime metric in the rotating frame. This new transformation introduces non-inertial eccentric observers on a uniformly rotating disk and the corresponding metric in the rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the rotation axis. Employing the threading formulation of spacetime decomposition, spatial distances and time intervals in the spacetime metric of a rotating observer's frame are also discussed.

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arXiv2014

Fermi coordinates and modified Franklin transformation : A comparative study on rotational phenomena

Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In this article, after a comparative study between Fermi metric of a uniformly rotating eccentric observer and the spacetime metric in the same observer's frame obtained through the modified Franklin transformation, we consider rotational phenomena including transverse Doppler effect and Sagnac effect in both formalisms and compare their predictions. We also discuss length measurements in the two formalisms.

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arXiv2014

Primordial black holes, zero-point energy and the CMB: The cosmic connection

We propose a possible resolution to the cosmological constant problem through a scenario in which the universe is composed of three components: matter, radiation (CMB) and vacuum energy such that vacuum energy is not constant and is decaying into the matter component. Matter in this scenario consists of baryonic matter and primordial black holes (PBHs) as the dark matter. Local equilibrium condition between PBHs and CMB confines the mass and the radius of PBHs. The mechanism accounting for the decaying process is nothing but the absorption of vacuum energy modes by the PBHs up to a wavelength of the order of their radius. Acting as a natural cut-off on the wavelength of vacuum energy modes, this leads to the observed value for the vacuum energy density.

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arXiv2013

Gaussian Curvature and Global effects : gravitational Aharonov-Bohm effect revisited

Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime. Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment).

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arXiv2010

Casimir effect in a weak gravitational field and the spacetime index of refraction

In a recent paper [arXiv:0904.2904] using a conjecture it is shown how one can calculate the effect of a weak stationary gravitational field on vacuum energy in the context of Casimir effect in an external gravitational field treated in 1+3 formulation of spacetime decomposition.. In this article, employing quntum field theory in curved spacetime, we explicitly calculate the effect of a weak static gravitational field on virtual massless scalar particles in a Casimir apparatus. It is shown that, as expected from the proposed conjecture, both the frequency and renormalized energy of the virtual scalar field are affected by the gravitational field through its index of refraction. This could be taken as a strong evidence in favour of the proposed conjecture. Generalizations to weak {\it stationary} spacetimes and virtual photons are also discussed.

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arXiv2010

Vacuum energy and the spacetime index of refraction: A new synthesis

In 1+3 (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea one could examine the response of vacuum energy to the presence of a stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. The results are given explicitly for a Casimir apparatus in the weak field limit of a Kerr hole.

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