arXiv subjects

Hyerim Noh

Publications and source records attributed to Hyerim Noh.

At least 19 recordsLinked to original sources

arXiv2025

Evolution of baryon density perturbation in a relativistic MOND model based on Lorentz-violating vector field

A candidate for relativistic MOND with successful cosmology was proposed recently by using a Lorentz-violating vector field in Einstein's gravity. We show that the dynamic nature of the vector field makes it challenging to realize the MOND. Only in the stationary limit, thus excluding cosmological situations, one can achieve the MOND limit. We study the evolution of density perturbations in the baryon-vector field system using both post-Newtonian approximation and relativistic perturbation theory. Our results show that, considering the dynamic nature of the vector field, the faster growth of structures expected in the low-acceleration MOND regime is not recovered in the relativistic MOND.

gr-qc↗

arXiv2025

Massive-photon electrodynamics and MHD in curved spacetime and cosmology

We study a massive-photon electrodynamics and magnetohydrodynamics (MHD) in the curved spacetime of Einstein's gravity. We consider a Proca-type photon mass and present equations in terms of electric and magnetic (EM) fields and the vector potential. We present the electrodynamics and MHD in the covariant and ADM formulations valid in general spacetime and in linearly perturbed cosmological spacetime. We present wave equations assuming the metric variations are negligible compared with the field variations. Equations are derived without fixing the temporal gauge condition and the gauge transformation properties of the EM fields and the vector potential are presented. Using the post-Newtonian approximation we show the dark Proca field behaves as dust in the non-relativistic limit under the Klein transformation.

gr-qc↗

arXiv2024

Cosmological perturbations of a relativistic MOND theory

A relativistic MOND theory, promising in reproducing cosmology as well as the MOND phenomenology in the low acceleration regime, was recently proposed. We present the post-Newtonian (PN) approximation and relativistic perturbation equations of this theory in cosmological context. The PN equations are presented to 1PN order and perturbation equations are presented in fully-nonlinear and exact forms. The gauge issues are clarified. The 1PN equations and linear perturbation equations are presented without imposing temporal gauge conditions. We show that to 0PN order baryon perturbation grows faster in the MOND regime. The MOND field can be interpreted as a fluid with specific equation of state without anisotropic stress, and the Jeans criterion is derived for the MOND field.

gr-qc↗

arXiv2024

Graviton-photon conversions in Euler-Heisenberg nonlinear electrodynamics

We study graviton-photon conversions in an environment of the uniform and constant magnetic field considering Euler-Köckel-Heisenberg-type nonlinear corrections in electrodynamics. We take the transverse-tracefree gauge for gravitons and employ both the field potential and the electric and magnetic (EM) fields for photons. The nonlinear correction causes parity violating (chiral) graviton propagation equations, which depend on the two treatments for photons. Thus, the medium becomes effectively birefringent for two polarizations of gravitational waves similar to the photon birefringence a characteristic of the nonlinear correction. In the presence of gravity, due to the nontrivial relation between the potential and EM fields, it is important to present the result using the EM fields.

gr-qc↗

arXiv2024

On graviton-photon conversions in magnetic environments

Graviton-photon conversions in a given external electric or magnetic field, known as the Gertsenshtein mechanism, are usually treated using the four-potential for photons. In terms of the electric and magnetic (EM) fields, however, proper identification of the fields in curved spacetime is important. By misidentifying the fields in Minkowski form, as is often practiced in the literature, we show that the final equation for photon conversion is correct in transverse-tracefree gauge only for planar gravitational waves in a uniform and constant external field. Even in the former method, to recover the EM fields from the four-potential in curved spacetime, one should properly take into account the metric involved in the relation. By including the metric perturbation in the graviton conversion equation, we show that a magnetic environment can cause tachyonic instability term in gravitational wave equation.

gr-qc↗

arXiv2024

On gravity as a medium property in Maxwell equations

The effect of gravity in Maxwell's equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell's equations in exactly the same form as in Minkowski spacetime and expressing the effect of gravity as a set of constitutive relations. We show that such a set of Maxwell's equations is, in fact, a combination of the electric and magnetic fields defined in two different non-covariant ways, both of which fail to identify the associated observer's four-vectors. The suggested constitutive relations are also ad hoc and unjustified. To an observer with a proper four-vector, the effect of gravity can be arranged as effective polarizations and magnetizations appearing in both the homogeneous and inhomogeneous parts. Modifying the homogeneous part by gravity is inevitable to any observer, and the result cannot be interpreted as the medium property. For optical properties one should directly handle Maxwell's equations in curved spacetime.

gr-qc↗

arXiv2023

Maxwell equations in curved spacetime

In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend on the observer's frame four-vector. We derive Maxwell's equations valid in general curved spacetime using the fields defined in the normal frame, the coordinate frame, and two other non-covariant methods used in the literature. By analyzing the case in the generic frame we show that the EM fields, as well as the charge and current densities, defined in non-covariant ways do not correspond to physical ones measured by an observer. We show that modification of the homogeneous part is inevitable to any observer, and such a modification is difficult to interpret as the effective medium property. The normal frame is the relevant one to use as it gives the EM fields measured by an Eulerian observer.

gr-qc↗

arXiv2023

Pulsar Timing Array Signature from Oscillating Metric Perturbations due to Ultra-light Axion

A coherently oscillating ultra-light axion can behave as dark matter. In particular, its coherently oscillating pressure perturbations can source an oscillating scalar metric perturbation, with a characteristic oscillation frequency which is twice the axion Compton frequency. A candidate in the mass range $10^{(-24,-21)}{\rm eV}$ can provide a signal in the frequency range tested by current and future Pulsar Timing Array (PTA) programs. Involving the pressure perturbations in a highly nonlinear environment, such an analysis demands a relativistic and nonlinear treatment. Here, we provide a rigorous derivation of the effect assuming weak gravity and slow-motion limit of Einstein's gravity in zero-shear gauge and show that dark matter's velocity potential determines the oscillation phase and frequency change. A monochromatic PTA signal correlated with the velocity field would confirm the prediction, for example, by cross-correlating the PTA results with the future local velocity flow measurements.

astro-ph.CO↗

arXiv2023

Definition of electric and magnetic fields in curved spacetime

Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In recent literature on using electromagnetic means to detect gravitational waves, an ad hoc definition based on regarding $F_{ab}$ with two covariant indices as the special relativistic one is popular. We show that by assigning physical fields to tensor components in that way, one cannot identify the frame four-vector allowing such a choice, thus failing to properly define the external charge and current densities in that frame. We propose the normal frame as the proper one. In this frame, the weak gravity corrections appear as the effective polarizations and magnetizations in both the homogeneous and inhomogeneous parts of Maxwell equations.

gr-qc↗

arXiv2023

Exact formulations of relativistic electrodynamics and magnetohydrodynamics with helically coupled scalar field

We present the general relativistic electrodynamics and magnetohydrodynamics with a helically coupled scalar field. We consider three component system with the fluid, scalar field and electromagnetic fields with the helical coupling. We derive three exact formulations: the covariant formulation, the ADM formulation, and the fully nonlinear and exact perturbation formulation. We also derive the weak-gravity limit with fully relativistic fluid and fields. The latter two formulations are presented in the cosmological context.

astro-ph.HE↗

arXiv2022

Axion cosmology with post-Newtonian corrections

We present first-order post-Newtonian (1PN) approximations of a general imperfect fluid and of an axion as a coherently oscillating massive scalar field, both in the cosmological context. For the axion, using the Klein transformation and Madelung transformation we derive the Schrödinger and Madelung hydrodynamic formulations, respectively, in exact covariant way and to 1PN order. Complete sets of equations for the 1PN formulations are derived without fixing the temporal gauge condition. We study the linear instability in cosmology and a static limit for both fluid and axion; these are presented independently of the gauge condition to 1PN order, thus are naturally gauge-invariant.

hep-th↗

arXiv2022

Axion electrodynamics and magnetohydrodynamics

We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(ϕ)$-coupling, and an axion as a massive scalar field with $ϕ^2$-coupling, with the helical electromagnetic field. The $α$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schrödinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $ϕ$ coupling; instead, $ϕ^2$ coupling allows successful formulations preserving the dark matter nature of the axion to nonlinear order. In the MHD formulation, direct couplings between the scalar and electromagnetic fields appear only for non-ideal MHD. We study gravitational and magnetic instabilities of the scalar field and axion MHDs.

hep-ph↗

arXiv2022

Axion as a fuzzy-dark-matter candidate: Proofs in different gauges

Axion as a coherently oscillating massive scalar field is known to behave as a zero-pressure irrotational fluid with characteristic quantum stress on a small scale. In relativistic perturbation theory, the case was proved in the axion-comoving gauge up to fully nonlinear and exact order. Our basic assumption is that the field is oscillating with Compton frequency and the Compton wavelength is smaller than the horizon scale. Here, we revisit the relativistic proof to the linear order in the other gauge conditions. We show that the same equation for density perturbation known in the non-relativistic treatment can be derived in two additional gauge conditions: the zero-shear gauge and the uniform-curvature gauge. The uniform-expansion gauge fails to get the aimed equation, and the quantum stress term is missing in the synchronous gauge. For comparison, we present the relativistic density perturbation equations in the zero-pressure fluid in these gauge conditions. Except for the comoving and the synchronous gauge, the equations strikingly differ from the axion case. We clarify that the relativistic analysis based on time averaging is valid for scales larger than the Compton wavelength. Below the Compton wavelength, the field is not oscillating, and our oscillatory ansatz does not apply. We suggest an equation valid in all scales in the comoving gauge. For comparison, we review the non-relativistic quantum hydrodynamics and present the Schrödinger equation to first-order post-Newtonian expansion in the cosmological context.

astro-ph.CO↗

arXiv2021

CMASS galaxy sample and the ontological status of the cosmological principle

The cosmological principle (CP), assuming spatially homogeneous and isotropic background geometry in the cosmological scale, is a fundamental assumption in modern cosmology. Recent observations of the galaxy redshift survey provide relevant data to confront the principle with observation. We present a homogeneity test for the matter distribution using the BOSS DR12 CMASS galaxy sample and clarify the ontological status of the CP. As a homogeneity criterion, we compare the observed data with similarly constructed random distributions using the number count in the truncated cones method. Comparisons are also made with three theoretical results using the same method: (i) the dark matter halo mock catalogs from the N-body simulation, (ii) the log-normal distributions derived from the theoretical matter power spectrum, and (iii) direct estimation from the theoretical power spectrum. We show that the observed distribution is statistically impossible as a random distribution up to 300 Mpc/h in radius, which is around the largest statistically available scale. However, comparisons with the three theoretical results show that the observed distribution is consistent with these theoretically derived results based on the CP. We show that the observed galaxy distribution (light) and the simulated dark matter distribution (matter) are quite inhomogeneous even on a large scale. Here, we clarify that there is no inconsistency surrounding the ontological status of the CP in cosmology. In practice, the CP is applied to the metric and the metric fluctuation is extremely small in all cosmological scales. This allows the CP to be valid as the averaged background in metric. The matter fluctuation, however, is decoupled from the small nature of metric fluctuation in the subhorizon scale. What is directly related to the matter in Einstein's gravity is the curvature, a quadratic derivative of the metric.

astro-ph.CO↗

arXiv2021

Oscillating gravitational potential due to ultralight axion: linear theory

We derive oscillating gravitational potential caused by an ultralight axion as the cosmic dark matter, assuming the Compton wavelength smaller than the horizon scale. A new oscillatory term is found which dominates the previously known one on scales larger than the quantum Jeans-scale. In the context of linear perturbations in cosmology this new term might be more relevant in future observation. Both the quantum stress in density perturbation and the quantum oscillation of the gravitational potential are derived in the zero-shear gauge. We show that the axion fluid in relativistic analysis is quite different from the relativistic and Newtonian zero-pressure fluids, corresponding to Newtonian fluid only in the density perturbation. The consistency demands the relativistic analysis valid on scales larger than the Compton wavelength.

astro-ph.CO↗

arXiv2021

Gauge-Invariant Tensor Perturbations Induced from Baryon-CDM Relative Velocity and the B-mode Polarization of the CMB

At second-order, scalar perturbations can source traceless and transverse perturbations to the metric, called induced gravitational waves (IGW). The apparent gauge-dependence of the IGW obscures the interpretation of the stochastic gravitational-wave signal. To elucidate the gauge dependence, we study the IGW from manifestly gauge-invariant scalar perturbations, namely, the relative velocity between the baryon and cold dark matter. From this relative velocity perturbation, we compute the dimensionless gravitational wave power spectrum and the corresponding expected angular power spectrum of the B-mode polarization of the cosmic microwave background. Although the effect turns out to be unobservably small, the calculation demonstrates both the importance of using observable quantities to remove the gauge ambiguity and the observable consequences of tensor perturbations which are not propagating gravitational waves.

astro-ph.CO↗

arXiv2020

Gravito-magnetic instabilities of Relativistic Magnetohydrodynamics

We study gravito-magnetic instabilities of a static homogeneous medium with an aligned magnetic field in the two contexts of relativistic magnetohydrodynamics (MHD): first, MHD with post-Newtonian (PN) corrections, and second, special relativistic (SR) MHD with weak gravity. The analysis in the PN MHD is made without taking the temporal gauge condition, thus results are gauge-invariant. The PN corrections of the internal energy, pressure, sound velocity and the Alfvén velocity lower the critical (Jeans) wavelength. {All relativistic effects tend to destabilize the system.} Although the SR MHD with weak gravity is presented in the harmonic gauge, in the presence of gravity the stability analysis is strictly valid to Newtonian order. In the absence of gravity, the SR MHD is independent of the gauge condition. We present the plane wave velocities and the stability criteria in both cases.

astro-ph.HE↗

arXiv2020

Perturbations and Linearization Stability of Closed Friedmann Universes

We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes.

gr-qc↗