arXiv subjects

Yi-Zen Chu

Publications and source records attributed to Yi-Zen Chu.

32 records · Page 2Linked to original sources

arXiv2014

A Line Source In Minkowski For The de Sitter Spacetime Scalar Green's Function: Massless Minimally Coupled Case

Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied to $(d \geq 2)$-dimensional de Sitter spacetime, and the scalar Green's function is demonstrated to be sourced by a line emanating infinitesimally close to the origin of the ambient $(d+1)$-dimensional Minkowski spacetime and piercing orthogonally through the de Sitter hyperboloids of all finite sizes. This method does not require solving the de Sitter wave equation directly. Only the zero mode solution to an ordinary differential equation, the "wave equation" perpendicular to the hyperboloid -- followed by a one dimensional integral -- needs to be evaluated. A topological obstruction to the general construction is also discussed by utilizing it to derive a generalized Green's function of the Laplacian on the $(d \geq 2)$-dimensional sphere.

gr-qc↗

arXiv2014

Scalar Wave Tails in Even Dimensional Weakly Curved Static Newtonian Spacetimes

In a 4-dimensional (4D) weak field geometry governed by the linearized Einstein's equations and sourced primarily by a static, spatially localized, but otherwise arbitrary mass density $T_{00}$, it is known that the leading order tail part of the Green's functions of the minimally coupled massless scalar, Lorenz gauge photon, and de Donder gauge graviton at late times are not only time translation symmetric, but also space-translation and spherically symmetric. Only the monopole moment of the matter source is responsible for the late-time tail of the Green's functions. We provide evidence, in this paper, that both of these statements will cease to hold for all even dimensions higher than 4. As a consequence, we anticipate that the late time behavior of massless fields propagating in higher even dimensional asymptotically flat spacetimes will exhibit richer phenomenology than their 4D counterparts.

gr-qc↗

arXiv2013

Galileon forces in the Solar System

We consider the challenging problem of obtaining an analytic understanding of realistic astrophysical dynamics in the presence of a Vainshtein screened fifth force arising from infrared modifications of General Relativity. In particular, we attempt to solve -- within the most general flat spacetime galileon model -- the scalar force law between well separated bodies located well within the Vainshtein radius of the Sun. To this end, we derive the exact static Green's function of the galileon wave equation linearized about the background field generated by the Sun, for the minimal cubic and maximally quartic galileon theories, and then introduce a method to compute the general leading order force law perturbatively away from these limits. We also show that the same nonlinearities which produce the Vainshtein screening effect present obstacles to an analytic calculation of the galileon forces between closely bound systems within the solar system, such as that of the Earth and Moon. Within the test mass approximation, we deduce that a large enough quartic galileon interaction would suppress the effect on planetary perihelion precession below the level detectable by even the next-generation experiments.

astro-ph.CO↗

arXiv2013

Capacitor Discharge and Vacuum Resistance in Massless QED_2

A charged parallel plate capacitor will create particle-antiparticle pairs by the Schwinger process and discharge over time. We consider the full quantum discharge process in 1+1 dimensions including backreaction, when the electric field interacts with massless charged fermions. We recover oscillatory features in the electric field observed in a semiclassical analysis and find that the amplitude of the oscillations falls off as t^{-1/2} and that stronger coupling implies slower decay. Remarkably, Ohm's law applies to the vacuum and we evaluate the quantum electrical conductivity of the vacuum to be e/π^{1/2}, where e is the fermionic charge. Similarities and differences with black hole evaporation are mentioned.

hep-th↗

arXiv2013

Gravitational Scattering Of Photons Off Cosmic Strings

Photons can gravitationally scatter off a cosmic string loop and gain or lose energy. We consider the spectral distortion induced by cosmic string loops placed in an ambient thermal bath of photons. The fractional deviation from a thermal spectrum caused by cosmic strings is estimated to scale as (G_N μ)^2 z^2, where G_N is Newton's constant, $μ$ is the string tension, and z is the cosmological redshift after which spectral distortions can survive. This effect is large enough to potentially be of observational interest.

hep-th↗

arXiv2012

Retarded Green's Function Of A Vainshtein System And Galileon Waves

Motivated by the desire to test modified gravity theories exhibiting the Vainshtein mechanism, we solve in various physically relevant limits, the retarded Galileon Green's function (for the cubic theory) about a background sourced by a massive spherically symmetric static body. The static limit of our result will aid us, in a forthcoming paper, in understanding the impact of Galileon fields on the problem of motion in the solar system. In this paper, we employ this retarded Green's function to investigate the emission of Galileon radiation generated by the motion of matter lying deep within the Vainshtein radius r_v of the central object: acoustic waves vibrating on its surface, and the motion of compact bodies gravitationally bound to it. If λis the typical wavelength of the emitted radiation, and r_0 is the typical distance of the source from the central mass, with r_0 << r_v, then, compared to its non-interacting massless scalar counterpart, we find that the Galileon radiation rate is suppressed by the ratio (r_v/λ)^{-3/2} at the monopole and dipole orders at high frequencies r_v/λ>> 1. However, at high enough multipole order, the radiation rate is enhanced by powers of r_v/r_0. At low frequencies r_v/λ<< 1, and when the motion is non-relativistic, Galileon waves yield a comparable rate for the monopole and dipole terms, and are amplified by powers of the ratio r_v/r_0 for the higher multipoles.

astro-ph.CO↗

arXiv2011

Retarded Green's Functions In Perturbed Spacetimes For Cosmology and Gravitational Physics

Electromagnetic and gravitational radiation do not propagate solely on the null cone in a generic curved spacetime. They develop "tails," traveling at all speeds equal to and less than unity. If sizeable, this off-the-null-cone effect could mean objects at cosmological distances, such as supernovae, appear dimmer than they really are. Their light curves may be distorted relative to their flat spacetime counterparts. These in turn could affect how we infer the properties and evolution of the universe or the objects it contains. Within the gravitational context, the tail effect induces a self-force that causes a compact object orbiting a massive black hole to deviate from an otherwise geodesic path. This needs to be taken into account when modeling the gravitational waves expected from such sources. Motivated by these considerations, we develop perturbation theory for solving the massless scalar, photon and graviton retarded Green's functions in perturbed spacetimes, assuming these Green's functions are known in the background spacetime. In particular, we elaborate on the theory in perturbed Minkowski spacetime in significant detail; and apply our techniques to compute the retarded Green's functions in the weak field limit of the Kerr spacetime to first order in the black hole's mass and angular momentum. Our methods build on and generalizes work appearing in the literature on this topic to date, and lays the foundation for a thorough, first principles based, investigation of how light propagates over cosmological distances, within a spatially flat inhomogeneous Friedmann-Lemaître-Robertson-Walker (FLRW) universe. This perturbative scheme applied to the graviton Green's function, when pushed to higher orders, may provide approximate analytic (or semi-analytic) results for the self-force problem in the weak field limits of the Schwarzschild and Kerr black hole geometries.

astro-ph.CO↗

arXiv2011

Magnetic Helicity in Sphaleron Debris

We develop an analytical technique to evaluate the magnetic helicity in the debris from sphaleron decay. We show that baryon number production leads to left-handed magnetic fields, and that the magnetic helicity is conserved at late times. Our analysis explicitly demonstrates the connection between sphaleron-mediated cosmic baryogenesis and cosmic magnetogenesis.

hep-th↗

arXiv2010

Aharonov-Bohm Radiation of Fermions

We analyze Aharonov-Bohm radiation of charged fermions from oscillating solenoids and cosmic strings. We find that the angular pattern of the radiation has features that differ significantly from that for bosons. For example, fermionic radiation in the lowest harmonic is approximately isotropically distributed around an oscillating solenoid, whereas for bosons the radiation is dipolar. We also investigate the spin polarization of the emitted fermion-antifermion pair. Fermionic radiation from kinks and cusps on cosmic strings is shown to depend linearly on the ultraviolet cut-off, suggesting strong emission at an energy scale comparable to the string energy scale.

hep-th↗

arXiv2010

It's Hard to Learn How Gravity and Electromagnetism Couple

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.

gr-qc↗

arXiv2009

The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory

Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski spacetime to O[(v/c)^4] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2 body problem, the major efforts underway to measure gravitational waves produced by in-spiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c)^7]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c)^6] beyond Newton are derived.

gr-qc↗

arXiv2007

Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.

hep-th↗

arXiv2006

Sterile neutrinos, lepton asymmetries, primordial elements: how much of each?

We investigate quantitatively the extent to which having a primordial leptonic asymmetry (n_nu \neq n_nubar) relaxes the bounds on light sterile neutrinos imposed by BBN and LSS. We adopt a few assumptions that allow us to solve the neutrino evolution equations over a broad range of mixing parameters and asymmetries. For the general cases of sterile mixing with the electron or muon neutrino, we identify the regions that can be reopened. For the particular case of a LSND-like sterile neutrino, soon to be rejected or confirmed by MiniBooNE, we find that an asymmetry of the order of 10^-4 is needed to lift the conflicts with cosmology.

astro-ph↗

arXiv2006

Asymptotics of d-dimensional Kaluza-Klein black holes: beyond the Newtonian approximation

We study the thermodynamics of small black holes in compactified spacetimes of the form R^(d-1)x S^1. This system is analyzed with the aid of an effective field theory (EFT) formalism in which the structure of the black hole is encoded in the coefficients of operators in an effective worldline Lagrangian. In this effective theory, there is a small parameter $λ$ that characterizes the corrections to the thermodynamics due to both the non-linear nature of the gravitational action as well as effects arising from the finite size of the black hole. Using the power counting of the EFT we show that the series expansion for the thermodynamic variables contains terms that are analytic in $λ$, as well as certain fractional powers that can be attributed to finite size operators. In particular our operator analysis shows that existing analytical results do not probe effects coming from horizon deformation. As an example, we work out the order $λ^2$ corrections to the thermodynamics of small black holes for arbitrary d, generalizing the results in the literature.

hep-th↗