arXiv subjects

Noah M. MacKay

Publications and source records attributed to Noah M. MacKay.

16 recordsLinked to original sources

arXiv2026

Non-Conservative Mechanics in the Compact-Body Mass-Shell Model and its Waveform Structuring

A novel reinterpretation on the effective one-body (EOB) mapping of compact-body binary (CBB) coalescence was previously considered. Instead of the conventional ``marble in a funnel" description of EOB, CBB coalescence is modeled as the concurrent rotation and contraction of a hollow shell with a constant reduced mass measure. Merger is achieved, therefore, when the shell radius reaches the total mass radius. While past works analyzed the energetics sector of the model and the radiated gravitational waves (GWs), this work considers the geometric waveform modeling aspect. More specifically, we mature the mass-shell waveform analysis initially discussed with toy-model conditions by imposing necessary non-conservative mechanics, leading to the analytical expression of usable mass-shell modeled GW-forms. This is to set the foundation for eventual computational endeavors with the analytical waveforms presented here, enabling a comparison against current and state-of-the-art models.

gr-qc↗

arXiv2026

The Heuristic Approach to General Relativity in the Laplace-Beltrami Formalism

The Laplace-Beltrami formalism, in which the Ricci tensor in the Einstein field equations (EFEs) is formulated at leading-order in terms of the partial-differential Laplace-Beltrami operator, was previously applied to coalescing compact binaries (CCBs) generating gravitational waves (GWs). Supposing that the CCB is an effective singular body -- a hollow mass-shell -- that follows a Kerr metric Ansatz, the EFEs were approached variationally such that the Ansatz geometric signature dictates the energetic output via $G_{μν}=8πGT_{μν}$. For the CCB mass-shell representation, the generated GW energy is treated as radiated surface energy via $E:=T_{00}V$. This surface energy yielded a close approximation to the cataloged GW coalescence energy, as previously shown in past comparisons. Given this success, it is logical to ask whether the Laplace-Beltrami formalism can be applied to other general relativistic systems, whether ``simple" or ``perturbative", beyond CCBs. This heuristic work focuses broadly on the EFEs themselves under the Laplace-Beltrami formalism, considering all differential orders up to second-order. This namely includes a deeper analysis on the variational methodology employed on the EFEs in the second-order sector, utilized in previous works, and the benchmark analysis of the lower first- and zeroth-order terms. This all-order report utilizes representative examples and select metric Ansätze to explore the formalism's practicality and its limitations; this is shown that the first-order decomposition showcases heuristically the mechanics of vector and scalar fields upon a curved spacetime.

gr-qc↗

arXiv2026

Comparing a Compact-Binary Mass-Shell Model with Select Observed Gravitational Waves

In a recent work, coalescing compact binaries (CCBs) were modeled as a rotating and contracting compact mass shell, providing an alternative effective representation to the state-of-the-art effective-one-body approach. Using a variational methodology, the Laplace-Beltrami formulation of the Ricci tensor was applied to a Kerr metric Ansatz, and the corresponding energy density $T_{00}$ of the CCB mass shell was obtained via the Einstein field equations. At the time of coalescence $t_C$, the resulting surface energy depends on the reduced mass $μ$, the symmetric mass ratio $α$, and the normalized orbital spin velocity of the CCB. In this work, we evaluate the radiated energy predicted by this variational approach for 45 select gravitational wave (GW) events from the O1--O4 runs, and compare these values with those inferred from observational catalogs, either directly or via the total-minus-remnant mass difference. For 38 of the 45 events analyzed, the predicted radiated energies agree with observationally inferred values within the reported uncertainties, with 1:1 ratios spanning from $0.828$ to $0.997$ (mean $0.942$, median $0.955$). Three events exhibit ratios in the range $0.721\sim0.779$, one event yields a ratio of $0.466$, and for the remaining events the radiated energy is either unconstrained or inaccessible due to undocumented total-minus-remnant mass differences. These results indicate that the analytical approximation captures, for the most part, the leading-order energy scaling of compact binary mergers, while also suggesting clear avenues for further systematic improvement, including incorporating post-Newtonian corrections due to e.g. a non-zero eccentricity or combined tidal deformability.

gr-qc↗

arXiv2026

Effective Field Theory Calculation of LIGO-like Compton Scattering

We use effective field theory (EFT) to calculate the scattering amplitude of a LIGO-like graviton-scalar Compton interaction. We gauge the center-of-momentum energy $\sqrt{s}$ between one gravitational-wave (GW) graviton (one quantum of the coherent bulk of an astrophysical GW, with energy $E_g=\hbarω_\mathrm{GW}$) and a resting heavy target (a suspended mass with rest energy $E_M=m_Mc^2$ found in laser interferometer observatories) to be of order $\sim10^{1.5}$ PeV -- at the energy scale within the extremes of astroparticle physical phenomena. This back-of-the-envelope calculation supports the calculation of a convergent cross section in our LIGO-like Compton analysis, which we indeed recover using standard EFT Feynman rules and relevant traceless-transverse gauges for the graviton polarizations. We obtain that the cross section $σ$ is largely dependent on the center-of-momentum energy, and from this we define the corresponding impact parameter via $σ=πb^2$. This impact parameter, after coherence-state population enhancement, scales with GW energetics along with the unique coupling (in natural units) $\sqrt{ω_\mathrm{GW}/m_M}\sim10^{-21}$ -- the same order of magnitude as astrophysical GW strain. One finds furthermore that, after isolating the GW energetics sector from the GW-mirror impact parameter, the revised length scale $\tilde{b}/(GM)\approx1.76π$ quantifies the pre-merger stage of compact binary coalescence, which is compared with $b/(GM)>14$ calculated from the early-inspiral worldline quantum field theory framework. Conventional insight of GW-mirror response is recovered, such that the impact parameter $b$ scales exactly with the mirror recoil $ΔL\sim10^{-18}\,\mathrm{m}$ after having made contact with the GW.

gr-qc↗

arXiv2026

Gravitational Wave Generation via the Einstein-Langevin Equation

Detections of gravitational waves (GWs) since GW150914 has gained a contemporary interest in a potential quantum-classical correspondence between GWs and hypothetical gravitons. One such correspondence theory is stochastic gravity, whereby graviton fluctuations are treated as the stochastic noise embedded in globally-flat manifolds and local gravitational interactions. Utilizing the Einstein-Langevin equation that describes graviton fluctuations, in attempt to form a correlation with GW generation, we utilize the hollow mass-shell model of coalescing compact binaries. This is to explore the second Newtonian postulate of neutralized internal gravitational fields, i.e. the stochastic noise of an enclosed, internal Minkowski manifold. This stochatic picture of GW formation implies the treatment of the enclosed gravitons as a Brownian bath. From the Einstein-Langevin equation, we establish a scaling relation where quanta dissipation depends inversely with the contracting volume (i.e., emission increases during coalescence). Using an Euler iteration scheme, we simulate the graviton fluctuations from inspiral to merger as a Wiener process, revealing a signal that qualitatively resembles macroscopic GW waveforms. While inherently heuristic and phenomenological, this approach provides a computational framework for exploring graviton-scale perturbations in GW formation. We discuss furthermore analytical waveform matching with the iteration scheme, as well as the justification of a Brownian analogy amidst current and state-of-the-art effective field theory frameworks.

gr-qc↗

arXiv2025

A Mass-Shell Model of Compact Binary Coalescence

The final pulse of gravitational wave (GW) emission is released at the peak of the chirp rise before compact binary merger. LIGO detections since GW150914 reveal a correlation between the radiated energy $E_\mathrm{rad}$ and the ad hoc scaling of one-tenth of the chirp mass $\mathcal{M}$, which begs to ask if this is physically grounded. Motivated by current effective one-body models, this work models compact binary coalescence (CBC) as a rotating, compact mass shell that is contracting towards the total mass horizon. Using a variational methodology, the Laplace-Beltrami formulation for the Ricci tensor is applied to a Kerr metric Ansatz, retrieving the energy density $T_{00}$ of the CB mass shell via the Einstein field equations. At the time of coalescence $t_C$, the corresponding surface energy ultimately depends on the reduced mass $μ$ of the CB, the symmetric mass ratio $α$, and the CB's normalized orbital spin velocity. In other words, this surface energy is the anticipated energy radiated as GWs, which is not one-tenth of the chirp mass systematically. Under simple assumptions, the anticipated energy for GW150914 -- a representative example -- is $2.08 M_\odot c^2$ using documented center values. Under a more rigorous analysis in comparison, the anticipated energy for GW150914 is $3.27M_\odot c^2$. This is compared with the GWTC recorded value of $3.1^{+0.4}_{-0.4}M_\odot c^2$ for GW150914, with the latter analysis providing a closer approximation to the actual value. This study also includes the derivation of gravitational waveforms from the CB mass shell model, which depend on dynamic frequencies and decreasing CB separations.

gr-qc↗

arXiv2025

The Statistical Mechanics of Hawking Radiation

Hawking radiation and black hole thermodynamics are well understood in the frameworks of quantum field theory and general relativity, with contemporary extensions in string theory, AdS/CFT, and loop quantum gravity. However, an open question remains: Can Hawking radiation be consistently described using statistical mechanics? This challenge arises due to the ambiguous quantum nature of Hawking particles and constraints imposed by information conservation. This study develops a heuristic statistical model using a worldine Lagrangian formalism, treating Hawking particles as timelike with an effective mass and following an arbitrary statistical distribution. The flow of information is modeled as a transfer of microstates from the event horizon to the radiation background within a closed ensemble. From this framework, the Hawking particle mass $m_H=\hbar/(2πr_S)$ is recovered, and the worldline Lagrangian yields the black hole's thermal energy, $E=\hbar/(8πGM)$. Beyond preserving conventional insights, reinforcing the statistical nature of black hole evaporation, this approach introduces novel perspectives: modeling the black hole as a structured energy well containing microstates, quantifying the evaporation rate of individual microstates, and determining the total number of microstates from the horizon's surface area. This study leaves the door open for a stochastic mechanical analysis, which is introduced in the Discussion section.

gr-qc↗

arXiv2025

A Lattice Physics Approach to Spin-Networks in Loop Quantum Gravity

In this study, we model a spin-network in loop quantum gravity as a regular tetrahedral lattice, applying lattice physics techniques to study its structure and vertex dynamics. Using the area eigenvalue, $A\propto 8πl_P^2$, we derive a lattice constant $a = 2.707\,l_P$ and construct a vertex Hamiltonian incorporating a Lennard-Jones potential, zero-point energy, and simple harmonic oscillations. A foliation approach enforces the Wheeler-DeWitt constraint via locally non-zero Hamiltonians that globally cancel. Graviton-like perturbations (treated here as spin-0 bosons) modify the vertex energy spectrum, with variational analysis suggesting twelve coherent excitations per vertex. This model frames flat spacetime as a graviton-rich lattice while enforcing a Brownian-like stochastic picture for the gravitons, and offers a basis for extension into curved quantum geometries.

gr-qc↗

arXiv2025

A Holographic, Hydrodynamic Model of a Schwarzschild Black Hole

Schwarzschild (non-rotating and chargeless) black holes are classically understood to be voids of extreme gravitation. In this study, we propose a holographic model for their interiors, envisioning them instead as a hydrodynamic medium. Motivated by the neutrino composition in Hawking radiation (81%), we model the interior as a degenerate fluid, mirrored by the horizon via AdS/CFT duality. A Schwarzschild metric revised with a signum function as the power of the ratio $r_S/r$ distinguishes interior linear-well dynamics from exterior Schwarzschild geometry, rimming the horizon with singularity-like gravitational attraction. A Hamiltonian analysis of the total action leads to formulating a Schrödinger-like equation, which offers an alternative representation as the contracted Einstein field equations under a holographic-hydrodynamic framework. This eventually yields an equation of state between holographic pressure and black hole mass density: $P=ρ/9$. Ideal gas analysis reveals a total particle count of $\sim2.8$ times the number of horizon quantum areas, with the Fermi energy far exceeding the Hawking thermal energy, ensuring degeneracy. As our discussion, we explore the mass shell free-fall model of a BH with holographic pressure, and dissect the spherical wave solutions to the Schrödinger-like equation describing confined interior fields and freely propagating exterior quanta (i.e., Hawking radiation).

physics.gen-ph↗

arXiv2025

The Stochastic Mechanics of Hawking Radiation

In Ref. arXiv:2502.08816, Hawking radiation was analyzed through a statistical mechanics framework, revealing a structured microstate description of black hole horizons and information transfer into the radiation background. This study extends that approach by formulating Hawking radiation and black hole evaporation in the language of stochastic mechanics, employing an analytical Langevin framework and a numerical Euler iteration scheme. Both methods confirm that small black holes behave as thermal systems with Gaussian noise, while larger black holes develop a structured noise spectrum that aligns with the gradual contraction of the horizon. This suggests an alternative interpretation of Hawking radiation as an effective surface fuzziness, encoding horizon-scale fluctuations. The appendix provides a Wolfram Mathematica blueprint for numerical simulations, open to heuristic modifications for further exploration of black hole noise spectra.

gr-qc↗

arXiv2025

Shear Viscosity of Collider-Produced QCD Matter II: Comparing a Multi-Component Chapman-Enskog Framework with AMPT in Full Equilibrium

Transport properties of the quark-gluon plasma are instrumental to testing perturbative quantum chromodynamics and understanding the extreme conditions of relativistic heavy-ion collisions. This study presents an analytical investigation of the shear viscosity $η$ and the shear viscosity-to-entropy density ratio $η/s$ of the QGP using a novel multi-component Chapman-Enskog framework assuming full thermalization. The approach incorporates species-specific contributions from gluons and (anti-)quarks into the plasma shear viscosity, temperature-dependent running parameters for the Debye mass and strong coupling, and a time-dependent cooling model. Our findings show that both $η$ and $η/s$ are enhanced by the inclusion of (anti-)quarks with gluons, and the parameters decrease over time due to the cooling and expansion of the QGP. These results align with perturbative QCD predictions, offering a more optimistic representation of QGP transport properties under dynamic conditions. This multi-component framework is compared with a multi-phase transport model that treats the QGP as a gluon gas with (anti-)quark augmentation.

nucl-th↗

arXiv2025

Remarks on "The Modification of Feynman Diagrams in Curved Space-Time"

The arXiv preprint 2411.15164v1 \cite{Li:2024ltx} discusses how a weak Schwarzschild spacetime modifies Feynman diagram calculations and the governing equations of scalar and spinor particles. This short review offers an extended analysis on concerning points involving massless particles and limitations of weak-field approximation. Written for the Universität Potsdam lecture \textit{New Developments in Astrophysics, Winter Semester 2024/25}.

physics.gen-ph↗

arXiv2024

Shear Viscosity of an $N$-Component Gas Mixture using the Chapman--Enskog Method under Anisotropic Scatterings

The analytical Chapman-Enskog formula for calculating the shear viscosity $η$ of a relativistic ideal gas, such as a massless quark-gluon plasma, has consistently demonstrated good agreement with the numerical results obtained using the Green-Kubo relation under both isotropic and anisotropic two-body scatterings. However, past analyses of massless, multicomponent quark-gluon plasma have focused on an effective single-component "gluon gas." The Chapman-Enskog formula for multicomponent mixtures with nonzero yet adjustable masses was previously developed for simpler cases of isotropic scatterings. This study aims to obtain the Chapman-Enskog shear viscosity formula for a massless, multicomponent mixture under general anisotropic scatterings. Since the shear viscosity depends on a linearized collision kernel, an approximation formula for the linearized collision kernel is derived under elastic and anisotropic $l+k\rightarrow l+k$ scatterings. This derived approximation agrees very well with the isotropic two-body kernels provided in previous works for both like and different species. Furthermore, for multicomponent mixtures beyond two species types, an alternative expansion method of the $N$-component Chapman-Enskog viscosity is presented. This is applied to a two-component "binary" mixture and compared with the conventional formula for binary viscosity. The agreement between the two, for interacting and noninteracting binary mixtures, varies from moderate to well.

nucl-th↗

arXiv2024

Shear Viscosity of Collider-Produced QCD Matter I: AMY Formalism vs. A Modified Relaxation Time Approximation in 0-flavor SU(3) Theory

The AMY formalism is widely used to describe the transport coefficients of asymptotically hot and dense QCD matter, such as shear viscosity $η$. In literature prior to AMY, the viscosity of an asymptotically hot QCD plasma was expressed by a $q^2$ momentum transfer-weighted relaxation time approximation. Recent studies that compared numerical transport calculations and analytical expressions for $η$ demonstrated that asymptotically high temperatures and densities induce anisotropic scatterings, which are exhibited in the quark-gluon plasma produced by relativistic heavy ion collisions. In these studies, the QGP was treated as a Maxwell-Boltzmann-distributed gluon gas with added (anti-)quark degrees of freedom. One such method used in the comparison was the ``modified'' $q^2$ transport-weighted RTA. In this study, a comparison between the AMY formalism (both numerical calculations and next-leading-log expression) and the modified RTA expression for $η$ is made in 0-flavor SU(3) theory for collider-produced QGP. The comparison between numerical AMY calculations and the modified RTA method shows perfect agreement under the temperatures relevant for collider-produced QGP. Additionally, AMY is compared with the Chapman-Enskog method, which is well understood to better describe anisotropic collider-produced QGP.

nucl-th↗

arXiv2024

Non-Equilibrium Noise in V-Shape Linear Well Profiles

Non-equilibrium noise is characterized as noise realizations where external agitations disrupt the harmonic equilibrium of Brownian motion. Excitations in a particle's random walk into a so-called Lévy flight changes the distribution of the noise from Gaussian to the fat-tailed Lévy distribution. Generalization between Gaussian and Lévy distributions is the $α$-stability distribution, where $1<α\leq2$. In this study, the $α$-stability distributed noise is subjugated into the Langevin and fractional Fokker--Planck equations that correspond to a V-shaped linear potential well $V(x)=F|x|$. From these equations, an Euler scheme for computational simulation via iterations is presented, and a probability density function that is normalizable under any $α\in(1,2]$ is obtained. This study is focused more on the theoretical framework of non-equilibrium noise in V-shaped linear well profiles, which is intended to be applied to systems known to exhibit self-organized criticality.

cond-mat.stat-mech↗

arXiv2022

The shear viscosity of parton matter under anisotropic scatterings

The shear viscosity $η$ of a quark-gluon plasma in equilibrium can be calculated analytically using multiple methods or numerically using the Green-Kubo relation. It has been realized, which we confirm here, that the Chapman-Enskog method agrees well with the Green-Kubo result for both isotropic and anisotropic two-body scatterings. We then apply the Chapman-Enskog method to study the shear viscosity of the parton matter from a multi-phase transport model. In particular, we study the parton matter in the center cell of central and midcentral Au+Au collisions at $200A$ GeV and Pb+Pb collisions at $2760A$ GeV, which is assumed to be a plasma in thermal equilibrium but partial chemical equilibrium. As a result of using a constant Debye mass or cross section $σ$ for parton scatterings, the $η/s$ ratio increases with time (as the effective temperature decreases), contrary to the trend preferred by Bayesian analysis of the experimental data or pQCD results that use temperature-dependent Debye masses. At $σ=3$ mb that enables the transport model to approximately reproduce the elliptic flow data of the bulk matter, the average $η/s$ of the parton matter in partial equilibrium is found to be very small, between one to two times $1/(4π)$.

nucl-th↗