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Michael R. R. Good

Publications and source records attributed to Michael R. R. Good.

At least 19 recordsLinked to original sources
arXiv2026

Squeezed quantum states and partner modes in the moving mirror model of black hole evaporation

The standard moving mirror model in (1+1)-dimensional spacetime is known to reproduce several quantum aspects of black hole evaporation. A perfectly reflecting, accelerating mirror can emit radiation whose frequency spectrum resembles that of Hawking radiation, although this correspondence holds only under certain approximations. Moreover, the standard in-out formulation does not provide a natural notion of the partner modes associated with the Hawking radiation. In this paper, we reformulate the moving mirror model in terms of Rindler/Milne modes. This formulation not only attributes the origin of the required approximations to mode squeezing effects but also naturally incorporates the notion of partner modes. Furthermore, as a consequence of these mode squeezing effects, the radiation received by an inertial observer at future null infinity exhibits additional nontrivial quantum correlations, even though its frequency spectrum approximately follows a Bose--Einstein or Fermi--Dirac distribution.

gr-qc↗
arXiv2026

Optical and thermodynamic properties of Kerr-Bertotti-Robinson black holes

We investigate the thermodynamic and optical properties of Kerr--Bertotti--Robinson black holes, namely rotating black holes immersed in an external Bertotti--Robinson electromagnetic background. In the fixed-$a$ ensemble, we derive the horizon mass relation, the Hawking temperature, the entropy, the Helmholtz-type free energy, the heat capacity, and the extremal remnant configuration. These quantities reduce smoothly to their Kerr counterparts as $B\to0$. In the weak-field regime, the leading thermodynamic corrections arise at order $B^2$; the extremal radius is shifted at this order, whereas the remnant mass receives its first correction only at order $B^4$. We also introduce a formal AdS-like thermodynamic interpretation of the Bertotti--Robinson scale, treating the associated pressure as an effective response variable rather than a genuine cosmological pressure. Because the spacetime is not asymptotically flat, we further compute the finite-radius Komar mass and the Komar charge associated with the horizon generator. Using the Hamilton--Jacobi formalism, we derive the separated null-geodesic potentials, the impact parameters of spherical photon orbits, and the celestial coordinates of the shadow boundary for a finite-distance observer. We then characterize the photon-region boundaries, ergosphere thickness, photon--ergosphere gap, shadow area, and magnetic shadow susceptibility. Within the perturbative regime considered, the Bertotti--Robinson background decreases the averaged ergosphere thickness and shadow area, increases the photon--ergosphere gap, and produces a negative shadow susceptibility whose magnitude is enhanced by rotation.

gr-qc↗
arXiv2026

An advanced undergraduate derivation of acceleration thermality

The thermal radioactivity of beta-decay photons, described by a 1D Planck distribution, can be modeled as classical radiation emitted by an accelerated electron. Here, we present the basics of the out-of-equilibrium computation to illustrate acceleration thermality. Suitable for advanced undergraduate calculations, we demonstrate that an exactly soluble non-uniformly accelerated trajectory enables spectral analysis of the emitted photons, facilitates time evolution, and reveals Planckian radiation.

physics.class-ph↗
arXiv2026

Frenet-Serret equations with variable proper acceleration in Minkowski spacetime

We study Frenet-Serret equations for timelike worldlines in Minkowski spacetime with proper-time-dependent curvature and torsion. This corresponds to relativistic motion with non-uniform proper acceleration and, when torsion is included, to trajectories whose Frenet-Serret frame rotates beyond the acceleration plane. Using the Gram-Schmidt construction of the tetrad from the four-velocity and its derivatives, we relate the intrinsic Frenet-Serret parameters to kinematic quantities such as proper acceleration, four-jerk, and four-snap. We then consider simple analytic cases for the jerk invariant and torsion, obtaining explicit curvature profiles and reduced Frenet-Serret equations. These examples clarify how non-constant acceleration and torsion modify the geometry of accelerated relativistic motion.

gr-qc↗
arXiv2026

Apparent Fermionic Spectra for Bosonic Radiation: Accelerated Charge Kinematics

An accelerated point charge can emit photons with an apparent Fermi-Dirac spectrum, even though the radiation is bosonic and its occupation numbers are not constrained to 0 or 1. The effect arises from a special class of acceleration kinematics and does not rely on thermal equilibrium, horizons, or statistical ensembles.

quant-ph↗
arXiv2026

Planckian Gravitons from an Imaginary-Time Clock

We present a simple derivation of the exact Planck spectrum of the quadrupole radiation from point masses moving apart nonrelativistically, essentially an analog for gravitational radiation. The standard Einstein quadrupole radiation formula gives emitted power proportional to the square of the third derivative of $x(t)^2$. In our moving-mass picture, imaginary-time periodicity appears as a product-log trajectory of a quadrupole source. In the frequency domain, the power becomes proportional to the Planck distribution, $ω^3/(e^{2πcω/κ}-1)$. The resulting Planckian graviton energy spectrum has finite total energy and finite graviton number. The emitted spectrum is purely kinematic in origin: no equilibrium, horizon, or stochastic source is assumed.

gr-qc↗
arXiv2026

Self-Reflection in a Moving Mirror

We present an analytic flat-spacetime accelerating boundary analog of Hawking-type emission that possesses infinite asymptotic acceleration (and radial acceleration in the black hole analog) but finite total radiated energy (and zero surface gravity in the black hole analog). We perform a unified study of its scattering symmetry, horizon formation, asymptotically extreme acceleration, finite total radiated energy, and the distinction between local energy flux and global particle production within a single closed-form model. The particle spectrum, energy spectrum, and equivalent spacetime metric are derived, revealing an interesting mix of normal and extremal black hole properties.

gr-qc↗
arXiv2025

Particle creation from entanglement entropy

We investigate how entanglement entropy can drive particle creation, deriving explicit relations between entropy and the radiated particle spectrum, the total number of particles, and the total energy. Particle production is computed for scenarios that include accelerated motion, black hole evaporation, and beta decay, validating against known results while also extending them. We focus primarily on the low-entropy limit (analogous to non-relativistic motion), but also examine cases of significant particle production arising from harmonic cycles. The results establish an explicit operational link between information flow and matter creation, providing a concrete demonstration of 'it from bit'.

quant-ph↗
arXiv2025

Through the Looking-Glass, and What AdS Found There: quantum particle production with a Whittaker spectrum

Parity-inverted anti-de Sitter space -- ``flipped AdS'' -- is studied through the accelerating boundary correspondence of a moving mirror trajectory. The particle production exhibits positive energy flux and a finite total energy (both unlike AdS). The particle spectrum is of Whittaker form, with some similarities to a Planck thermal spectrum. We also derive the corresponding spacetime metric, with similarities to regular de Sitter space, but exhibiting a tower of repeated causal regions with horizons.

hep-th↗
arXiv2025

Cosmic Acceleration from Nothing

We demonstrate that if the universe started as a vacuum fluctuation rather than from a singular Big Bang state, the universe must have a late-time cosmic acceleration. This is required by a ``cosmological sum rule'' derived using the Schwarzian form of the Friedmann equations. We discuss possible connections to conformal and Möbius transformations, and also compute that the best fit present cosmic data is consistent with the necessary crossing of the Schwarzian through zero having occurred (while it would not yet have happened in a $Λ$CDM cosmology).

gr-qc↗
arXiv2025

Hawking Temperature and the Inverse-Radius Scale of the Horizon

The Hawking temperature of a Schwarzschild black hole can be heuristically derived by identifying the temperature with the inverse radius of the horizon up to a multiplicative constant. This does not work for more general black holes such as the Kerr and Reissner-Nordström solutions. Expounding on the details of how it fails to work nevertheless uncovers interesting connections with the "spring constant" of black holes and with black hole thermodynamics.

gr-qc↗
arXiv2024

There and Back Again: Quantum Radiation from Round-trip Flying Mirrors

Erasing a black hole leaves spacetime flat, so light passing through the region before any star forms and after black hole's evaporation shows no time delay, just like a flying mirror that returns to its initial starting point. Quantum radiation from a round-trip flying mirror has not been solved despite the model's mathematical simplicity and physical clarity. Here, we solve the particle creation from worldlines that asymptotically start and stop at the same spot, resulting in interesting spectra and symmetries, including the time dependence of thermal radiance associated with Bose-Einstein and Fermi-Dirac Bogolubov coefficients. Fourier analysis, intrinsically linked to the Bogolubov mechanism, shows that a thermal Bogolubov distribution does not describe the spin statistics of the quantum field.

quant-ph↗
arXiv2024

Electron-mirror duality and thermality

Classical electromagnetic radiation from moving point charges is foundational, but the thermal dynamics responsible for classical acceleration temperature are poorly understood. We investigate the thermal properties of classical electromagnetic radiation in the context of the correspondence between accelerated electrons and moving mirrors, focusing on three trajectories with asymptotically infinite (Davies-Fulling), asymptotically zero (Walker-Davies), and eternally uniform acceleration. The latter two are argued not to be thermal, while the former is found to emit thermal photons with a temperature that depends on the electron's speed. Thermal radiation from the mirror reveals a zero-jerk condition.

quant-ph↗
arXiv2024

Classical Acceleration Temperature (CAT) in a Box

A confined, slow-moving, accelerating electron is shown to emit thermal radiation. Since laboratories face spatial constraints when dealing with rectilinear motion, focusing on a finite total travel distance combines the benefits of simple theoretical analysis with prospects for table-top experimentation. We demonstrate an accelerated moving charge along an asymptotically static worldline with fixed transit distance and slow maximum speed, emitting self-consistent analytic power, spectra, and energy. The classical radiation is Planck distributed with an associated acceleration temperature. This is the first fully parametrized, spectrum-solved, finite-distance worldline.

physics.class-ph↗
arXiv2024

IR-finite thermal acceleration radiation

A charge accelerating in a straight line following the Schwarzschild-Planck moving mirror motion emits thermal radiation for a finite period. Such a mirror motion demonstrates quantum purity and serves as a direct analogy of a black hole with unitary evolution and complete evaporation. Extending the analog to classical electron motion, we derive the emission spectrum, power radiated, and finite total energy and particle count, with particular attention to the thermal radiation limit. This potentially opens the possibility of a laboratory analog of black hole evaporation.

gr-qc↗
arXiv2023

Accelerated electron thermometer: observation of 1D Planck radiation

We report on the observation of thermal photons from an accelerated electron via examination of radiative beta decay of free neutrons measured by the RDK II collaboration. The emitted photon spectrum is shown to corroborate a thermal distribution consistent with the dynamical Casimir effect. Supported by a robust chi-squared statistic, we find the photons reside in a one-dimensional Planck spectrum with a temperature predicted by the moving mirror model.

nucl-ex↗
arXiv2023

Phenomenological footprints of Lambda varying gravity theories inspired from quantum gravity models in the multi-messenger era

An interesting phenomenological consequence of Lambda varying gravity theories inspired by quantum gravity models is reported. The treatment in the present work is quite general and applicable to several different actions with Lambda varying, especially those used in RG approaches to quantum gravity. An effective gravitational action with a scale varying cosmological constant, Lambda, which depends on the system's characteristics, like the length and the energy density, is the key feature. If the system is an astrophysical object, like a cluster of galaxies, a black hole, etc, non-negligible corrections arise to several observable quantities. Distinctive footprints could refer to luminosity distance and strong/weak lensing measurements, among others. The present study focuses on the SNIa luminosity distance observable.

gr-qc↗