arXiv subjects

Daniel R. Terno

Publications and source records attributed to Daniel R. Terno.

At least 19 recordsLinked to original sources

arXiv2026

Covariant variation for point-particle Lagrangians

Structureless test particles in general relativity follow geodesics. For extended bodies, higher-order multipole moments lead to departures from geodesic motion; in particular, spinning test bodies obey the Mathisson--Papapetrou--Dixon (MPD) equations. Similarly, the leading correction to the eikonal approximation for electromagnetic-wave propagation can be formulated as the nongeodesic propagation of spinning null particles. When the resulting equations are treated as standalone worldline models, with the relevant dynamical quantities defined only along the representative worldline, their variational formulation requires particular care.Following DeWitt's construction, we distinguish several types of variation, define the corresponding covariant variation for each, and identify the role of parallel transport in models that couple worldline variables to tensor fields. This framework simplifies the variational treatment of the MPD equations and yields a simple Lagrangian for the null-particle model of light propagation.

gr-qc↗

arXiv2026

Apparent horizon as a membrane

The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of the near-horizon geometry of these physical black holes is complete and shows marked differences from their eternal counterparts. Whether these differences lead to observable signatures remains unclear. We construct an approximate near-horizon metric that encapsulates them and is suitable for modeling. The timelike apparent horizon of physical black holes provides a natural surface for a consistent membrane description: we obtain closed-form expressions for the redshift, proper acceleration, and extrinsic curvature, and assign a two-dimensional viscous-fluid stress tensor via junction conditions. These results also provide an additional perspective on the relation between Rindler and near-horizon geometries. Among dynamical generalizations of surface gravity, only a subset applies to these models. We complete their analysis and recover the intuitive definition of surface gravity -- the acceleration in the frame of a near-horizon observer, redshifted to infinity -- directly from the membrane acceleration.

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arXiv2026

Classical-quantum gravity as quantum gravity in disguise

Whether gravity must be quantized remains one of the biggest open problems in fundamental physics. Classical-quantum hybrid theories have recently attracted attention as a possible framework in which gravity is treated classically yet interacts consistently with quantum matter. Schemes based on completely positive dynamics satisfy most formal consistency requirements and enable a systematic treatment of quantum backreaction, but they also invite the question of whether the hybrid description is fundamental or instead an effective sector of a larger quantum theory. Here, we demonstrate that classical-quantum gravity based on completely positive dynamics admits an embedding into a fully quantum theory on an enlarged Hilbert space. As a complementary illustration, we consider a qubit interacting with a classical particle and demonstrate that the corresponding hybrid system violates angular momentum conservation despite rotational symmetry of the underlying equations of motion. This provides an explicit example of a fully closed, rotationally invariant classical-quantum system with completely positive dynamics that violates a conservation law.

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arXiv2025

Exotic Encounters: Buchdahl's Conditions and Physical Black Holes

Black holes are among the most well-known astrophysical objects, yet their physical realisation remains conceptually subtle. We analyse physical black holes -- light-trapping regions that form in finite time as seen by a distant observer -- and investigate the properties of the matter required to support them. Taking Buchdahl's theorem as a benchmark, we show that these configurations necessarily violate at least two of its four original conditions, and the post-formation state violates them all. These violations are substantial: they include the null energy condition, non-monotonic energy profiles, and strong pressure anisotropies. Thus, the requirement of truly forming a horizon places physical black holes in a class of solutions that are more exotic than exotic compact objects.

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arXiv2025

Padé metrics for black hole perturbations and light rings

Most distinguishing features of black holes and their mimickers are concentrated near the horizon. In contrast, astrophysical observations and theoretical considerations primarily constrain the far-field geometry. In this work we develop tools to effectively describe both, using the two-point Padé approximation to construct interpolating metrics connecting the near and far-field. We extend our previous work by computing the quasinormal modes of gravitational perturbations for static, spherically symmetric metrics that deviate from Schwarzschild spacetime. Even at the lowest order, this approach compares well with existing methods in both accuracy and applicability. Additionally, we show that the lowest-order interpolating metric reliably predicts light ring locations. It closely matches exact results, even when unsuitable for quasinormal frequency calculations.

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arXiv2025

Gravity-induced birefringence in spherically symmetric spacetimes

Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light propagation in a vacuum is typically modeled by rays that follow null geodesics. However, general relativity predicts that polarization-dependent deviations from these geodesics occur in an inhomogeneous gravitational field. In this article, we evaluate the corrections for the deflection and emission of light by a massive gravitating body. Additionally, we derive the scaling behavior of the physical parameters characterizing the trajectories. The calculations are performed at leading order in frequency. We use these results to assess the significance of the birefringence effect in various astrophysical observations. We find that the effect cannot be measured with current instruments but may be detectable in the near future.

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arXiv2025

Horizon-bound objects: Kerr--Vaidya solutions

Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are consistent with the formation of a trapped region in finite time according to distant observers. We examine different classes of Kerr-Vaidya metrics, and find two which possess spherically-symmetric counterparts that are compatible with the finite formation time of a trapped region. These solutions describe evaporating black holes and expanding white holes. We demonstrate a consistent description of accreting black holes based on the ingoing Kerr--Vaidya metric with increasing mass, and show that the model can be extended to cases where the angular momentum to mass ratio varies. For such metrics we describe conditions on their dynamical evolution required to maintain asymptotic flatness. Pathologies are also identified in the evaporating white hole geometry in the form of an intermediate singularity accessible by timelike observers. We also describe a generalization of the equivalence between Rindler and Schwarzschild horizons to Kerr--Vaidya black holes, and describe the relevant geometric constructions.

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arXiv2024

Structure and statistical properties of the semiclassical Einstein equations

We treat the semiclassical Einstein equation as a quantum-classical hybrid and demonstrate the formal equivalence of its two derivation methods. This approach identifies the left-hand side of the equation as the expectation value of the Einstein tensor given the state of matter, and not its actual value in each realization of the set-up. As a result, standard criticisms of semiclassical gravity do not apply, and stochastic gravity emerges as a necessary extension

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arXiv2024

Semi-classical imprints on quasinormal mode spectra

We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity. These assumptions lead to a highly constrained yet non-trivial form of the metric and components of the energy-momentum tensor near the horizon, which contain as a special case many known models of black holes. Using a two-point M-fraction approximation to construct an interpolating metric which captures the essential near-horizon and asymptotic properties of black holes, we explore a large part of the parameter space that characterizes the near-horizon geometry. We cast the perturbation problem as a discretized homogeneous eigensystem and compute the low-lying quasinormal mode frequencies for perturbations of a massless scalar field. Working in spherical symmetry, we provide rough constraints on leading and subleading deviations from the Schwarzschild solution which arise in a semi-classical setting, and demonstrate the potential for mimicking signatures of axially-symmetric geometries from a spherically-symmetric source.

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arXiv2024

Paradoxes before the paradox: surface gravity and the information loss problem

The information loss paradox is widely regarded as one of the biggest open problems in theoretical physics. Several classical and quantum features must be present to enable its formulation. First, an event horizon is needed to justify the objective status of tracing out degrees of freedom inside the black hole. Second, evaporation must be completed (or nearly completed) in finite time according to a distant observer, and thus the formation of the black hole should also occur in finite time. In spherical symmetry these requirements constrain the possible metrics strongly enough to obtain a unique black hole formation scenario and match their parameters with the semiclassical results. However, the two principal generalizations of surface gravity, the quantity that determines the Hawking temperature, do not agree with each other on the dynamical background. Neither can correspond to the emission of nearly-thermal radiation. We infer from this that the information loss problem cannot be consistently posed in its standard form.

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arXiv2024

From reasonable postulates to generalised Hamiltonian systems

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In both quantum and classical mechanics, Hamiltonian mechanics demands a precise relationship between time evolution and observable energy, albeit using slightly different terminology. We distil basic conditions satisfied in both quantum and classical mechanics, including canonical coordinate symmetries and inner product invariance. We express these conditions in the framework of generalised probabilistic theories, which includes generalizing the definition of energy eigenstates in terms of time-invariant properties of the Hamiltonian system. By postulating these conditions to hold, we derive a unified Hamiltonian system model. This unified framework describes quantum and classical mechanics in a consistent language, facilitating their comparison. We moreover discuss alternative theories: an equation of motion given by a mixture of commutation relations, an information-restricted version of quantum theory, and Spekken's toy theory. The findings give a deeper understanding of the Hamiltonian in quantum and classical theories and point to several potential research topics.

quant-ph↗

arXiv2024

Unification of energy concepts in generalised phase space theories

We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. We give general operational definitions of energy-related concepts. We define generalised energy eigenstates as the purest stationary states. Planck's constant plays two different roles in the framework: the phase space volume taken up by a pure state and a dynamical factor. The Hamiltonian is a linear combination of generalised energy eigenstates. This allows for a generalised Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics and more. The approach enables a unification of quantum and classical energy concepts and a route to discussing energy in a wider set of theories.

quant-ph↗

arXiv2024

Classical-Quantum Hybrid Models

Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the motivation for such models, outline the requirements they must satisfy, and provide explanations for their development. Then we review various popular non-relativistic schemes and their associated limitations, with a particular emphasis on reversible dynamics.

quant-ph↗

arXiv2023

Models of cosmological black holes

We study various aspects of modeling astrophysical black holes using the recently introduced semiclassical formalism of physical black holes (PBHs). This approach is based on the minimal requirements of observability and regularity of the horizons. We demonstrate that PBHs do not directly couple to the cosmological background in the current epoch, and their equation of state renders them unsuitable for describing dark energy. Utilizing their properties for analysis of more exotic models, we present a consistent semiclassical scenario for a black-to-white hole bounce and identify obstacles to the transformation from a black hole horizon to a wormhole mouth.

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arXiv2023

Black holes as spherically-symmetric horizon-bound objects

Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption of regularity of the renormalized expectation value of the energy-momentum tensor, and derive explicit coordinate transformations in the near-horizon region. We examine the boundary conditions appropriate for embedding the model into a cosmological background, describe their evaporation in the linear regime and highlight the observational consequences, while also discussing the implications for the laws of black hole mechanics.

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arXiv2023

Proposal for an optical interferometric measurement of the gravitational red-shift with satellite systems

The Einstein Equivalence Principle (EEP) underpins all metric theories of gravity. One of its key aspects is the local position invariance (LPI) of non-gravitational experiments, which is captured by the gravitational red-shift. The iconic gravitational red-shift experiment places two fermionic systems, used as clocks, in different gravitational potentials and compares them using the electromagnetic field. However, the electromagnetic field itself can be used as a clock, by comparing the phases acquired by two optical pulses propagating through different gravitational potentials. A fundamental point in the implementation of a satellite large-distance optical interferometric experiment is the suppression of the first-order Doppler effect, which dominates the weak gravitational signal necessary to test the EEP. Here, we propose a novel scheme to suppress it, by subtracting the phase-shifts measured in the one-way and in the two-way configuration between a ground station and a satellite. We present a detailed analysis of this technique within the post-Newtonian framework and perform some simulations of its performance using realistic satellite orbits and the state-of-the-art fiber technology at the telecom wavelength of 1550 nm.

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arXiv2022

Matter and forces near physical black holes

We describe general features of formation and disappearance of regular spherically symmetric black holes in semiclassical gravity. The allowed models are critically dependent on the requirement that the resulting objects evolve in finite time according to a distant observer. Violation of the null energy condition (NEC) is mandatory for this to happen, and we study the properties of the necessary energy-momentum tensor in the vicinity of the apparent horizon. In studies of the kinematics of massive test particles, it is found that the escape from a black hole is possible only on the ingoing trajectories when the particles are overtaken by the contracting outer apparent horizon. Tidal forces experienced by geodesic observers, infalling or escaping, are shown to be finite at the apparent horizon, although this is not true for nongeodesic trajectories.

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arXiv2022

Physical black holes in semiclassical gravity

We derive and critically examine the consequences that follow from the formation of a regular black or white hole horizon in finite time of a distant observer. In spherical symmetry, only two distinct classes of solutions to the semiclassical Einstein equations are self-consistent. Both are required to describe the formation of physical black holes and violate the null energy condition in the vicinity of the outer apparent horizon. The near-horizon geometry differs considerably from that of classical solutions. If semiclassical physics is valid, accretion into a black hole is no longer possible after the horizon has formed. In addition, the two principal generalizations of surface gravity to dynamical spacetimes are irreconcilable, and neither can describe the emission of nearly-thermal radiation. Comparison of the required energy and timescales with established semiclassical results suggests that if the observed astrophysical black holes indeed have horizons, their formation is associated with new physics.

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