arXiv subjects

Sebastian Murk

Publications and source records attributed to Sebastian Murk.

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.

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arXiv2026

Connecting Quantum Tomography and Quantum Retrodiction

Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks: tomography reconstructs quantum states from measurement data, whereas retrodiction infers past quantum states from observed outcomes. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map associated with a measurement channel is precisely the gradient update of the log-likelihood used in maximum-likelihood tomography. Consequently, repeated applications of the Petz map monotonically increase the likelihood. Extending beyond measurement channels, we derive a noncommutative generalization of the Petz map from the gradient of a generalized likelihood for arbitrary quantum channels. The resulting iterative procedure maximizes the likelihood and provides a general framework for quantum tomography, establishing a direct bridge between retrodiction, recovery maps, and statistical inference.

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arXiv2025

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

Thermodynamics of Regular Black Holes in Anti-de Sitter Space

We construct regular black holes with anti-de Sitter asymptotics in theories incorporating infinite towers of higher-order curvature corrections in any dimension $D \ge 5$. We find that regular black branes are generically inner-extremal, potentially evading instabilities typically associated with inner horizons. Considering minimally coupled matter, we establish general criteria for the existence of singularity-free solutions. We analyze solutions coupled to Maxwell and nonlinear (Born--Infeld and RegMax) electrodynamics, demonstrating in the latter case the first examples of fully regular gravitational and electromagnetic fields for all parameter values. Here, we find that the ratio of the gravitational mass to the electrostatic self-energy determines whether the regular core is de Sitter or anti-de Sitter. We perform a detailed analysis of the black hole thermodynamics and show that the equation of state exhibits features akin to those of fluids with a finite molecular volume induced by the regularization parameter.

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arXiv2024

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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arXiv2024

Light rings and causality for nonsingular ultracompact objects sourced by nonlinear electrodynamics

We study observational signatures of nonsingular ultracompact objects regularized by nonlinear electrodynamics. The phenomenon of birefringence causes photons of different polarizations to propagate with respect to two distinct metrics, which manifests itself in the appearance of additional light rings surrounding the ultracompact object. We analyze the observational consequences of this result and illustrate our findings based on three regular black hole models commonly considered in the literature. We find that nonsingular horizonless ultracompact objects sourced by nonlinear electrodynamics possess an odd number of light rings and discuss the viability of this model as an effective description of their properties. In addition, we compare the phase velocities of polarized light rays propagating in nonsingular geometries sourced by nonlinear electrodynamics to the corresponding phase velocity in the Schwarzschild spacetime and demonstrate that regularizing the singularity by means of a theory that does not adhere to the Maxwell weak-field limit may lead to the emergence of acausal regions.

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arXiv2024

Categorical Quantum Volume Operator

We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with irreducible representations of $\mathrm{SU}(2)$. Here, we show two equivalent constructions that allow general objects in fusion categories as degrees of freedom. First, we compute the volume operator for ribbon fusion categories. This includes the important class of modular tensor categories (such as quantum doubles), which are the building blocks of anyon models. Second, we further generalize the volume operator to spherical fusion categories by relaxing the categorical analog of the closure constraint (known as tetrahedral symmetry). In both cases, we obtain a volume operator that is Hermitian, provided that the input category is unitary. As an illustrative example, we consider the case of $\mathrm{SU}(2)_k$ and show that the standard $\mathrm{SU}(2)$ volume operator is recovered in the limit $k\rightarrow\infty$.

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arXiv2023

Probability vector representation of the Schr\"odinger equation and Leggett-Garg-type experiments

Leggett-Garg inequalities place bounds on the temporal correlations of a system based on the principles of macroscopic realism $\textit{per se}$ and noninvasive measurability. Their conventional formulation relies on the ensemble-averaged products of observables measured at different instants of time. However, a complete description that enables a precise understanding and captures all physically relevant features requires the study of probability distributions associated with noncommuting observables. In this article, we propose a scheme to describe the dynamics of generic $N$-level quantum systems ("qudits") via a probability vector representation of the Schr\"odinger equation and define a precise notion of no-signaling in time (NSIT) for the probability distributions of noncommuting observables. This provides a systematic way of identifying the interferences responsible for nonclassical behavior. In addition, we introduce an interference witness measure to quantify violations of NSIT for arbitrary general probabilistic states. For single-qubit systems, we pinpoint the pivotal relation that establishes a connection between the disturbance of observables incurred during a measurement and the resulting NSIT violation. For large-$N$ systems where a manual determination is infeasible, the classification of states as either NSIT-conforming or NSIT-violating may be performed by a machine learning algorithm. We present a proof-of-principle implementation of such an algorithm in which the classifier function is prepared via supervised learning using pseudorandomly generated training data sets composed of states whose corresponding classifications are known $\textit{a priori}$.

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arXiv2023

Kinematic and energy properties of dynamical regular black holes

Nonsingular black holes have received much attention in recent years as they provide an opportunity to avoid the singularities inherent to the mathematical black holes predicted by general relativity. Based on the assumption that semiclassical physics remains valid in the vicinity of their horizons, we derive kinematic properties of dynamically evolving spherically symmetric regular black holes. We review the Hawking--Ellis classification of their associated energy-momentum tensors and examine the status of the null energy condition in the vicinity of their horizons as well as their interior. In addition, we analyze the trajectory of a moving observer, find that the horizons can be crossed on an ingoing geodesic, and thus entering and exiting the supposedly trapped spacetime region is possible. We outline the ramifications of this result for the information loss problem and black hole thermodynamics. Throughout the article, we illustrate relevant features based on the dynamical generalization of the regular black hole model proposed in J. High Energy Phys. 09, 118 (2022) and elucidate connections to the only self-consistent dynamical physical black hole solutions in spherical symmetry.

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arXiv2023

Regular black holes and the first law of black hole mechanics

Singularity-free regular black holes are a popular alternative to the singular mathematical black holes predicted by general relativity. Here, we derive a generic condition that spherically symmetric dynamical regular black holes must satisfy to be compatible with the first law of black hole mechanics based on an expression for the surface gravity at the outer horizon. We examine the dynamical generalizations of models typically considered in the literature and demonstrate that none of them satisfies the condition required for compatibility with the first law, suggesting that modifications are required to maintain its physical meaning. We show that the need for corrections is inherently linked to the introduction of a minimal length scale and can therefore be seen as a direct consequence of the spacetime regularization. We explicitly identify the additional work terms in the extended first law, comment on their thermodynamic interpretation, and show that the linear coefficient of the Misner-Sharp mass suffices to determine the relevant thermodynamic properties.

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arXiv2022

Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes

Black holes play a pivotal role in the foundations of physics, but there is an alarming discrepancy between what is considered to be a black hole in observational astronomy and theoretical studies. Despite claims to the contrary, we argue that identifying the observed astrophysical black hole candidates as genuine black holes is not justified based on the currently available observational data, and elaborate on the necessary evidence required to support such a remarkable claim. In addition, we investigate whether the predictions of semiclassical gravity are equally compatible with competing theoretical models, and find that semiclassical arguments favor horizonless configurations.

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arXiv2021

Black holes and their horizons in semiclassical and modified theories of gravity

For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

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arXiv2021

Constraining modified gravity theories with physical black holes

We review the constraints modified theories of gravity must satisfy to be compatible with the spherically symmetric black hole solutions of semiclassical gravity that describe the formation of an apparent horizon in finite time of a distant observer. The constraints are satisfied in generic modified gravity theories with up to fourth-order derivatives in the metric, indicating that the semiclassical solutions correspond to zeroth-order terms in perturbative solutions of these models. From an observational point of view, this result implies that it may not be possible to distinguish between the semiclassical theory and modifications including up to fourth-order derivatives based on the observation of an apparent horizon alone.

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arXiv2021

Physical black holes in fourth-order gravity

The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the formation of an apparent horizon in finite time of a distant observer. Moreover, the formation of black holes follows a unique scenario involving both types of solutions. To be compatible with their existence, any self-consistent theory of modified gravity must satisfy several constraints. We derive properties of the modified gravity terms of f(R) and generic fourth-order gravity theories and find that they naturally accommodate both classes of solutions. Consequently, the observation of an apparent horizon by itself may not suffice to distinguish between general relativity and modifications including up to fourth-order derivatives in the metric.

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arXiv2021

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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arXiv2021

Semiclassical black holes and horizon singularities

In spherical symmetry, solutions of the semiclassical Einstein equations belong to one of two possible classes. Both classes contain solutions that -- depending on the dynamic behavior of the horizon -- describe evaporating physical black holes or expanding white holes (trapped/anti-trapped regions that form in finite time of a distant observer). These solutions are real-valued only if the null energy condition (NEC) is violated in the vicinity of the Schwarzschild sphere. We review their properties and describe the only consistent black hole formation scenario. While the curvature scalars are finite on the outer apparent/anti-trapping horizon, it is still a weakly singular surface. This singularity manifests itself in a mild firewall. Near the inner apparent horizon, the NEC is satisfied. Models of static regular black holes are known to be unstable, but since dynamic models of regular black holes are severely constrained by self-consistency requirements, their stability requires further investigation.

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arXiv2021

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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arXiv2020

Spherically symmetric black holes in metric gravity

The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and its regularity is consistent with only two distinct classes of physical black holes. Here we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Both of the GR solutions can be regarded as zeroth-order terms in perturbative solutions of this model. We also show how to construct nonperturbative solutions without a well-defined GR limit.

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