arXiv subjects

Albert Huber

Publications and source records attributed to Albert Huber.

13 recordsLinked to original sources

arXiv2025

Bloch Motions and Spinning Tops

This work investigates the dynamics of closed quantum systems in the Bloch vector representation using methods from rigid body dynamics and the theory of integrable systems. To this end, equations of motion for Bloch components are derived from the von Neumann equation that are mathematically equivalent to equations of motion for a distribution of point masses from classical mechanics. Furthermore, using the Heisenberg equation, another system of Bloch vector equations is derived, which constitutes an Euler-Poinsot system of the type commonly encountered in the theory of torque-free spinning tops. This insight is used to prove the Liouville integrability of the corresponding Hamilton equations of motion and to construct an explicit closed-form solution using the Arnold-Liouville theorem. Within the same framework, stability criteria for quantum dynamics are then derived which correspond to the Energy-Casimir method of classical Newtonian mechanics. Following that, specific solutions to the equations of motion are constructed that encode the complex dynamics of composite quantum systems. Eventually, to show that this formalism provides concrete physical predictions, an analogue of the intermediate axis theorem is derived and the effect of oscillating entanglement is discussed. As a basis for this, special types of solutions to the equations of motion are derived that constitute oscillating entangled states, i.e., dynamical quantum states that change their entanglement structure from maximally entangled to separable and vice versa.

quant-ph↗

arXiv2025

Dynamical Horizons and Black Hole Soft Hair

In the present work, quasilocal Brown-York charges are derived that coincide in the large sphere limit with the conserved supertranslation hair and superrotation charges introduced by Hawking, Perry and Strominger in [45, 46]. Given these charges, a general scenario is outlined in which a non-rotating black hole completely evaporates after its collapse due to particle creation effects, whereby a genuine one-way traversable event horizon is never formed, but merely a two-way traversable dynamical (resp. future trapping) horizon. The formation of such a dynamical horizon has the consequence, as is demonstrated, that quasilocal energy transported by the considered charges, and thus information, can continuously escape through the black hole horizon to infinity; a mechanism which, as is argued, could possibly prevent information loss once the black hole formation and evaporation process comes to an end.

gr-qc↗

arXiv2025

General Shells and Generalized Functions

In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular regularizations of the Heaviside step function and the delta distribution, instead of working directly with the corresponding Schwartz distributions. Based on this change of method, the resulting extended thin shell formalism is shown to offer a decisive advantage over traditional approaches to the subject: it avoids dealing with ill-defined products of distributions in the calculation of nonlinear curvature expressions, thereby allowing for the treatment of problems that prove intractable with the 'conventional' thin-shell formalism. This includes, in particular, the problem of matching singular spacetimes with distributional metrics (containing a delta distribution term) across a joint boundary hypersurface in spacetime, the problem of setting up the dominant energy condition for thin shells, and the problem of defining reasonably rigorously nonlinear distribution-valued curvature invariants needed in higher-derivative theories of gravity. Eventually, as a further application, close links to Penrose's cut-and-paste method are established by proving that results of said method can be re-derived using the generalized formalism presented.

gr-qc↗

arXiv2023

Quasilocal Corrections to Bondi's Mass-Loss Formula and Dynamical Horizons

In this work, a null geometric approach to the Brown-York quasilocal formalism is used to derive an integral law that describes the rate of change of mass and/or radiative energy escaping through a dynamical horizon of a non-stationary spacetime. The result thus obtained shows - in accordance with previous results from the theory of dynamical horizons of Ashtekar et al. - that the rate at which energy is transferred from the bulk to the boundary of spacetime through the dynamical horizon becomes zero at equilibrium, where said horizon becomes non-expanding and null. Moreover, it reveals previously unrecognized quasilocal corrections to the Bondi mass-loss formula arising from the combined variation of bulk and boundary components of the Brown-York Hamiltonian, given in terms of a bulk-to-boundary inflow term akin to an expression derived in an earlier paper by the author [#huber2022remark]. For clarity, this is discussed with reference to the Generalized Vaidya family of spacetimes, for which derived integral expressions take a particularly simple form.

gr-qc↗

arXiv2021

Hidden Killing Fields, Geometric Symmetries and Black Hole Mergers

In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields - so-called hidden Killing vector fields - are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner-Nordstr\"om black holes.

gr-qc↗

arXiv2021

A remark on the quasilocal calculation of tidal heating: energy transfer through the quasilocal surface

In this note, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton. To this end, by performing a variation of the total gravitational Hamiltonian (bulk plus boundary part), it is shown that associated tidal heating and deformation effects generally are larger than expected. This is because this variation leads to previously unrecognized correction terms, including a bulk-to-boundary inflow term that does not appear in the original calculation of the time derivative of the Brown-York energy and leads to corrective extensions of Einstein's quadrupole formula in the large sphere limit.

gr-qc↗

arXiv2021

On the Stability of MOTS

In this paper, it is shown (using the NP-spin coefficient formalism) that the MOTS eigenvalue problem can be formulated - for certain classes of geometric models in GR - such that the MOTS stability operator takes a self-adjoint form, despite being a manifestly non-self-adjoint differential operator. This form is obtained by performing a suitable null rotation, which is chosen so that the MOTS under consideration remain such, i.e., transition into new MOTS. Next to the requirement that certain components of the Einstein tensor - resp. the stress-energy tensor - be zero, the main prerequisite for bringing the MOTS operator into the required form is the existence of a non-expanding null horizon together with a set of eigenfunctions of the MOTS operator that does not change along the Lie flow of the generator of said horizon. For illustration, the developed method is applied to the Kerr-Newman family of spacetimes.

gr-qc↗

arXiv2020

Distributional Metrics and the Action Principle of Einstein-Hilbert Gravity

In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry. Considering Colombeau's nonlinear theory of generalized functions, this result is extended to apply to an associated class of distributional Kerr-Schild geometries, and then used to formulate a variational principle for these singular spacetimes. More specifically, it is shown in this regard that a variation of a suitably regularized Einstein-Hilbert action can be performed even if the metric of one of the corresponding generalized Kerr-Schild representatives contains a generalized delta function that converges in a suitable limit to a delta distribution.

gr-qc↗

arXiv2019

The gravitational Field of a massless Particle on the Horizon of a stationary Black Hole

In this work, the field of a gravitational shockwave generated by a massless point-like particle is calculated at the event horizon of a stationary Kerr-Newman black hole. Using the geometric framework of generalized Kerr-Schild deformations in combination with the spin-coefficient formalism of Newman and Penrose, it is shown that the field equations of the theory, at the event horizon of the black hole, can be reduced to a single linear ordinary differential equation for the so-called profile function of the geometry. This differential relation is solved exactly. Based on the results obtained, a physical interpretation is given for the found shockwave spacetime, and it is clarified how these results lead back to those of previous works on the subject, which deal with the much simpler cases of gravitational shockwaves in static black hole backgrounds.

gr-qc↗

arXiv2019

On the Form of Solutions of Fuchsian differential Equations with n regular singular Points

The form of the coefficients of power series expressions corresponding to solutions of Fuchsian differential equations (or their associated degenerated confluent forms) with n regular singular points is determined by solving the corresponding n-term recurrence relations in full generality. Some important special cases are discussed in which the solutions coincide with special functions of mathematical physics.

math-ph↗

arXiv2019

On Kerr-Schild Symmetries and Conservation Laws in General Relativity

In the present work, the spin-coefficient formalism of Newman and Penrose is used to formulate geometric constraints for the existence of Kerr-Schild groups, i.e. continuous groups of generalized Kerr-Schild transformations. In addition, by characterizing the geometric structure of the deformed Einstein tensor of the generalized Kerr-Schild class, restrictions are imposed on the existence of apparent conservation laws in generic spacetimes, which are defined via considering special Kerr-Schild currents whose associated Kerr-Schild vector fields coincide with timelike Killing vector fields of pairs of stationary background geometries. The feasibility of the derived conditions is demonstrated by considering concrete, suitably simple models of generalized Kerr-Schild spacetimes.

gr-qc↗

arXiv2019

Null Foliations of Spacetime and the Geometry of Black Hole Horizons

In this work, a method for constructing null foliations of spacetime is presented. This method is used to specify equivalence classes of null generators, whose representatives can be associated lightlike co-normals that are locally affine geodesic and thus locally orthogonal to embedded null hypersurfaces of spacetime. The main benefit of the proposed procedure is the fact that it is less geometrically restrictive than the traditional dual-null approaches to general relativity, but nevertheless allows for the conclusion that spacetimes can be foliated by suitable pairs of normalized null geodesic vector fields. This is demonstrated by the example of different black hole spacetimes, that is, by members of the Kerr-Newman family, according to which a said foliation and an associated equivalence class of null generators are explicitly constructed.

gr-qc↗

arXiv2019

Junction Conditions and local Spacetimes in General Relativity

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is shown that two Lorentzian manifolds can be matched in agreement with the well-known Darmois-Israel junction conditions by locally deforming the associated spacetime metrics in relation to each other. Based on the insight that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in General Relativity. In addition, it is shown that this approach allows the treatment of problems that cannot be treated by using standard gluing techniques.

gr-qc↗