arXiv subjects

Andrea Fuster

Publications and source records attributed to Andrea Fuster.

13 recordsLinked to original sources

arXiv2026

Einstein-Kropina Metrics and Their Application in Finsler Gravity

We generalize the Einstein condition for Kropina metrics obtained in the positive definite setting by Zhang, Shen and others to all signatures. As examples of Einstein-Kropina metrics $L=L_{a,b}$, we construct new explicit positive definite ones and the first ones with Lorentzian signature. Next, we classify all Einstein-Kropina solutions to the vacuum equation of Finsler gravity by Pfeifer and Wohlfarth, in arbitrary dimension and including a possible cosmological constant $\Lambda$. For the Lorentzian and positive definite cases, the local picture is as follows. In dimension 4 or lower, only the trivial solution exists: a Minkowski or Euclidean space, essentially. In dimension 5 and higher, the solutions are those $L_{a,b}$ for which the metric $a$ is a product of the real line with a Ricci-flat metric (Lorentzian or Riemannian) and the vector field $b$ is the unique unit vector on the first factor. As a very surprising rigidity phenomenon, all Einstein-Kropina solutions to the $\Lambda$-vacuum equation are Berwald and Ricci-flat, and the cosmological constant necessarily vanishes.

math-ph↗

arXiv2025

Higher-curvature corrections and the endpoint of black hole evaporation in gravitational effective field theory

The endpoint of black hole evaporation remains uncertain once the semiclassical description approaches the Planck scale. In this work we study late-stage evaporation within four-dimensional gravitational effective field theory. We consider the leading local correction to the Schwarzschild solution arising from a cubic curvature operator, and use the corrected geometry to analyze the resulting evaporation dynamics and associated thermodynamic properties. We show that the cubic correction induces a parametric slow-down of the evaporation rate at small masses, which within the truncated theory can appear as a freeze-out at a finite mass scale. We demonstrate that this behavior is not an independent physical prediction, but instead occurs precisely when the dimensionless expansion parameter of the effective theory becomes of order unity. The corresponding mass scale coincides parametrically with the onset of Planckian curvature at the horizon, establishing that the evaporation dynamics provide a direct diagnostic of the breakdown of the effective field theory. A scaling analysis of higher-order curvature operators shows that once the cubic term becomes comparable to the Einstein-Hilbert contribution, generic higher-order terms are no longer parametrically suppressed. The apparent remnant-like behavior therefore arises at the boundary of validity of the effective description rather than within a controlled perturbative regime. These results demonstrate that late-stage evaporation encodes the limits of gravitational effective field theory, providing a dynamical criterion for its breakdown.

gr-qc↗

arXiv2024

New class of non-Einstein pp-wave solutions to quadratic gravity

We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves obtained by Madsen, a subset of which forms precisely the vacuum pp-waves of general relativity. If, on the other hand, the wave surfaces have non-vanishing constant curvature then all our solutions are non-Einstein (i.e. they do not solve Einstein's equations in vacuum, with or without cosmological constant) and we find that the curvature is linearly related to the value of the cosmological constant. We show that the vacuum field equations reduce to a simple linear biharmonic equation on the curved wave surfaces, and as consequence, the general solution can be written down. We also provide some simple explicit examples.

gr-qc↗

arXiv2023

A Cosmological Unicorn Solution to Finsler Gravity

We present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with the conformal factor depending only on the timelike coordinate. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe.

gr-qc↗

arXiv2023

Finsler gravitational waves of $(\alpha,\beta)$-type and their observational signature

We introduce a new class of $(\alpha,\beta)$-type exact solutions in Finsler gravity closely related to the well-known pp-waves in general relativity. Our class contains most of the exact solutions currently known in the literature as special cases. The linearized versions of these solutions may be interpretted as Finslerian gravitational waves, and we investigate the physical effect of such waves. More precisely, we compute the Finslerian correction to the radar distance along an nterferometer arm at the moment a Finslerian gravitational wave passes a detector. We come to the remarkable conclusion that the effect of a Finslerian gravitational wave on an interferometer is indistinguishable from that of standard gravitational wave in general relativity. Along the way we also physically motivate a modification of the Randers metric and prove that it has some very interesting properties.

gr-qc↗

arXiv2022

On the metrizability of $m$-Kropina spaces with closed null 1-form

We investigate the local metrizability of Finsler spaces with $m$-Kropina metric $F = \alpha^{1+m}\beta^{-m}$, where $\beta$ is a closed null 1-form. We show that such a space is of Berwald type if and only if the (pseudo-)Riemannian metric $\alpha$ and 1-form $\beta$ have a very specific form in certain coordinates. In particular, when the signature of $\alpha$ is Lorentzian, $\alpha$ belongs to a certain subclass of the Kundt class and $\beta$ generates the corresponding null congruence, and this generalizes in a natural way to arbitrary signature. We use this result to prove that the affine connection on such an $m$-Kropina space is locally metrizable by a (pseudo-)Riemannian metric if and only if the Ricci tensor constructed form the affine connection is symmetric. In particular we construct all counterexamples of this type to Szabo's metrization theorem, which has only been proven for positive definite Finsler metrics that are regular on all of the slit tangent bundle.

math.DG↗

arXiv2020

Randers pp-waves

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer and Wohlfarth's vacuum field equation of Finsler gravity for this class. We show that in this case the field equation is equivalent to the vanishing of the Finsler Ricci tensor, analogously to Einstein gravity. This implies that the considered vacuum field equation and Rutz's equation coincide in this scenario. We also construct all exact solutions of Berwald-Randers type to vacuum Finsler gravity, which turn out to be composed of a CCNV (covariantly constant null vector) Lorentzian spacetime, commonly known as pp-wave, and a 1-form given by the pp-wave distinguished null vector. We therefore refer to the found solutions as Randers pp-waves.

gr-qc↗

arXiv2020

On the non metrizability of Berwald Finsler spacetimes

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern-Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi-Civita connection of some Riemannian metric. We show for the first time that this result does not extend to Finsler spacetimes. More precisely, we find a large class of Berwald spacetimes for which the Ricci tensor of the affine connection is not symmetric. The fundamental difference from positive definite Finsler spaces that makes such an asymmetry possible, is the fact that generally, Finsler spacetimes satisfy certain smoothness properties only on a proper conic subset of the slit tangent bundle. Indeed, we prove that when the Finsler Lagrangian is smooth on the entire slit tangent bundle, the Ricci tensor must necessarily be symmetric. For large classes of Finsler spacetimes, however, the Berwald property does not imply that the affine structure is equivalent to the affine structure of a pseudo-Riemannian metric. Instead, the affine structure is that of metric-affine geometry with vanishing torsion.

math.DG↗

arXiv2019

Identifying Berwald Finsler Geometries

Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces to a necessary and sufficient condition for the Levi-Civita covariant derivative of the defining $1$-form. We illustrate our results with novel examples of $(\alpha,\beta)$-Berwald geometries which represent Finslerian versions of Kundt (constant scalar invariant) spacetimes. The results generalize earlier findings by Tavakol and van den Bergh, as well as the Berwald conditions for Randers and m-Kropina resp. very special/general relativity geometries.

math.DG↗

arXiv2018

Berwald spacetimes and very special relativity

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.

gr-qc↗

arXiv2016

Finsler pp-waves

In this work we present a Finslerian version of the well-known pp-waves, which generalizes the very special relativity (VSR) line element. Our Finsler pp-waves are an exact solution of Finslerian Einstein's equations in vacuum.

gr-qc↗

arXiv2005

Non-abelian Yang-Mills in Kundt spacetimes

We present new exact solutions of the Einstein-Yang-Mills system. The solutions are described by a null Yang-Mills field in a Kundt spacetime. They generalize a previously known solution for a metric of $pp$ wave type. The solutions are formally of Petrov type III.

gr-qc↗

arXiv2005

BRST-antifield Quantization: a Short Review

Most of the known models describing the fundamental interactions have a gauge freedom. In the standard path integral, it is necessary to "fix the gauge" in order to avoid integrating over unphysical degrees of freedom. Gauge independence might then become a tricky issue, especially when the structure of the gauge symmetries is intricate. In the modern approach to this question, it is BRST invariance that effectively implements gauge invariance. This set of lectures briefly reviews some key ideas underlying the BRST-antifield formalism, which yields a systematic procedure to path-integrate any type of gauge system, while (usually) manifestly preserving spacetime covariance. The quantized theory possesses a global invariance under the so-called BRST transformation, which is nilpotent of order two. The cohomology of the BRST differential is the central element that controls the physics. Its relationship with the observables is sketched and explained. How anomalies appear in the "quantum master equation" of the antifield formalism is also discussed. These notes are based on lectures given by MH at the 10th Saalburg Summer School on Modern Theoretical Methods from the 30th of August to the 10th of September, 2004 in Wolfersdorf, Germany and were prepared by AF and AM. The exercises which were discussed at the school are also included.

hep-th↗