Searcharxiv⌕ Search

arXiv subjects

Frank Saueressig

Publications and source records attributed to Frank Saueressig.

At least 19 recordsLinked to original sources
arXiv2026

Starobinsky-inflation in asymptotically safe shift-symmetric scalar-tensor theory

We investigate the constraining power of scalaron-driven inflation on asymptotically safe scalar-tensor theories. Starting from a Horndeski-type theory and applying a renormalization group improvement procedure generates higher-derivative couplings which are fixed in terms of the microscopic parameters - a structure that is expected to occur also within first principle computations based on the asymptotic safety mechanism. The latter are taken to be the free parameters appearing at the Gaussian fixed point. We find that the free parameter initially associated with the non-minimal gravity-matter coupling is not confined to the gravity-matter sector of the theory and also enters the effective higher-derivative couplings in the gravitational sector. We review the setting of multi-field inflationary models which is appropriate to analyze the inflationary dynamics in this context and illustrate their applicability by working out the explicit bounds on the non-minimal gravity-matter coupling resulting from cosmological observations. Given the fixed point structure of asymptotically safe scalar-tensor theories, the results indicate that UV-completions by two of the three available non-Gaussian fixed points can be ruled out while pinpointing phenomenologically viable RG trajectories emanating from the third fixed point.

gr-qc↗
arXiv2026

Scaling Solutions of Matter Form Factors in Asymptotically Safe Quantum Gravity

We investigate the renormalization group flow of a gravity--matter system in which a scalar field is minimally coupled to Einstein gravity and its kinetic term is given by a scale-dependent form factor $f_Λ(-\Box)$. Employing the Wilsonian proper-time flow equation, we derive a closed integro-differential equation that encodes the dependence of the form factor on the UV cutoff $Λ$. We solve the resulting fixed-point problem with a pseudospectral discretization and find a non-trivial fixed point for which $f_\ast(-\Box)$ departs from the canonical $-\Box$ behavior. Linearizing the flow about this solution yields a discrete spectrum of perturbations and a corresponding set of critical exponents, indicating a non-trivial scaling structure in this non-local sector compatible with asymptotic safety. We also observe that the form factor becomes local once the UV cutoff is removed, suggesting that the bare action associated with this fixed point is local in the scalar two-point sector.

hep-th↗
arXiv2025

Cauchy Horizon (In)Stability of Regular Black Holes

A common feature of regular black hole spacetimes is the presence of an inner Cauchy horizon. The analogy to the Reissner-Nordström solution then suggests that these geometries suffer from a mass-inflation effect, rendering the Cauchy horizon unstable. Recently, it was shown that this analogy fails for certain classes of regular black holes, including the Hayward solution, where the late-time behavior of the mass function no longer grows exponentially but follows a power law. In this work, we extend these results in a two-fold way. First, we determine the basin-of-attraction for the power-law attractor, showing that the tamed growth of the mass function is generic. Second, we extend the systematic analysis to the Bardeen geometry, the Dymnikova black hole, and a spacetime arising from a non-singular collapse model newly proposed in the context of asymptotically safe quantum gravity. Remarkably, in the latter solution, the Misner-Sharp mass at the Cauchy horizon remains of the same order of magnitude of the mass of the black hole, since its growth is just logarithmic.

gr-qc↗
arXiv2025

Foliated Asymptotically Safe Gravity: Lorentzian Signature Fluctuations from the Wick Rotation

Asymptotic Safety constitutes a promising mechanism for a consistent and predictive high-energy completion of the gravitational interactions. To date, most results on the interacting renormalization group fixed point underlying the construction are obtained for Euclidean signature spacetimes. In this work, we use the Arnowitt-Deser-Misner (ADM) decomposition of the metric degrees of freedom and investigate the relations between the Euclidean and Lorentzian renormalization group flows resulting from the analytic continuation of the lapse function. We discuss the general conditions which guarantee the equivalence of the beta functions. These insights are illustrated based on the flow of the graviton two-point function within the Einstein-Hilbert truncation, demonstrating agreement of the Euclidean and Lorentzian settings. Hence the UV- and IR-completions identified in the Euclidean case are robust when changing spacetime signature. We take this as an important indicator that the Euclidean asymptotic safety mechanism carries over to Lorentzian signature spacetimes.

hep-th↗
arXiv2025

Zooming into the horizon region of black hole-type objects

A universal prediction of quantum gravity is that the dynamics of general relativity is augmented by interactions that are of higher order in the spacetime curvature. Numerical explorations indicate that such terms may have a drastic impact on black hole-type solutions by modifying the geometry close to the would-be event horizon in a substantial way. In this work, we perform the first systematic investigation of this blow-up mechanism within general relativity supplemented by quadratic gravity terms, the Goroff-Sagnotti counterterm, the combination of the two, and Einstein-Cubic Gravity. By studying linear perturbations of the Schwarzschild solution close to the Schwarzschild radius, we discover the following picture: the higher-derivative terms giving rise to extra degrees of freedom play a distinguished role. Once couplings associated with these terms enter the solution in the asymptotically flat region, a blow-up mechanism removes the event horizon and one deals with either a naked singularity or a wormhole. We believe that this finding is highly relevant when constraining the coefficients appearing in the Wilsonian description of gravity by observations.

gr-qc↗
arXiv2025

Dust collapse and horizon formation in Quadratic Gravity

Quadratic Gravity supplements the Einstein-Hilbert action by terms quadratic in the spacetime curvature. This leads to a rich phase space of static, compact gravitating objects including the Schwarzschild black hole, wormholes, and naked singularities. For the first time, we study the collapse of a spherically symmetric star with uniform dust density in this setting. We assume that the interior geometry respects the symmetries of the matter configuration, i.e., homogeneity and isotropy, thus it is insensitive to the Weyl-squared term and the interior dynamics is fully determined by $R$ and $R^2$. As our main result, we find that the collapse leads to the formation of a horizon, implying that the endpoint of a uniform dust collapse with a homogeneous and isotropic interior is not a horizonless spacetime. We also show that the curvature-squared contribution is responsible for making the collapse into a singularity faster than the standard Oppenheimer-Snyder scenario. Furthermore, the junction conditions connecting spacetime inside and outside the matter distribution are found to be significantly more constraining than their counterparts in General Relativity and we discuss key properties of any exterior solution matching to the spacetime inside the collapsing star. Finally, we comment on the potentially non-generic behavior entailed by our assumptions.

gr-qc↗
arXiv2024

On harvesting physical predictions from asymptotically safe quantum field theories

Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges on an interacting fixed point of the Wilsonian renormalization group flow which controls the microscopic dynamics. Connecting the fixed point to observations requires constructing the set of effective actions compatible with this microscopic dynamics. Technically, this information is stored in the UV-critical surface of the fixed point. In this work, we describe a novel approach for extracting this information based on analytical and pseudo-spectral methods. Our construction is illustrated at the level of the two-dimensional Ising model and easily generalizes to any asymptotically safe quantum field theory. It also constitutes an important step towards setting up a well-founded swampland program within the gravitational asymptotic safety program.

hep-th↗
arXiv2024

Rethinking the Effective Field Theory formulation of Gravity

General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory is not fundamental though, but constitutes the lowest order term in an effective field theory description of the gravitational force. As a consequence, the gravitational dynamics should receive corrections by higher-derivative terms. This essay discusses structural aspects associated with these corrections and summarizes their imprint on static, spherically symmetric geometries. Along these lines, we critically reassess the common practice of using local field redefinitions in order to simplify the dynamics at the danger of shifting physics effects into sectors which are beyond the approximation under consideration.

gr-qc↗
arXiv2024

On the impact of perturbative counterterms on black holes

We determine the corrections to the Schwarzschild geometry arising from including the Goroff- Sagnotti counterterm in the gravitational dynamics. We find that static, asymptotically flat, and spherically symmetric geometries are completely characterized by their asymptotic mass and the coupling associated with the counterterm. The latter induces distinct corrections at sixth order of the parameterized post-Newtonian expansion. The resulting spacetime geometries still exhibit an event horizon. In the parameter space accessible to numerical integration, the horizon area is smaller than its Schwarzschild counterpart, leading to an increase in the Hawking temperature. Corrections to the shadow size can be determined analytically and are used to give a first bound on the new coupling. While it is difficult to access the geometry inside of the event horizon, our analysis also provides evidence that the counterterm could resolve the curvature singularity appearing in the Schwarzschild geometry.

gr-qc↗
arXiv2024

Reply to "Comment" on "Regular evaporating black holes with stable cores"

We reply to the ``Comment'' on ``Regular evaporating black holes with stable cores'' by R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser. As a key result, we show that the regime of mass-inflation identified in the comment connects smoothly to the late-time attractors discovered in our works [A. Bonanno et. al., Regular black holes with stable cores, Phys. Rev. D 103, 124027 (2021) and Regular evaporating black holes with stable cores, Phys. Rev. D 107, 024005 (2023)]. Hence, the late-time stability of regular black holes is not affected by this intermediate phase.

gr-qc↗
arXiv2024

On the origin of almost-Gaussian scaling in asymptotically safe quantum gravity

The gravitational asymptotic safety program envisions the high-energy completion of gravity through an interacting renormalization group fixed point, the Reuter fixed point. The predictive power of the construction is encoded in the spectrum of the stability matrix which is obtained from linearizing the renormalization group flow around this fixed point. A key result of the asymptotic safety program is that parts of this spectrum exhibits an almost-Gaussian scaling behavior, entailing that operators which are classically highly UV-irrelevant do not induce new free parameters. In this article, we track down the origin of this property by contrasting the structure of the stability matrix computed from the Wetterich equation and the Composite Operator equation within the realm of f(R)-truncations. We show that the almost-Gaussian scaling is not linked to the classical part of the beta functions. It is a quantum-induced almost-Gaussian scaling originating from the quantum corrections in the flow equation. It relies on a subtle interplay among the analytic structure of the theory's two-point function and the way the Wetterich equation integrates out fluctuation modes. As a byproduct we determine the parts of the eigenmode spectrum which is robust with respect to changing the regularization procedure.

hep-th↗
arXiv2024

Global Flows of Foliated Gravity-Matter Systems

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation structure by encoding the gravitational degrees of freedom in a lapse function, shift vector, and a metric measuring distances on the spatial slices. We use the Wetterich equation to study the renormalization group flow of the graviton 2-point function extracted from the spatial metric. The flow is driven by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert action supplemented by minimally coupled scalar and vector fields. We derive bounds on the number of matter fields cast by asymptotic safety. Moreover, we show that the phase diagram obtained in the pure gravity case is qualitatively stable within these bounds. An intriguing feature is the presence of an IR-fixed point for the graviton mass which prevents the squared mass taking negative values. This feature persists for any number of matter fields and, in particular, also in situations where there is no suitable interacting fixed point rendering the theory asymptotically safe. Our work complements earlier studies of the subject by taking contributions from the matter fields into account.

hep-th↗
arXiv2023

Foliated asymptotically safe gravity in the fluctuation approach

The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key step in this program is the transition from Euclidean to Lorentzian signature spacetimes. One way to address this challenge is to formulate the quantum theory based on the Arnowitt-Deser-Misner decomposition of the metric field. This equips the Euclidean spacetime with a preferred direction which may serve as the time-direction in the Lorentzian setting. In this work we use the Wetterich equation in order to compute the renormalization group flow of the graviton two-point function. The resulting beta functions possess a non-Gaussian renormalization group fixed point suitable for rendering the theory asymptotically safe. The phase diagram underlying the flow of the two-point function is governed by the interplay between this non-Gaussian fixed point, the Gaussian fixed point, and an infrared fixed point. The latter ensures that the renormalized squared graviton mass cannot take negative values. These results are in qualitative agreement with fluctuation computations carried out in the covariant setting. We take this as non-trivial evidence that the asymptotic safety mechanism remains intact when considering quantum gravity on spacetimes carrying a foliation structure. Technically, our work constitutes the first fluctuation computation carried out within the ADM-framework. Therefore, we also provide a detailed discussion of the conceptual framework, highlighting the elements which differ from fluctuation computations in the covariant setting.

hep-th↗
arXiv2023

The Functional Renormalization Group in Quantum Gravity

The gravitational asymptotic safety program envisions a high-energy completion of the gravitational interactions by an interacting renormalization group fixed point, the Reuter fixed point. The primary tool for investigating this scenario are functional renormalization group equations, foremost the Wetterich equation. This equation implements the idea of the Wilsonian renormalization group by integrating out quantum fluctuations shell-by-shell in momentum space and gives access to the theory's renormalization group flow beyond the realm of perturbation theory. This chapter gives a pedagogical introduction to the gravitational asymptotic safety program with a specific focus on clarifying conceptual points which led to confusion in the past. We provide a step-by-step introduction to the Wetterich equation and its most commonly used non-perturbative approximations. This exposition also introduces recent developments including the minimal essential scheme and $N$-type cutoffs. The use of the Wetterich equation in explicit computations is illustrated within the Einstein-Hilbert truncation which constitutes the simplest non-perturbative approximation of the gravitational renormalization group flow. We conclude with a brief summary and comments on recent developments originating from other quantum gravity programs.

hep-th↗
arXiv2022

Stability properties of Regular Black Holes

Black holes encountered in general relativity are characterized by spacetime singularities hidden within an event horizon. These singularities provide a key motivation to go beyond general relativity and look for regular black holes where the spacetime curvature remains bounded everywhere. A prominent mechanism achieving this replaces the singularity by a regular patch of de Sitter space. The resulting regular geometries exhibit two horizons: the outer event horizon is supplemented by an inner Cauchy horizon. The latter could render the geometry unstable against perturbations through the so-called mass-inflation effect, i.e., an exponential growth of the mass function. This chapter reviews the mass-inflation effect for spherically symmetric black hole spacetimes contrasting the dynamics of the mass function for Reissner-Nordstöm and regular black holes. We also cover recent developments related to the late-time attractors induced by Hawking radiation which exorcise the exponential growth of the spacetime curvature encountered in the standard mass-inflation scenario. In order to make the exposition self-contained, we also briefly discuss basic properties of regular black holes including their thermodynamics.

gr-qc↗
arXiv2022

Regular black holes with stable cores

Non-singular black hole geometries typically come with two spacetime horizons: an (outer) event horizon and an (inner) Cauchy horizon. This nurtures the speculation that they may be subject to a mass-inflation effect which renders the Cauchy horizon unstable. We analyze the dynamics associated with spherically symmetric, regular black holes taking the full backreaction between the infalling matter and geometry into account. On this basis, we identify the crucial features taming the growth of the mass function and diminishing the curvature singularity at the Cauchy horizon. It is demonstrated explicitly that the regular black hole solutions proposed by Hayward and obtained from Asymptotic Safety satisfy these properties.

gr-qc↗
arXiv2022

Form Factors in Asymptotically Safe Quantum Gravity

Asymptotic Safety implies that observables including scattering amplitudes remain finite at the highest energy scales. Traditionally, this feature is connected to an interacting fixed point of the Wilsonian renormalization group that provides the high-energy completion of the theory. In this article, we discuss a different facet of Asymptotic Safety, reviewing its imprint on the quantum effective action. We start with a concise introduction to the form factor framework for gravity and gravity-matter systems, before giving an encyclopaedic overview of gravity-mediated scattering amplitudes derived from the quantum effective action. We illustrate the use of the framework based on form factors appearing in the context of quadratic gravity and Asymptotic Safety, before making the connections to positivity bounds derived for low-energy effective field theories and the computation of form factors from first principles. We conclude that the form factor framework offers a unique, unifying perspective on quantum gravity. In particular, it plays a pivotal role in determining the phenomenological consequences of Asymptotic Safety at the level of observables.

hep-th↗