arXiv subjects

Aaron Held

Publications and source records attributed to Aaron Held.

At least 37 records · Page 2Linked to original sources

arXiv2023

Global and Local Stability for Ghosts Coupled to Positive Energy Degrees of Freedom

Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy degree of freedom interacts with a ghost. These theories have Hamiltonians unbounded from above and from below, are integrable, and contain free functions. We show analytically that their classical motion is bounded for all initial data. Moreover, we derive conditions allowing for Lyapunov stable equilibrium points. A subclass of these stable systems has simple polynomial potentials with stable equilibrium points entirely due to interactions with the ghost. All these findings are fully supported by numerical computations which we also use to gather evidence for stability in various nonintegrable systems.

gr-qc↗

arXiv2023

Scale-invariance at the core of quantum black holes

We study spherically-symmetric solutions to a modified Einstein-Hilbert action with Renormalization Group scale-dependent couplings, inspired by Weinberg's Asymptotic Safety scenario for Quantum Gravity. The Renormalization Group scale is identified with the Tolman temperature for an isolated gravitational system in thermal equilibrium with Hawking radiation. As a result, the point of infinite local temperature is shifted from the classical black-hole horizon to the origin and coincides with a timelike curvature singularity. Close to the origin, the spacetime is determined by the scale-dependence of the cosmological constant in the vicinity of the Reuter fixed point: the free components of the metric can be derived analytically and are characterized by a radial power law with exponent $α= \sqrt{3}-1$. Away from the fixed point, solutions for different masses are studied numerically and smoothly interpolate between the Schwarzschild exterior and the scale-invariant interior. Whereas the exterior of objects with astrophysical mass is described well by vacuum General Relativity, deviations become significant at a Planck distance away from the classical horizon and could lead to observational signatures. We further highlight potential caveats in this intriguing result with regard to our choice of scale-identification and identify future avenues to better understand quantum black holes in relation to the key feature of scale-invariance.

gr-qc↗

arXiv2022

Black holes in asymptotically safe gravity and beyond

Asymptotically safe quantum gravity is an approach to quantum gravity that achieves formulates a standard quantum field theory for the metric. Therefore, even the deep quantum gravity regime, that is expected to determine the true structure of the core of black holes, is described by a spacetime metric. The essence of asymptotic safety lies in a new symmetry of the theory -- quantum scale symmetry -- which characterizes the short-distance regime of quantum gravity. It implies the absence of physical scales. Therefore, the Newton coupling, which corresponds to a scale, namely the Planck length, must vanish asymptotically in the short-distance regime. This implies a weakening of the gravitational interaction, from which a resolution of classical spacetime singularities can be expected. In practise, properties of black holes in asymptotically safe quantum gravity cannot yet be derived from first principles, but are constructed using a heuristic procedure known as Renormalization Group improvement. The resulting asymptotic-safety inspired black holes have been constructed both for vanishing and for nonvanishing spin parameter. They are characterized by (i) the absence of curvature singularities, (ii) a more compact event horizon and photon sphere, (iii) a second (inner) horizon even at vanishing spin and (iv) a cold remnant as a possible final product of the Hawking evaporation. Observations can start to constrain the quantum-gravity scale that can be treated as a free parameter in asymptotic-safety inspired black holes. For slowly-spinning black holes, constraints from the EHT and X-ray observations can only constrain quantum-gravity scales far above the Planck length. In the limit of near-critical spin, asymptotic-safety inspired black holes may ``light up" in a way the ngEHT may be sensitive to, even for a quantum-gravity scale equalling the Planck length.

gr-qc↗

arXiv2022

Instability of spherically-symmetric black holes in Quadratic Gravity

We investigate the linear stability of the two known branches of spherically-symmetric black holes in Quadratic Gravity. We extend previous work on the long-wavelength (Gregory-Laflamme) instability of the Schwarzschild branch to a corresponding long-wavelength instability in the non-Schwarzschild branch. In both cases, the instability sets in below a critical horizon radius at which the two black-hole branches intersect. This suggests that classical perturbations enforce a lower bound on the horizon radius of spherically-symmetric black holes in Quadratic Gravity.

gr-qc↗

arXiv2022

Quantum gravity lights up spinning black holes

Quantum-gravity effects in black holes are generally expected to be unobservable if they set in at transplanckian curvature scales. Here, we challenge this expectation. A near-critical spin parameter can serve as a lever arm that translates Planckian quantum-gravity effects to a global change in the spacetime: the horizon dissolves and the black hole "lights up". We investigate this transition between a black hole and a horizonless spacetime and find that additional lensing features appear instantaneously, when the quantum-gravity effect is added. In the presence of an accretion disk, a second set of internal photon rings appears in addition to the exponentially stacked set of external photon rings. The internal and external photon rings merge into cresent-like features as a function of increasing spin parameter. We explore how these simulated images would be reconstructed by a radio-very-long-baseline-interferometry array like the Event Horizon Telescope. We find that a future next-generation Event Horizon Telescope may be sensitive to the additional lensing features.

gr-qc↗

arXiv2022

Parameterizations of black-hole spacetimes beyond circularity

We discuss parameterizations of black-hole spacetimes in and beyond General Relativity in view of their symmetry constraints: within the class of axisymmetric, stationary spacetimes, we propose a parameterization that includes non-circular spacetimes, both in Boyer-Lindquist as well as in horizon-penetrating coordinates. We show how existing parameterizations, which make additional symmetry assumptions (first, circularity; second, a hidden constant of motion), are included in the new parameterization. Further, we explain why horizon-penetrating coordinates may be more suitable to parameterize non-circular deviations from the Kerr geometry. Our investigation is motivated by our result that the regular, spinning black-hole spacetimes proposed in [1,2] are non-circular. This particular deviation from circularity can result in cusps, a dent and an asymmetry in the photon rings surrounding the black-hole shadow. Finally, we explore a new class of non-circular deviations from Kerr black holes, which promote the spin parameter to a function, and find indications that regularity cannot be achieved in this setting. This result strengthens the case for regular black holes based on a promotion of the mass parameter to a function.

gr-qc↗

arXiv2022

Horizonless spacetimes as seen by present and next-generation Event Horizon Telescope arrays

We study the capabilities of present and future radio very-long-baseline-interferometry arrays to distinguish black holes from horizonless spacetimes. We consider an example of a horizonless spacetime, obtained by overspinning a regular black hole. Its image is distinct from the image of a Kerr spacetime due to a second set of photon rings interior to the shadow. These photon rings cannot be directly resolved by present and even next-generation Event Horizon telescope arrays, but instead imprint themselves in horizon-scale images as excess central brightness relative to that of a black hole. We demonstrate that future arrays can detect such indirect imprints.

astro-ph.HE↗

arXiv2022

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature. The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value. We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction. In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling. We also consider solutions to the mode equations corresponding to quasi-bound states and static configurations. Our results for quasi-bound states provide strong evidence for the stability of the spectrum, indicating the impossibility of a vectorization mechanism within our set-up. For static solutions, we analytically and numerically derive results for the electromagnetic susceptibilities (the spin-1 analogs of the tidal Love numbers), which we show to be non-zero in the presence of the non-minimal coupling.

gr-qc↗

arXiv2022

Dynamically vanishing Dirac neutrino mass from quantum scale symmetry

We present a mechanism which drives Dirac neutrino masses to tiny values along the Renormalization Group flow, starting from an asymptotically safe ultraviolet completion of the third generation of the Standard Model including quantum gravity. At the same time, the mechanism produces a mass-splitting between the neutrino and the quark sector and also generates the mass splitting between top and bottom quark. The mechanism hinges on the hypercharges of the fermions and produces a tiny neutrino Yukawa coupling, because the right-handed neutrino is sterile and does not carry hypercharge.

hep-ph↗

arXiv2022

Grand unification and the Planck scale: An $\mathit{SO}(10)$ example of radiative symmetry breaking

Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible. Here, we initiate a systematic study of radiative symmetry breaking to thereby constrain viable initial conditions for the scalar couplings, for instance, at the Planck scale. We combine these new constraints on an admissible scalar potential with well-known constraints in the gauge-Yukawa sector into a general blueprint that carves out the viable effective-field-theory parameter space of any underlying theory of quantum gravity. We exemplify the constraining power of our blueprint within a non-supersymmetric $\mathit{SO}(10)$ GUT containing a $\mathbf{16}_H$- and a $\mathbf{45}_H$-dimensional scalar representation. We explicitly demonstrate that the requirement of successful radiative symmetry breaking to the correct subgroups significantly constraints the underlying microscopic dynamics. The presence of non-admissible radiative minima can even entirely exclude specific breaking chains: In the $\mathit{SO}(10)$ example, Pati-Salam breaking chains cannot be realised since the respective minima are never the deepest ones.

hep-ph↗

arXiv2022

Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects

Within quantum-gravity approaches and beyond, different mechanisms for singularity resolution in black holes exist. Under a set of assumptions that we spell out in detail, these mechanisms leave their imprint in shadow images of spherically symmetric black holes. We find that even current EHT accuracy is sufficient to place nontrivial constraints on the scale of new physics within one modified spacetime, if the EHT measurement of M87* is combined with an independent measurement of the black-hole mass. In other spacetimes, increased accuracy is required that the next-generation EHT may deliver. We show how the combination of $n=1$ and $n=2$ photon rings is a powerful probe of the spacetime geometry of regular black holes, even when considering astrophysical uncertainties in accretion disks. Further, we generate images containing a localized emission region, inspired by the idea of hotspots in accretion flows. Finally, we investigate the photon-ring structure of a horizonless object, which is characterized by either two or no photon spheres. We show how photon rings annihilate each other, when there is no photon sphere in the spacetime.

gr-qc↗

arXiv2021

Nonlinear Dynamics of Quadratic Gravity in Spherical Symmetry

We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (Quadratic Gravity) in the spherically-symmetric sector. The formulation relies on (i) harmonic gauge to cast the evolution system into quasi-linear form (ii) the Cartoon method to reduce to spherical symmetry in keeping with harmonic gauge, and (iii) order-reduction to 1st-order (in time) by means of introducing auxiliary variables. Well-posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. Our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.

gr-qc↗

arXiv2021

Destabilization of black holes and stars by generalized Proca fields

We demonstrate that black holes and stars in general relativity can be destabilized by perturbations of non-minimally coupled vector fields. Focusing on static and spherically symmetric backgrounds, our analysis shows that black holes with sufficiently small mass and stars with sufficiently high densities are subject to ghost or gradient-type instabilities. This holds for a large class of vector-tensor theories whenever non-minimal couplings contribute to linearized dynamics about a state with vanishing vector field and applies to generalized Proca models that have sparked attention for their potential role in cosmology and astrophysics. The stability criteria translate into bounds of relevance for low-scale theories of dark energy and for ultra-light dark matter scenarios.

gr-qc↗

arXiv2021

Invariant Renormalization-Group improvement

Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish that: On the one hand, RG improvement at the level of the metric is coordinate-dependent. On the other hand, a newly proposed RG improvement at the level of curvature invariants is coordinate-independent. Spherically-symmetric and axially-symmetric black-hole spacetimes serve as physically relevant examples.

gr-qc↗

arXiv2021

From a locality-principle for new physics to image features of regular spinning black holes with disks

Current observations present unprecedented opportunities to probe the true nature of black holes, which must harbor new physics beyond General Relativity to provide singularity-free descriptions. To test paradigms for this new physics, it is necessary to bridge the gap all the way from theoretical developments of new-physics models to phenomenological developments such as simulated images of black holes embedded in astrophysical disk environments. In this paper, we construct several steps along this bridge. We construct a novel family of regular black-hole spacetimes based on a locality principle which ties new physics to local curvature scales. We then characterize these spacetimes in terms of a complete set of curvature invariants and analyze the ergosphere and both the outer event as well as distinct Killing horizon. Our comprehensive study of the shadow shape at various spins and inclinations reveals characteristic image features linked to the locality principle. We also explore the photon rings as an additional probe of the new-physics effects. A simple analytical disk model enables us to generate simulated images of the regular spinning black hole and test whether the characteristic image-features are visible in the intensity map.

gr-qc↗

arXiv2021

Image features of spinning regular black holes based on a locality principle

To understand the true nature of black holes, fundamental theoretical developments should be linked all the way to observational features of black holes in their natural astrophysical environments. Here, we take several steps to establish such a link. We construct a family of spinning, regular black-hole spacetimes based on a locality principle for new physics and analyze their shadow images. We identify characteristic image features associated to regularity (increased compactness and relative stretching) and to the locality principle (cusps and asymmetry) that persist in the presence of a simple analytical disk model. We conjecture that these occur as universal features of distinct classes of regular black holes based on different sets of construction principles for the corresponding spacetimes.

gr-qc↗

arXiv2020

Predictive power of grand unification from quantum gravity

If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of the minimum of the effective potential.

hep-th↗

arXiv2020

Effective asymptotic safety and its predictive power: Gauge-Yukawa theories

Effective field theory provides a new perspective on the predictive power of Renormalization Group fixed points. Critical trajectories between different fixed points confine the regions of UV-complete, IR-complete, as well as conformal theories. The associated boundary surfaces cannot be crossed by the Renormalization Group flow of any effective field theory. We delineate cases in which the boundary surface acts as an infrared attractor for generic effective field theories. Gauge-Yukawa theories serve as an example that is both perturbative and of direct phenomenological interest. We identify additional matter fields such that all the observed coupling values of the Standard Model, apart from the Abelian hypercharge, lie within the conformal region. We define a quantitative measure of the predictivity of effective asymptotic safety and demonstrate phenomenological constraints for the associated beyond Standard-Model Yukawa couplings.

hep-th↗