In recent works (M.D. Piano, S. Hohenegger, F. Sannino, Quantum black hole physics from the event horizon. Phys. Rev. D (2), 024045 (2024). . [gr-qc], M.D. Piano, S. Hohenegger, F. Sannino, Effective metric descriptions of quantum black holes. Eur. Phys. J. C (12), 1273 (2024). . [gr-qc]), a framework has been developed to describe (quantum) deformed, spherically symmetric and static black holes in four dimensions. The key idea of this so-called $\textit{Effective Metric Description}$ (EMD) is to parametrise deformations of the classical Schwarzschild geometry by two functions that depend on a physical quantity and which are calculated in a self-consistent way as series expansions in the vicinity of the horizon. In this work we further strengthen this framework by first demonstrating that the corresponding series expansion coefficients can be completely and uniquely determined from measurements that are accessible for observers outside of the event horizon: we propose a Gedankenexperiment, consisting of probes following a free-falling trajectory that send signals to a stationary observer and show how an EMD can be constructed from suitable telemetric data. Furthermore, by linking the expansion coefficients of the EMD to the invariant eigenvalues of the energy momentum tensor, we determine a system of physical fields that provides an effective Einstein equation for the deformed black hole geometry. In the case of a simplified geometry and assuming that the metric deformations are small, we can write the leading order of the physical fields in a closed form in the metric functions. We illustrate our results at the example of the Hayward space-time.

France

Stefan Hohenegger

Probing effective black hole deformations

Charged black holes arise as solutions of General Relativity (GR) coupled to Maxwell theory. As functions of the mass and charge, they can exhibit extremal behavior, in which case they are stable against thermal decay. (Quantum) corrections to GR are expected to alter the classical features of these objects, especially near extremality. To capture such effects in a model-independent way, we extend the Effective Metric Description (EMD) previously introduced in (Del Piano et al. in Phys Rev D 109(2):024045, 2024, , [gr-qc]; Eur Phys J C 84(12):1273, 2024, , [gr-qc]) for spherically symmetric and static black holes. The EMD parametrizes deformations of the metric in terms of physical quantities, such as the radial spatial distance to the event horizon. While the latter is still viable for non-extremal charged black holes, we argue that the proper time of a free-falling observer is better suited in the extremal case: we derive the necessary conditions for the parameters of such an EMD for constructing a consistent space-time in the vicinity of the (extremal) horizon. Finally, we illustrate our framework through a concrete example, and mention implications of the Weak Gravity Conjecture on the effective metric parameters.

Denmark

Mattia Damia Paciarini

Italy

Manuel Piano

Francesco Sannino

Effective metric description of charged black holes

Gravitational wave observation has provided numerous insights into the merger of astrophysical black holes. In contrast to other violent events ( <italic>e.g.</italic> supernovae), they are, however, not expected to lead to significant emissions of photons and neutrinos. In this paper we discuss a scenario that would lead to characteristic observable gamma ray bursts, which would provide numerous hints to physics beyond General Relativity. Starting from the hypothesis that micro-black holes (called <italic>morsels</italic>) are formed during the merger process, we show that it is possible to observe their Hawking radiation, which takes the form of gamma ray bursts of a uniquely characteristic form: with energies in the TeV range, their temporal structure is unlike that stemming from any other astrophysical event. Notably, the time delay from the gravitational wave event is correlated to the mass distribution of the morsels. The integrated mass of the morsels, allowed by the unaccounted merger mass, leads to a Hawking radiation in photons that is above the sensitivity of atmospheric Cherenkov telescopes such as HESS, LHAASO and HAWC, and gamma ray space telescopes, such as Fermi-LAT. This renders the hypothesis of morsel creation experimentally testable, and we provide the first concrete bounds on the total mass of morsels formed in specific events.

Giacomo Cacciapaglia

Looking for black hole morsels in astrophysical mergers via Hawking radiation

$\textit{A}$-type Little String Theories (LSTs) are engineered from parallel M5-branes on a circle $$ {\mathbbm{S}}_{\perp}^1 $$ , probing a transverse ℝ /ℤ background. Below the scale of the radius of $$ {\mathbbm{S}}_{\perp}^1 $$ , these theories resemble a circular quiver gauge theory with $\textit{M}$ nodes of gauge group U($\textit{N}$) and matter in the bifundamental representation (or adjoint in the case of $\textit{M}$ = 1). In this paper, we study these LSTs in the presence of a surface defect, which is introduced through the action of a ℤ orbifold that breaks the gauge groups into [U(1)] . We provide a combinatoric expression for the non-perturbative BPS partition function for this system. This form allows us to argue that a number of non-perturbative symmetries, that have previously been established for the LSTs, are preserved in the presence of the defect. Furthermore, we discuss the Nekrasov-Shatashvili (NS) limit of the defect partition function: focusing in detail on the case ($\textit{M}$, $\textit{N}$) = (1, 2), we analyse two distinct proposals made in the literature. We unravel an algebraic structure that is responsible for the cancellation of singular terms in the NS limit, which we generalise to generic ($\textit{M}$, $\textit{N}$). In view of the dualities of higher dimensional gauge theories to quantum many-body systems, we provide indications that our combinatoric expression for the defect partition are useful in constructing and analysing quantum integrable systems in the future.

Baptiste Filoche

Taro Kimura

Surface defects in $\textit{A}$-type Little String Theories

We develop an effective metric description of 2+1 dimensional black holes describing deviations from the classical Ban̈ados–Teitelboim–Zanelli (BTZ) black hole. The latter is a classical 2+1 dimensional rotating black hole with constant negative curvature. The effective metric is constrained by imposing the black hole symmetries and asymptotic classical behavior. The deformed metric is parametrized in terms of a physical quantity that we choose to be a physical distance. The latter can be solved for in three main regions of interest, the one around the horizon, origin, and spatial infinity. The finiteness of physical quantities at the horizon, such as the Ricci and Kretschmann scalars, leads to universal constraints on the physical parameters of the metric around the horizon. This allows us to further derive the general form of the corrected Hawking temperature in terms of the physical parameters of the effective metric. Assuming that the approach can be generalized to the interior of the black hole, we further develop an effective metric description near the origin. To illustrate the approach, we show how to recast the information encoded in a specific model of quantum BTZ known as quBTZ black hole in terms of the effective metric coefficients.

Mikołaj Myszkowski

Effective metric description of 2+1 dimensional quantum black holes

Little Strings are a type of non-gravitational quantum theories that contain extended degrees of freedom, but behave like ordinary Quantum Field Theories at low energies. A particular class of such theories in six dimensions is engineered as the world-volume theory of an M5-brane on a circle that probes a transverse orbifold geometry. Its low energy limit is a supersymmetric gauge theory that is described by a quiver in the shape of the Dynkin diagram of the affine extension of an ADE-group. While the so-called $$ \hat{A} $$ -type Little String Theories (LSTs) are very well studied, much less is known about the $$ \hat{D} $$ -type, where for example the Seiberg-Witten curve (SWC) is only known in the case of the $$ {\hat{D}}_4 $$ theory. In this work, we provide a general construction of this curve for arbitrary $$ {\hat{D}}_M $$ that respects all symmetries and dualities of the LST and is compatible with lower-dimensional results in the literature. For $\textit{M}$ = 4 our construction reproduces the same curve as previously obtained by other methods. The form in which we cast the SWC for generic $$ {\hat{D}}_M $$ allows to study the behaviour of the LST under modular transformations and provides insights into a dual formulation as a circular quiver gauge theory with nodes of Sp($\textit{M}$ − 4) and SO(2$\textit{M}$).

Seiberg-Witten curves of $$ \hat{D} $$ -type Little Strings

In a recent work (Del Piano et al. in Phys Rev D 109(2):024045, 2024), we have described spherically symmetric and static quantum black holes as deformations of the classical Schwarzschild metric that depend on the physical distance to the horizon. We have developed a framework that allows us to compute the latter in a self-consistent fashion from the deformed geometry, in the vicinity of the horizon. However, in this formalism, the distance can be replaced by other physical quantities, e.g. curvature invariants such as the Ricci- or Kretschmann scalar. Here, we, therefore, define a more general framework, which we call an (EMD), that captures the deformed geometry based on a generic physical quantity. We develop in detail the Ricci- and Kretschmann scalar EMD, in particular demonstrating how to compute the geometry in a self-consistent manner. Moreover, we provide explicit relations that allow us to express one EMD in terms of the others, thus demonstrating their equivalence.

Effective metric descriptions of quantum black holes

We consider Little String Theories (LSTs) that are engineered by N parallel M5-branes probing a transverse ℤ M  geometry. By exploiting a dual description in terms of F-theory compactified on a toric Calabi-Yau threefold X  N,M , we establish numerous symmetries that leave the BPS partition function 𝒵 N,M  invariant. They furthemore act in a non-perturbative fashion from the point of view of the low energy quiver gauge theory associated with the LST. We present different group theoretical organisations of these symmetries, thereby generalising the results of [1] to the case of generic M ≥ 1. We also provide a Mathematica package that allows to represent them in terms of matrices that act linearly on the Kähler parameters of X  N,M . From the perspective of dual realisations of the LSTs the symmetries found here act in highly nontrivial ways: as an example, we consider a formulation of 𝒵 N,M  in terms of correlation functions of a vertex operator algebra, whose commutation relations are governed by an affine quiver algebra. We show the impact of the symmetry transformations on the latter and discuss invariance of 𝒵 N,M  from this perspective for concrete examples.

Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Canada

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

We discuss a class of Little String Theories (LSTs) whose low energy descriptions are supersymmetric gauge theories on the Ω-background with gauge group U(N) and matter in the adjoint representation. We show that the instanton partition function of these theories can be written in terms of Kronecker-Eisenstein series, which in a particular limit of the deformation parameters of the Ω-background organise themselves into Greens functions of free scalar fields on a torus. We provide a concrete identification between (differences of) such propagators and Nekrasov subfunctions. The latter are also characterised by counting specific holomorphic curves in a Calabi-Yau threefold X  N,1 which engineers the LST. Furthermore, using the formulation of the partition function in terms of the Kronecker-Eisenstein series, we argue for new recursive structures which relate higher instanton contributions to products of lower ones.