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In a series of recent papers we put forward a ``fractional gravity'' framework striking an intermediate course between a modified gravity theory and an exotic dark matter (DM) scenario, which envisages the DM component in virialized halos to feel a non-local interaction mediated by gravity. The remarkable success of this model in reproducing several aspects of DM phenomenology motivates us to look for a general relativistic extension. Specifically, we propose a theory, dubbed Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stress-energy tensor couples to the scalar curvature via a non-local operator constructed with a fractional power of the d'Alembertian. We derive the field equations starting from an action principle, and then we investigate their weak field limit, demonstrating that in the Newtonian approximation the fractional gravity setup of our previous works is recovered. We compute the first-order post-Newtonian parameter $\gamma$ and its relation with weak lensing, showing that although in RSFG the former deviates from its GR values of unity, the latter is unaffected. We also perform a standard scalar-vector-tensor-decomposition of RSFG in the weak field limit, to highlight that gravitational waves propagate at the speed of light, though also an additional scalar mode becomes dynamical. Finally, we derive the modified conservation laws of the DM stress energy tensor in RSFG, showing that a new non-local force emerges, and hence that the DM fluid deviates from the geodesic solutions of the field equations., Comment: 21 pages. Accepted by Classical and Quantum Gravity

This investigation delves into the ringdown signals produced by semiclassical stars, which are ultra-compact, regular solutions of the Einstein equations incorporating stress-energy contributions from quantum vacuum polarization. These stars exhibit an approximately Schwarzschild exterior and an interior composed of a constant-density classical fluid and a cloud of vacuum polarization. By adjusting their compactness and density, we can alter the internal structure of these stars without modifying the exterior. This adaptability enables us to examine the sensitivity of the ringdown signal to the innermost regions of the emitting object and to compare it with similar geometries that differ substantially only at the core. Our results indicate that echo signals are intrinsically linked to the presence of stable light rings and can be very sensitive to the internal structure of the emitting object. This point was previously overlooked, either due to the imposition of reflective boundary conditions at the stellar surface or due to the assumption of low curvature interior geometries. Specifically, for stellar-sized semiclassical stars, we find that the interior travel time is sufficiently prolonged to render the echoes effectively unobservable. These findings underscore the potential efficacy of ultra-compact objects as black hole mimickers and emphasize that any phenomenological constraints on such objects necessitate a detailed understanding of their specific properties and core structure.

Analogue Hawking radiation from acoustic horizons is now a well-established phenomenon, both theoretically and experimentally. Its persistence, despite the modified dispersion relations characterising analogue models, has been crucial in advancing our understanding of the robustness of this phenomenon against ultraviolet modifications of our spacetime description. However, previous theoretical approaches, such as the Bogoliubov transformation relating asymptotic states, have somewhat lacked a straightforward physical intuition regarding the origin of this robustness and its limits of applicability. To address this, we revisit analogue Hawking radiation using the tunneling method. We present a unified treatment that allows us to consider flows with and without acoustic horizons and with superluminal or subluminal dispersion relations. This approach clarifies the fundamental mechanism behind the resilience of Hawking radiation in these settings and explains the puzzling occurrence of excitations even in subcritical (supercritical) flows with subluminal (superluminal) dispersion relations., Comment: 20 pages, 12 figures -- submitted to the special issue of Comptes Rendus Physique in memory of Renaud Parentani

While the standard point of view is that the ultimate endpoint of black hole evolution is determined by Hawking evaporation, there is a growing evidence that classical and semi-classical instabilities affect both black holes with inner horizons as well as their ultra-compact counterparts. In this essay we start from this evidence pointing towards extremal black holes as stable endpoints of the gravitational collapse, and develop a general class of spherical and axisymmetric solutions with multiple extremal horizons. Excluding more exotic possibilities, entailing regular cores supporting wormhole throats, we argue that these configuration could be the asymptotic graveyard, the end-point, of dynamical black hole evolution -- albeit the timescale of such evolution are still unclear and possibly long and compatible with current astrophysical observations., Comment: Essay awarded the Fifth Prize in the Gravity Research Foundation 2024 Awards; 18 pages. V2: Minor clarifications and re-phrasing

This work introduces a novel prescription for the expression of the thermodynamic potentials associated with the couplings of a Lanczos-Lovelock theory. These potentials emerge in theories with multiple couplings, where the ratio between them provide intrinsic length scales that break scale invariance. Our prescription, derived from the covariant phase space formalism, differs from previous approaches by enabling the construction of finite potentials without reference to any background. To do so, we consistently work with finite-size systems with Dirichlet boundary conditions and rigorously take into account boundary and corner terms: including these terms is found to be crucial for relaxing the integrability conditions for phase space quantities that were required in previous works. We apply this prescription to the first law of (extended) thermodynamics for stationary black holes, and derive a version of the Smarr formula that holds for static black holes with arbitrary asymptotic behaviour., Comment: 38 pages, 2 figures; references added, minor rephrasing

Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards several regularized geometries, in which limited spacetime regions requiring full quantum gravitational description can be safely covered by an extension of some suitable spacetime geometry. Motivated by these premises, in recent years, a systematic, quantum gravity agnostic, study has been carried out to catalogue all the conceivable non-singular, continuous, and globally hyperbolic geometries arising from evading Penrose's focusing theorem in gravitational collapse. In this study, we extend this inquiry by systematically examining all potential non-singular, continuous, and globally hyperbolic extensions into the past of Friedmann-Lema\^itre-Robertson-Walker (FLRW) metrics. As in the black hole case, our investigation reveals a remarkably limited set of alternative scenarios. The stringent requisites of homogeneity and isotropy drastically restrict the viable singularity-free geometries to merely three discernible non-singular cosmological spacetimes: a bouncing universe (where the scale factor reaches a minimum in the past before re-expanding), an emergent universe (where the scale factor reaches and maintains a constant value in the past), and an asymptotically emergent universe (where the scale factor diminishes continually, asymptotically approaching a constant value in the past). We also discuss the implications of these findings for the initial conditions of our universe, and the arrow of time.

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are generically present for dynamical geometries endowed with slowly-evolving inner trapping horizons, even in the absence of Cauchy horizons. This provides a more general definition of mass inflation based on quasi-local concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with non-extremal inner horizons, including the Kerr geometry in general relativity, and non-extremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived endpoint of gravitational collapse., Comment: 6 pages, 3 figures

While non-rotating black-hole solutions are well known in Einstein--\ae{}ther gravity, no axisymmetric solutions endowed with Killing horizons have been so far found outside of the slowly rotating limit. Here we show that the Kerr spacetime is also an exact vacuum solution of Einstein--\ae{}ther gravity in a phenomenologically viable corner of the parameter space; the corresponding \ae{}ther flow is characterised by a vanishing expansion. Such solution displays all the characteristic features of the Kerr metric (inner and outer horizons, ergoregion, etc.) with the remarkable exception of the causality-violating region in proximity of the ring singularity. However, due to the associated \ae{}ther flow, it is endowed with a special surface, inside the Killing horizon, which exhibits many features normally related to the universal horizon of the non-rotating solutions -- to which it tends in the limit of zero angular momentum. Hence, these Kerr black holes are very good mimickers of their general relativity counterparts while sporting important differences and specific structures. As such, they appear particularly well-suited candidates for future phenomenological studies., Comment: 9 pages, 3 figures. (v2) Discussion on closed timelike curves expanded, some minor changes and corrections, two references added, title (slightly) changed; conclusions unchanged, matches published version

While the robustness of Hawking radiation in the presence of UV Lorentz breaking is well-established, the Unruh effect has posed a challenge, with a large literature concluding that even the low-energy restoration of Lorentz invariance may not be sufficient to sustain this phenomenon. Notably, these previous studies have primarily focused on Lorentz-breaking matter on a conventional Rindler wedge. In this work, we demonstrate that considering the complete structure of Lorentz-breaking gravity, specifically the presence of a hypersurface orthogonal aether field, leads to the selection of a new Rindler wedge configuration characterized by a uniformly accelerated aether flow. This uniform acceleration provides a reference scale for comparison with the Lorentz-breaking one, thus ensuring the persistence of the Unruh effect in this context. We establish this by calculating the expected temperature using a Bogolubov approach, and by analyzing the response of a uniformly accelerated detector. We suggest that this resilience of the Unruh effect opens interesting possibilities towards future developments for using it as a tool to constrain Lorentz breaking theories of gravity., Comment: 30 pages, 6 figures

We study gravitational and test-field perturbations for the two possible families of spherically symmetric black-hole mimickers that smoothly interpolate between regular black holes and horizonless compact objects accordingly to the value of a regularization parameter. One family can be described by the Bardeen-like metrics, and the other by the Simpson-Visser metric. We compute the spectrum of quasi-normal modes (QNMs) of these spacetimes enlightening a common misunderstanding regarding this computation present in the recent literature. In both families, we observe long-living modes for values of the regularization parameter corresponding to ultracompact, horizonless configurations. Such modes appear to be associated with the presence of a stable photon sphere and are indicative of potential non-linear instabilities. In general, the QNM spectra of both families display deviations from the standard spectrum of GR singular BHs. In order to address the future detectability of such deviations in the gravitational-wave ringdown signal, we perform a preliminary study, finding that third generation ground-based detectors might be sensible to macroscopic values of the regularization parameter.

Since their proposal, Lorentz violating theories of gravity have posed a potential threat to black hole thermodynamics, as superluminal signals appeared to be incompatible with the very black hole notion. Remarkably, it was soon realized that in such theories causally disconnected regions of space-time can still exist thanks to the presence of universal horizons: causal barriers for signals of arbitrary high speed. Several investigations, sometimes with contrasting results, have been performed so to determine if these horizons can be associated with healthy thermodynamic properties similar to those associated with Killing horizons in General Relativity. In this work we offer what we deem to be the final picture emerging from this and previous studies. In summary we show that: 1) there is a thermal, and most of all species-independent, emission associated to universal horizons, determined by their surface gravity; 2) due to the modified dispersion relation of the matter fields, the low energy part of the emitted spectrum is affected by the presence of the Killing horizon, in a way similar to an effective refractive index, leading at low energies (w.r.t. the Lorentz breaking scale) to an emission that mimics a standard Hawking spectrum (i.e. one determined by the Killing horizon surface gravity); 3) the whole picture is compatible with a globally well defined vacuum state i.e. an Unruh state associated with preferred observers, which however at very low energies it is basically indistinguishable from the standard Unruh vacuum associated to metric free-falling observers. One can then conclude that Hawking radiation is remarkably resilient even within the context of gravitational theories entailing the breakdown of local Lorentz invariance., Comment: 37 pages, 10 figures

We introduce a generalization of the continued fraction and Chakravala algorithms for solving the Pell equation, utilizing the LLL-algorithm for rank 2 lattices.

A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators with those multiplying the boundary ones. A typical example of this construction is the Gibbons-Hawking-York boundary action that needs to be added to the Einstein-Hilbert one in order to have a well-defined metric variation for General Relativity with Dirichlet boundary conditions. Quantum fluctuations of matter fields lead to the renormalization of said coefficients which may or may not preserve this balance. Indeed, already at the level of General Relativity, the resilience of the matching between bulk and boundary constants is far from obvious and it is anyway incomplete given that matter generically induces quadratic curvature operators. We investigate here the resilience of the matching of higher-order couplings upon renormalization by a non-minimally coupled scalar field and show that a problem is present. Even though we do not completely solve the latter, we show that it can be greatly ameliorated by a wise splitting between dynamical and topological contributions. Doing so, we find that the bulk-boundary matching is preserved up to a universal term, whose nature and possible cancellation we shall discuss in the end., Comment: 27 pages

Infrared observations of Sgr A$^*$ and M87$^*$ are incompatible with the assumption that these sources have physical surfaces in thermal equilibrium with their accreting environments. In this paper we discuss a general parametrization of the energy balance in a horizonless object, which permits to quantify how close a horizonless object is in its behavior to a black hole, and analyze the timescale in which its surface can thermalize. We show that the thermalization timescale is unbounded, growing large for objects that mimic closely the behavior of a black hole (and being infinite for the latter). In particular, the thermalization timescale is proportional to the time that energy spends inside the horizonless object due to propagation and interactions with the bulk. Hence, these observations can be used to quantitatively restrict the dynamical behavior of horizonless objects, without being able to discard the existence of a physical surface., Comment: 17 pages, 2 figures

This paper discusses the challenges faced by cyber-physical microgrids (MGs) due to the inclusion of information and communication technologies in their already complex, multi-layered systems. The work identifies a research gap in modeling and analyzing stealthy intermittent integrity attacks in MGs, which are designed to maximize damage and cancel secondary control objectives. To address this, the paper proposes a nonlinear residual-based observer approach to detect and mitigate such attacks. In order to ensure a stable operation of the MG, the formulation then incorporates stability constraints along with the detection observer. The proposed design is validated through case studies on a MG benchmark with four distributed generators, demonstrating its effectiveness in detecting attacks while satisfying network and stability constraints., Comment: Accepted at IEEE Transactions on Power Systems

We look for possible evidence of a non-minimal coupling (NMC) between dark matter (DM) and gravity using data from the X-COP compilation of galaxy clusters. We consider a theoretically motivated NMC that may dynamically arise from the collective behavior of the coarse-grained DM field (e.g., via Bose-Einstein condensation) with averaging/coherence length $\L_{\mathrm{nmc}}$. In the Newtonian limit, the NMC modifies the Poisson equation by a term $\L_{\mathrm{nmc}}^2 \nabla^2 \rho$ proportional to the Laplacian of the DM density itself. We show that this term when acting as a perturbation over the standard Navarro-Frenk-White (NFW) profile of cold DM particles, can yield DM halo density profiles capable of correctly fitting galaxy clusters' pressure profiles with an accuracy comparable and in some cases even better than the standard cold DM NFW profile. We also show that the observed relation between the non-minimal coupling length scale and the virial mass found in Gandolfi et al., 2022 for Late Type Galaxies is consistent with the relation we find in the current work, suggesting that the previously determined power-law scaling law holds up to galaxy cluster mass scales., Comment: 15 pages, 6 figures, accepted for publication in the Astrophysical Journal

Using a quantum tunneling derivation, we show the resilience of Hawking radiation in Lorentz violating gravity. In particular, we show that the standard derivation of the Hawking effect in relativistic quantum field theory can be extended to Lorentz breaking situations thanks to the presence of universal horizons (causal boundaries for infinite speed signals) inside black hole solutions. Correcting previous studies, we find that such boundaries are characterized by a universal temperature governed by their surface gravity. We also show that within the tunneling framework, given the pole structure and the tunneling path, only a vacuum state set in the preferred frame provides a consistent picture. Our results strongly suggest that the robustness of black hole thermodynamics is ultimately linked to the consistency of quantum field theories across causal boundaries., Comment: 16 pages, 4 figures, contribution to the proceedings of the conference: "Avenues of Quantum Field Theory in Curved Space-time", Genova, 14-16. September 2022

Penrose's singularity theorem implies that if a trapped region forms in a gravitational collapse, then a singularity must form as well within such region. However, it is widely expected that singularities should be generically avoided by quantum gravitational effects. Here we shall explore both the minimum requirements to avoid singularities in a gravitational collapse as well as discuss, without relying on a specific quantum gravity model, the possible regular spacetimes associated to such regularization of the spacetime fabric. In particular, we shall expose the intimate and quite subtle relationship between regular black holes, black bounces and their corresponding horizonless object limits. In doing so, we shall devote specific attention to those critical (extremal) black hole configurations lying at the boundary between horizonful and horizonless geometries. While these studies are carried out in stationary configurations, the presence of generic instabilities strongly suggest the need for considering more realistic time-dependent dynamical spacetimes. Missing specific dynamical models, much less rigorous statements can be made for evolving geometries. We shall nonetheless summarize here their present understanding and discuss their implications for future phenomenological studies., Comment: 36 pages, 11 figures; invited chapter to appear in the book ''Regular Black Holes: Towards a New Paradigm of the Gravitational Collapse''

There is growing evidence that Ho\v{r}ava gravity may be a viable quantum theory of gravity. It is thus legitimate to expect that gravitational collapse in the full, non-projectable version of the theory should result in geometries that are free of spacetime singularities. Previous analyses have shown that such geometries must belong to one of the following classes: simply connected regular black holes with inner horizons; non-connected black holes "hiding" a wormhole mouth (black bounces); simply connected or non-connected horizonless compact objects. Here, we consider a singular black hole in the low-energy limit of non-projectable Ho\v{r}ava gravity, i.e. khronometric theory, and describe examples of its possible "regularisations", covering all of the viable classes. To our knowledge, these examples constitute the first instances of black holes with inner universal horizons, of black bounces and of stars with a de Sitter core in the context of Lorentz-violating theories of gravity., Comment: 30 pages, 5 figures. (v2) Some improvements to the exposition, physics unchanged; matches published version

Regular black holes are generically unstable because of the classical phenomenon that goes by the name of "mass inflation" which destabilizes the inner horizon. In a recent article, [Phys.Rev.D~107~(2023)~2,~024005], it is argued that semiclassical effects due to Hawking radiation can cure this instability, and some concerns are raised against the validity of previous analyses showing its existence in the first place. In this short comment, we explain our reservations regarding these recent claims, and reiterate the relevance of the mass inflation instability for regular black holes of astrophysical interest., Comment: v2: 8 pages, as published in Physical Review D

We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner--Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt--Deser--Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that semiclassical physics contains the necessary ingredients to trigger the early stages of such dynamical evolution., Comment: 29 pages with references, 6 figures

We discuss the tension between the possible existence of Painleve-Gullstrand coordinate systems versus the explicit geometrical features of the Kerr spacetime; a subject of interest to Professor Thanu Padmanabhan in the weeks immediately preceding his unexpected death. We shall carefully distinguish strong and weak Painleve-Gullstrand coordinate systems, and conformal variants thereof, cataloguing what we know can and cannot be done -- sometimes we can make explicit global statements, sometimes we must resort to implicit local statements. For the Kerr spacetime the best that seems to be achievable is to set the lapse function to unity and represent the spatial slices with a 3-metric in factorized unimodular form; this arises from considering the Doran version of Kerr spacetime in Cartesian coordinates. We finish by exploring the (limited) extent to which this construction might possibly lead to implementing an "analogue spacetime" model suitable for laboratory simulations of the Kerr spacetime., Comment: 22 pages. Dedicated to the memory of Professor Thanu Padmanabhan. To appear in the Professor Thanu Padmanabhan memorial volume published by General Relativity and Gravitation

We consider possible perturbations of the black hole event horizon induced by matter with spin, extending the derivation of the Hawking-Hartle formula (tidal heating) in the presence of torsion. When specialised to theories with a non-vanishing (pseudo-)traceless component of the (con)torsion tensor, we remarkably find that the tidal heating phenomenon gets modified by additional torsion-dependent terms, in agreement with previous investigations based on Jacobson's spacetime thermodynamics approach. These results lead to relevant phenomenological and theoretical consequences: modifications in the Hawking-Hartle term change the Bondi mass associated with the gravitational radiation observed at infinity, and modify the Hawking radiation spectrum of evaporating black holes.

Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations of physics. Despite this common goal, the community of quantum gravity researchers is sometimes seen as divided into sub-communities working on different, mutually exclusive approaches. In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and interaction between traditionally distinct approaches. In this White Paper we discuss some of the common themes which have seen a growing interest from various directions, and argue that focusing on them will help the quantum gravity community as a whole towards shared objectives., Comment: Contribution to Snowmass 2021, 11 pages

We present a rotating regular black hole whose inner horizon has zero surface gravity for any value of the spin parameter, and is therefore stable against mass inflation. Our metric is built by combining two successful strategies for regularizing singularities, i.e. by replacing the mass parameter with a function of $r$ and by introducing a conformal factor. The mass function controls the properties of the inner horizon, whose displacement away from the Kerr geometry's inner horizon is quantified in terms of a parameter $e$; while the conformal factor regularizes the singularity in a way that is parametrized by the dimensionful quantity $b$. The resulting line element not only avoids the stability issues that are common to regular black hole models endowed with inner horizons, but is also free of problematic properties of the Kerr geometry, such as the existence of closed timelike curves. While the proposed metric has all the phenomenological relevant features of singular rotating black holes -- such as ergospheres, light ring and innermost stable circular orbit -- showing a remarkable similarity to a Kerr black hole in its exterior, it allows nonetheless sizable deviations, especially for large values of the spin parameter $a$. In this sense, the proposed rotating "inner-degenarate" regular black hole solution is not only amenable to further theoretical investigations but most of all can represent a viable geometry to contrast to the Kerr one in future phenomenological tests., Comment: 15 pages, 8 figures. (v2) Formatting matched to submitted version. (v3) Sec. V.A on causal structure added, sec. V.B on effective matter content expanded, other minor revisions; matches published version

Black holes in Lorentz violating gravity, such as Einstein--Aether or Horava--Lifshitz Gravity, are drastically different from their general relativistic siblings. Although they allow for superluminal motion in their vicinity, they still exhibit an absolute causal boundary in the form of a universal horizon. By working in the tunneling picture for a gravitating scalar field, we show that universal horizons emit Hawking radiation in a manner akin to standard results in General Relativity, with a temperature controlled by the high-energy behavior of the dispersion relation of the gravitating field, and in agreement with alternative derivations in the literature. Our results substantiate the link between the universal horizon and thermodynamics in Lorentz violating theories., Comment: 16 pages, 2 figures, journal version