Publications

Authors: Carlo Rovelli and Andrea Di Biagio Year: 2020 Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between re.lative and stable facts resolves the difficulties pointed out by the no-go theorems of Frauchiger and Renner, Brukner, Bong et. al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the `linear evolution’ and `projection’ postulates.

Authors: Carlo Rovelli
Year:
2020

I discuss three aspects of the notion of agency from the standpoint of physics: (i) what makes a physical system an agent; (ii) the reason for agency’s time orientation; (iii) the source of the information generated in choosing an action. I observe that agency is the breaking of an approximation under which dynamics appears closed. I distinguish different notions of agency, and observe that the answer to the questions above differ in different cases. I notice a structural similarity between agency and memory, that allows us to model agency, trace its time asymmetry to thermodynamical irreversibility, and identify the source of the information generated by agency in the growth of entropy. Agency is therefore a physical mechanism that transforms low entropy into information. This may be the general mechanism at the source of the whole information on which biology builds.

Authors: Multiple authors including Carlo Rovelli 
Year:
2020

We present the status of the art of the Archimedes experiment, devoted to measuring the debated interaction of quantum vacuum fluctuations and gravity. The method is essentially the weighing of the transition energy of a layered superconductor where the contribution of vacuum energy to the transition energy is expected to be relevant. The transition is obtained by modulating the temperature of the superconducting sample at a frequency of about 10 mHz and the expected change of weight is measured with a suitably designed high sensitivity cryogenic beam balance. In this paper, we present an overview of the experiment, discussing the expected signal to be measured, and presenting in particular the result of a prototype balance operated in our present laboratory. In the frequency range of the measurement, the sensitivity is affected mainly by seismic, thermal, sensor, and control noise. We discuss these points showing in particular the design of the cryogenic apparatus, the final balance, and the quiet seismic site that will host the final measurement.

Authors: Kate J. Jeffery and Carlo Rovelli
Year: 2020

How did brains evolve to become so complex, and what is their future? Brains pose an explanatory challenge because entropy, which inexorably increases over time, is commonly associated with disorder and simplicity. Recently we showed how evolution is an entropic process, building structures – organisms – which themselves facilitate entropy growth. Here we suggest that key transitional points in evolution extended organisms’ reach into space and time, opening channels into new regions of a complex multidimensional state space that also allow entropy to increase. Brain evolution enabled representation of space and time, which vastly enhances this process. Some of these channels lead to tiny, dead-ends in the state space: the persistence of complex life is thus not thermodynamically guaranteed.

Authors: Carlo Rovelli
Year: 2019

Is reality three-dimensional and becoming real (Presentism), or is reality four-dimensional and becoming illusory (Eternalism)? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations.

Authors: Alejandro Perez, Daniel Sudarsky and Edward Wilson-Ewing
Year: 2020

The tension between the value of the Hubble constant H0 determined from local supernovae data and the one inferred from the cosmic microwave background based on the ΛCDM cosmological model may indicate the need for new physics. Here, we show that this `Hubble tension’ can be resolved in models involving an effective energy flux from the matter sector into dark energy resulting naturally from a combination of unimodular gravity and an energy diffusion process. The scheme is one where dark energy has the standard equation of state w=−1. This proposal provides an alternative phenomenological paradigm accounting for the observations, while offering a general framework to study diffusion effects coming from novel fundamental physical processes.

Authors: Lautaro Amadei, Hongguang Liu, and Alejandro Perez
Year: 2019

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom and thus break unitarity. This is applicable also to trivial gravitational field (low energy) idealizations realized by the use of the Minkowski background geometry which, as any other spacetime geometry, corresponds, in the fundamental description, to infinitely many different and closely degenerate discrete microstates. The existence of such microstates provides a large reservoir for information to be coded at the end of black hole evaporation and thus opens the way to a natural resolution of the black hole evaporation information puzzle. In this paper we show that these expectations can be made precise in a simple quantum gravity model for cosmology motivated by loop quantum gravity. Concretely, even when the model is fundamentally unitary, when microscopic degrees of freedom irrelevant to low-energy cosmological observers are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. Moreover, in the relevant physical regime these hidden degrees freedom do not carry any `energy’ and thus realize in a fully quantum gravitational context the idea (emphasized before by Unruh and Wald) that decoherence can take place without dissipation, now in a concrete gravitational model strongly motivated by quantum gravity. All this strengthen the perspective of a quite conservative and natural resolution of the black hole evaporation puzzle where information is not destroyed but simply degraded (made unavailable to low energy observers) into correlations with the microscopic structure of the quantum geometry at the Planck scale.

Authors: Kate Jeffery, Robert Pollack, and Carlo Rovelli
Year: 2019

We study the statistical underpinnings of life, in particular its increase in order and complexity over evolutionary time. We question some common assumptions about the thermodynamics of life. We recall that contrary to widespread belief, even in a closed system entropy growth can accompany an increase in macroscopic order. We view metabolism in living things as microscopic variables directly driven by the second law of thermodynamics, while viewing the macroscopic variables of structure, complexity and homeostasis as mechanisms that are entropically favored because they open channels for entropy to grow via metabolism. This perspective reverses the conventional relation between structure and metabolism, by emphasizing the role of structure for metabolism rather than the converse. Structure extends in time, preserving information along generations, particularly in the genetic code, but also in human culture. We argue that increasing complexity is an inevitable tendency for systems with these dynamics and explain this with the notion of metastable states, which are enclosed regions of the phase-space that we call “bubbles,” and channels between these, which are discovered by random motion of the system. We consider that more complex systems inhabit larger bubbles (have more available states), and also that larger bubbles are more easily entered and less easily exited than small bubbles. The result is that the system entropically wanders into ever-larger bubbles in the foamy phase space, becoming more complex over time. This formulation makes intuitive why the increase in order/complexity over time is often stepwise and sometimes collapses catastrophically, as in biological extinction.

Authors: Carlo Rovelli
Year: 2020

I study the physical nature of traces (or memories). Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times, are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories, as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information.

Authors: Carlo Rovelli
Year: 2019

The Einstein equations allow solutions containing closed timelike curves. These have generated much puzzlement and suspicion that they could imply paradoxes. I show that puzzlement and paradoxes disappears if we discuss carefully the physics of the irreversible phenomena in the context of these solutions.

Authors: Fabio D’Ambrosio, Marios Christodoulou, Pierre Martin-Dussaud, Carlo Rovelli, and Farshid Soltani
Year: 2021

At the end of Hawking evaporation, the horizon of a black hole enters a physical region where quantum gravity cannot be neglected. The physics of this region has not been much explored. We characterise its physics and introduce a technique to study it.

Authors: Johannes Münch
Year: 2020

The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validity of a static quantum black hole spacetime outside the collapsing matter, 2) homogeneity of the collapsing matter, and 3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model [1] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in- and outside observers can be answered.

Authors: Pietro Dona and Simone Speziale
Year: 2021

We describe a technique to study the asymptotics of SL(2,C) invariant tensors associated to graphs, with unitary irreps and lowest SU(2) spins, and apply it to the Lorentzian EPRL-KKL (Engle, Pereira, Rovelli, Livine; Kaminski, Kieselowski, Lewandowski) model of quantum gravity. We reproduce the known asymptotics of the 4-simplex graph with a different perspective on the geometric variables and introduce an algorithm valid for any graph. On general grounds, we find that critical configurations are not just Regge geometries, but a larger set corresponding to conformal twisted geometries. These can be either Euclidean or Lorentzian, and include curved and flat 4d polytopes as subsets. For modular graphs, we show that multiple pairs of critical points exist, and there exist critical configurations of mixed signature, Euclidean and Lorentzian in different subgraphs, with no 4d embedding possible.

Authors: Andrea Calcinari, Laurent Freidel, Etera Livine and Simone Speziale
Year: 2020

We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar features for the area and the holonomy operators, but improved peakedness in the direction of the flux. At the gauge-invariant level, the new family is built from tensor products of coherent intertwiners. To study the peakedness of the holonomy operator, we introduce a new shift operator based on the harmonic oscillator representation associated with the twisted geometry parametrization. The new shift operator captures the components of the holonomy relevant to disentangle its action into a simple positive shift of the spins.

Authors: Pietro Dona, Marco Fanizza, Pierre Martin-Dussaud and Simone Speziale
Year: 2019

We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of SL(2,C) of the principal series, corresponding to generalized Clebsch-Gordan coefficients with n≥3 legs. We find critical configurations of the quantum labels with a power-law decay of the invariants. They describe 3d polygons that can be deformed into one another via a Lorentz transformation. This is defined viewing the edge vectors of the polygons are the electric part of bivectors satisfying a (frame-dependent) relation between their electric and magnetic parts known as γ-simplicity in the loop quantum gravity literature. The frame depends on the SU(2) spin labelling the basis elements of the invariants. We compute a saddle point approximation using the critical points and provide a leading-order approximation of the invariants. The power-law is universal if the SU(2) spins have their lowest value, and n-dependent otherwise. As a side result, we provide a compact formula for γ-simplicity in arbitrary frames. The results have applications to the current EPRL model, but also to future research aiming at going beyond the use of fixed time gauge in spin foam models.

Authors: Carlo Rovelli
Year: 2020

Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge invariant variables of the original system; the missing information regards degrees of freedom that express relations between the subsystems. All this shows that gauge invariance is a formalization of the relational nature of physical degrees of freedom. The recent developments on boundary variables and boundary charges are clarified by this observation.

Authors: Johannes Münch
Year: 2021

The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of ℏ, it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in- and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel through matter to causally connect the regions in- and outside the horizon — the causal horizon is not present in the collapsing scenario. It is worked out that this is related to the shock wave and spacetime discontinuity, which allows matter travelling super-luminal along a space-like trajectory from the vacuum point of view, but remaining time-like from the matter perspective. The final causal diagram is a nice compact patch of a Reissner-Nordström causal diagram. Further, possibilities of a continuous matter collapse with only time-like evolution are studied. It was found that the time-reversed vacuum metric is also a solution of the dynamical equations and a once continuously differentiable matching of the vacuum spacetime across the minimal radius is possible. This allows an everywhere continuous and time-like collapse process at the cost of an infinite extended causal diagram. This solution is part of an infinitely extended eternal black hole solution with a bounce, whose global extension is constructed. Due to the analysis of radial light rays, it is possible to sketch causal diagrams of these spacetimes.

Authors: Carlo Rovelli
Year: 2021

A number of thorny issues such as the nature of time, free will, the clash of the manifest and scientific images, the possibility of a naturalistic foundation of morality, and perhaps even the possibility of accounting for consciousness in naturalistic terms, seem to me to be plagued by the conceptual confusion nourished by a single fallacy: the old fisherman’s mistake.

Published in PhilSci Archive

Authors: Carlo Rovelli

Year: 2021

Scientists can provide governments with essential knowledge to take informed decisions, but cannot decide on their behalf, according to Carlo Rovelli.

Published in Nature Materials

Authors: Carlo Rovelli Year: 2021 They are out there in the sky in huge numbers. They are the most astonishing objects in the universe. Their existence was predicted and understood before we detected them. They behave precisely as the theory predicted. Yet, we do not know what happens at their center, nor in their future. But this confusion is our key towards what we most lack in fundamental physics: understanding quantum gravity.
Authors: Carlo Rovelli
Year: 2021

Rovelli introduced the relational interpretation of quantum mechanics in 1994.
Published in Oxford Handbook of the History of Interpretations of Quantum Physics

Authors: Enrico Calloni, Archimedes Collaboration and Virgo Collaboration

Year: 2021

We report the experimental results of a prototype balance for the Archimedes experiment, devoted to measure the interaction between quantum vacuum energy and gravity. The prototype is a beam balance working at room temperature which shares with the final balance several mechanical and optical components. The balance sensitivity has been tested at the site of the Virgo gravitational wave detector in order to benefit from its quiet environment and control facilities. This allowed also the test of the coherence of the balance data with the Virgo interferometer signal and with the environmental data. In the low-frequency regime, the balance has shown a sensitivity of about 8×10−12Nm/Hz−−−√, which is among the best in the world, and it is very promising toward the final Archimedes measurement. In the high-frequency region, above a few Hz, relying on the behavior of the balance as a rotational sensor, the ground tilt has been measured in view of the next work devoted to Newtonian noise subtraction (NNS) in Virgo. The measured ground tilt reaches a minimum of about 8×10−11rad/Hz−−−√ in the few Hz region and ranges from 10−10 to 10−9rad/Hz−−−√ in the 10–20 Hz region, where a very interesting coherence, at some frequencies, with the Virgo interferometer signal is shown.

Published in The European Physical Journal Plus

Authors: Carlo Rovelli
Year: 2021

A recent paper by Mucino, Okon and Sudarsky attempts an assessment of the Relational Interpretation of quantum mechanics. The paper presupposes assumptions that are precisely those questioned in the Relational Interpretation, thus undermining the value of the assessment.

Authors: Carlo Rovelli
Year: 2021

Confusion and disagreement around the notion of time is due to the fact that we often fail to recognize that we call ‘time’ a variety of distinct notions, only partially related to one another. Many apparently obvious properties of time are results of different kinds of approximations, idealizations, or special contexts. I illustrate a number of distinct notions of time, their differences and relations; they are all relevant for describing the real world. To understand time, we have to break it apart.

Authors: Carlo Rovelli
Year: 2021

According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.

Authors: Fabio M. Mele, Johannes Münch and Stratos Pateloudis
Year: 2021

In this paper, we continue the analysis of the effective model of quantum Schwarzschild black holes recently proposed by some of the authors in [1,2]. In the resulting spacetime the central singularity is resolved by a black-to-white hole bounce, quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon and classical geometry is approached asymptotically. This is the case independently of the relation between the black and white hole masses, which are thus freely specifiable independent observables. A natural question then arises about the phenomenological implications of the resulting non-singular effective spacetime and whether some specific relation between the masses can be singled out from a phenomenological perspective. Here we focus on the thermodynamic properties of the effective polymer black hole and analyse the corresponding quantum corrections as functions of black and white hole masses. The study of the relevant thermodynamic quantities such as temperature, specific heat and horizon entropy reveals that the effective spacetime generically admits an extremal minimal-sized configuration of quantum-gravitational nature characterised by vanishing temperature and entropy. For large masses, the classically expected results are recovered at leading order and quantum corrections are negligible, thus providing us with a further consistency check of the model. The explicit form of the corrections depends on the specific relation among the masses. In particular, a first-order logarithmic correction to the entropy is obtained for a quadratic mass relation. The latter corresponds to the case of proper finite length effects which turn out to be compatible with a minimal length generalised uncertainty principle associated with an extremal Planck-sized black hole.

Authors: Carlo Rovelli
Year: 2021

Formulata da Albert Einstein con qualche con­tributo da parte di amici e colleghi tra il 1907 e il 1917, la relatività generale è la teoria che og­gi meglio descrive lo spazio, il tempo e la gravi­tà. Con la chiarezza espositiva che lo ha reso ce­lebre in tutto il mondo, Rovelli ne illustra i fon­damenti fisici, filosofici e matematici, ne presen­ta la struttura formale, e ne deriva nel modo più semplice le sue stupefacenti predizioni – buchi neri, onde gravitazionali, espansione dell’uni­verso, dilatazione del tempo… –, senza trascu­rare alcune idee di base su come potrebbe es­sere estesa ai fenomeni quantistici. Per il letto­re con formazione scientifica questo libro rap­presenterà dunque una agile introduzione agli aspetti fondamentali della teoria, ma nel con­tempo lo scienziato e lo studente avanzato vi tro­veranno una discussione approfondita e origi­nale della sua struttura concettuale. Nel secolo scorso la relatività generale ha rivo­luzionato la fisica, ma è con le applicazioni e le osservazioni degli ultimi anni, coronate da nu­merosi premi Nobel, che sono esplose e diven­tate evidenti la sua vitalità e fecondità: Rovelli descrive questi risultati recenti, guidando così il lettore ad apprezzare «la scintillante bellezza e la semplicità delle idee su cui essa si basa».

Authors: Carlo Rovelli
Year: 2021

In June 1925, twenty-three-year-old Werner Heisenberg, suffering from hay fever, had retreated to the treeless, wind-battered island of Helgoland in the North Sea in order to think. Walking all night, by dawn he had wrestled with an idea that would transform the whole of science and our very conception of the world. In Helgoland Carlo Rovelli tells the story of the birth of quantum physics and its bright young founders who were to become some of the most famous Nobel winners in science. It is a celebration of youthful rebellion and intellectual revolution. An invitation to a magical place. Here Rovelli illuminates competing interpretations of this science and offers his own original view, describing the world we touch as a fabric woven by relations. Where we, as every other thing around us, exist in our interactions with one another, in a never-ending game of mirrors. A dazzling work from one of our most celebrated scientists and master storyteller, Helgoland transports us to dizzying heights, reminding us of the many pleasures of the life of the mind. Translated by Erica Segre and Simon Carnell

Authors: Alejandro Perez, Salvatore Ribisi
Year: 2021

Since the appearance of Einstein’s paper {\em”On the Electrodynamics of Moving Bodies”} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell’s equations. The celebrated mass-energy equivalence relation, E=mc2, is derived by Einstein using thought experiments involving the kinematics of the emission of light (electromagnetic energy) and the relativity principle. Text book derivations often follow paths similar to Einstein’s, or the analysis of the kinematics of particle collisions interpreted from the perspective of different inertial frames. All the same, in such derivations the direct dynamical link with hypothetical fundamental fields describing matter (e.g. Maxwell theory or other) is overshadowed by the use of powerful symmetry arguments, kinematics, and the relativity principle. Here we show that the formula can be derived directly form the dynamical equations of a massless matter model confined in a box (which can be thought of as a toy model of a composite particle). The only assumptions in the derivation are that the field equations hold and the energy-momentum tensor admits a universal interpretation in arbitrary coordinate systems. The mass-energy equivalence relation follows from the inertia or (taking the equivalence principle for granted) weight of confined field radiation. The present derivation offers an interesting pedagogical perspective on the formula providing a simple toy model on the origin of mass and a natural bridge to the foundations of general relativity.

Authors: Antoine Rignon-Bret, Carlo Rovelli
Year: 2021

We present an exact solution of the Maxwell-Einstein equations, which describes the exterior of a charged spherical mass collapsing into its own trapping horizon and then bouncing back from an anti-trapping horizon at the same space location of the same asymptotic region. The solution is locally but not globally isometric to the maximally extended Reissner-Nordström metric and depends on seven parameters. It is regular, and defined everywhere except for a small region, where quantum tunnelling is expected. This region lies outside the mass: the mass-bounce and its near exterior are governed by classical general relativity. We discuss the relevance of this result for the fate of realistic black holes. We comment on possible effects of the classical instabilities and the Hawking radiation.

Authors: Carlo Rovelli
Year: 2021

In this short book, renowned theoretical physicist and author Carlo Rovelli gives a straightforward introduction to Einstein’s General Relativity, our current theory of gravitation. Focusing on conceptual clarity, he derives all the basic results in the simplest way, taking care to explain the physical, philosophical and mathematical ideas at the heart of “the most beautiful of all scientific theories”. Some of the main applications of General Relativity are also explored, for example, black holes, gravitational waves and cosmology, and the book concludes with a brief introduction to quantum gravity. Written by an author well known for the clarity of his presentation of scientific ideas, this concise book will appeal to university students looking to improve their understanding of the principal concepts, as well as science-literate readers who are curious about the real theory of General Relativity, at a level beyond a popular science treatment.

Authors: L. Burderi et al
Year: 2020

GrailQuest (Gamma Ray Astronomy International Laboratory for QUantum Exploration of Space-Time) is a mission concept based on a constellation (hundreds/thousands) of nano/micro/small-satellites in low (or near) Earth orbits. Each satellite hosts a non-collimated array of scintillator crystals coupled with Silicon Drift Detectors with broad energy band coverage (keV-MeV range) and excellent temporal resolution ( below or equal 100 nanoseconds) each with effective area around 100 cm2. This simple and robust design allows for mass-production of the satellites of the fleet. This revolutionary approach implies a huge reduction of costs, flexibility in the segmented launching strategy, and an incremental long-term plan to increase the number of detectors and their performance: a living observatory for next-generation, space-based astronomical facilities. GrailQuest is conceived as an all-sky monitor for fast localisation of high signal-to-noise ratio transients in the X/gamma-ray band, e.g. the elusive electromagnetic counterparts of gravitational wave events. Robust temporal triangulation techniques will allow unprecedented localisation capabilities, in the keV-MeV band, of a few arcseconds or below, depending on the temporal structure of the transient event. The ambitious ultimate goal of this mission is to perform the first experiment, in quantum gravity, to directly probe space-time structure down to the minuscule Planck scale, by constraining or measuring a first order dispersion relation for light in vacuo. This is obtained by detecting delays between photons of different energies in the prompt emission of Gamma-ray Bursts.

Authors: Carlo Rovelli
Year: 2021

in “Einstein vs. Bergson: an Enduring Quarrel of Time”, A. Campo, S. Gozzano (eds.). Preface. De Gruyter, Berlin 2021.

Authors: Lautaro Amadei, Alejandro Perez
Year: 2021

We propose a model of inflation driven by the relaxation of an initially Planckian cosmological constant due to diffusion. The model can solve the horizon and flatness problem, and generate a (approximately) scale invariant spectrum of (adiabatic) primordial perturbations with the correct amplitudes and blue tilt without an inflaton. The inhomogeneities observable in the CMB arise from those associated to the fundamental Planckian granularity that are imprinted into the standard model Higgs scalar fluctuations during the inflationary phase. The process admits a semiclassical interpretation and avoids the trans-Planckian problem of standard inflationary scenarios based on the role of vacuum fluctuations. The deviations from scale invariance observed in the CMB are controlled by known parameters of the standard model of particle physics. If an order one portion of these fluctuations collapses to form primordial black holes the model produces the amount of cold dark matter required by observations.

Authors: Emanuel Gallo, Carlos Kozameh, Thomas Mädler, Osvaldo M. Moreschi, Alejandro Pérez
Year: 2021

The definition of well-behaved coordinate charts for black hole spacetimes can be tricky, as they can lead for example to either unphysical coordinate singularities in the metric (e.g. r=2M in the Schwarzschild black hole) or to an implicit dependence of the chosen coordinate to physical relevant coordinates (e.g. the dependence of the null coordinates in the Kruskal metric). Here we discuss two approaches for coordinate choices in spherical symmetry allowing us to discuss explicitly “solitary” and spherically symmetric black holes from a regular horizon to null infinity. The first approach relies on a construction of a regular null coordinate (where regular is meant as being defined from the horizon to null infinity) given an explicit solution of the Einstein-matter equations. The second approach is based on an affine-null formulation of the Einstein equations and the respective characteristic initial value problem. In particular, we present a derivation of the Reissner-Nordström black holes expressed in terms of these regular coordinates.