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The laser ablation threshold is an important parameter that governs the response of materials to intense laser irradiation. Here we study the ablation threshold of liquid tin, by irradiating tin microdroplets with nanosecond laser pulses having finely controlled temporal shape and duration. We use the time-dependent reflection from the droplet as the main observable, which exhibits a sharp decrease in magnitude at a given time instance that depends on the laser intensity. This moment marks the generation of a plasma that strongly absorbs the following incident laser light, rapidly expands, and thereby sets in motion the remainder of the liquid droplet. We find an inverse-square dependence of this plasma-onset time on laser intensity and attribute this scaling to the presence of one-dimensional heat diffusion during irradiation. This scaling and its one-dimensional thermal origin is strongly established in literature and follows from a square-root scaling of the thermal diffusion depth with time. Our experiment unambiguously shows that this scaling law holds for our specific case of nanosecond laser impact on tin microdroplets. The results presented in this work are of particular interest to target preparation and metrology in extreme-ultraviolet sources utilizing tin microdroplet targets.

Observations support the idea that supermassive black holes (SMBHs) power the emission at the center of active galaxies. However, contrary to stellar-mass BHs, there is a poor understanding of their origin and physical formation channel. In this article, we propose a new process of SMBH formation in the early Universe that is not associated with baryonic matter (massive stars) or primordial cosmology. In this novel approach, SMBH seeds originate from the gravitational collapse of fermionic dense dark matter (DM) cores that arise at the center of DM halos as they form. We show that such a DM formation channel can occur before star formation, leading to heavier BH seeds than standard baryonic channels. The SMBH seeds subsequently grow by accretion. We compute the evolution of the mass and angular momentum of the BH using a geodesic general relativistic disk accretion model. We show that these SMBH seeds grow to $\sim 10^9$-$10^{10} M_\odot$ in the first Gyr of the lifetime of the Universe without invoking unrealistic (or fine-tuned) accretion rates., 11 pages, 9 figures, 2 appendices. Accepted for publication in MNRAS

We analyze neutrino ($\nu$) emission channels in energetic ($\gtrsim 10^{52}$ erg) long gamma-ray bursts within the binary-driven hypernova model. The binary-driven hypernova progenitor is a binary system composed of a carbon-oxygen star and a neutron star (NS) companion. The gravitational collapse leads to a type Ic supernova (SN) explosion and triggers an accretion process onto the NS. For orbital periods of a few minutes, the NS reaches the critical mass and forms a black hole (BH). Two physical situations produce MeV $\nu$s. First, during the accretion, the NS surface emits $\nu$-$\bar{\nu}$ pairs by thermal production. We calculate the properties and the flavor evolution of such a $\nu$ emission. Second, if the angular momentum of the SN ejecta is high enough, an accretion disk might form around the BH. The disk's high density and temperature are ideal for MeV-$\nu$ production. We estimate the flavor evolution and find that $\nu$ oscillation inside the disk leads to flavor equipartition. This effect reduces (compared to assuming frozen flavor content) the energy deposition rate of $\nu$-$\bar{\nu}$ annihilation into electron-positron ($e^+e^-$) pairs in the BH vicinity. We then analyze the production of GeV-TeV $\nu$s around the BH. The magnetic field surrounding the BH interacts with the BH gravitomagnetic field producing an electric field that leads to spontaneous $e^+e^-$ pairs by vacuum breakdown. The pairs plasma self-accelerates due to its internal pressure and engulfs protons during the expansion. The hadronic interaction of the protons in the expanding plasma with the ambient protons leads to $\nu$ emission via the decay chain of $\pi$ and $\mu$, around and far from the BH, along different directions. These $\nu$s have GeV-TeV energies, and we calculate their spectrum and luminosity. We also outline the detection probability by some current and future $\nu$ detectors., Comment: 23 pages, 13 figures, 5 tables

We simulate the first minutes of the evolution of a binary-driven hypernova (BdHN) event, with a special focus on the associated accretion processes of supernova (SN) ejecta onto the newborn neutron star ($\nu$NS) and the NS companion. We calculate the rotational evolution of the $\nu$NS and the NS under the torques exerted by the accreted matter and the magnetic field. We take into account general relativistic effects and use realistic hypercritical accretion rates obtained from three-dimensional smoothed-particle-hydrodynamics (SPH) numerical simulations of the BdHN for a variety of orbital periods. We show that the rotation power of the $\nu$NS has a unique double-peak structure while that of the NS has a single peak. These peaks are of comparable intensity and can occur very close in time or even simultaneously depending on the orbital period and the initial angular momentum of the stars. We outline the consequences of the above features in the early emission and their consequent observation in long gamma-ray bursts (GRBs)., Comment: Accepted for publication in Physical Review D

Gamma-ray bursts (GRBs) are systems of unprecedented complexity across all the electromagnetic spectrum, including the radio, optical, X-rays, gamma-rays in the megaelectronvolt (MeV) and gigaelectronvolt (GeV) regime, as well as ultrahigh-energy cosmic rays (UHECRs), each manifested in seven specific physical processes with widely different characteristic evolution timescales ranging from $10^{-14}$ s to $10^{7}$ s or longer. We here study the long GRB 180720B originating from a binary system composed of a massive carbon-oxygen (CO) star of about $10 M_\odot$ and a companion neutron star (NS). The gravitational collapse of the CO star gives rise to a spinning newborn NS ($\nu$NS), with an initial period of $P_0=1$ ms that powers the synchrotron radiation in the radio, optical, and X-ray wavelengths. We here only investigate the GRB 180720B afterglows and present a detailed treatment of its origin based on the synchrotron radiation released by the interaction of the $\nu$NS and the SN ejecta. We show that in parallel to the X-ray afterglow, the spinning $\nu$NS also powers the optical and radio afterglows and allows us to infer the $\nu$NS and ejecta parameters that fit the observational data., Comment: Accepted for publication in The Astrophysical Journal

We show that the gravitomagnetic interaction of a Kerr black hole (BH) with a surrounding magnetic field induces an electric field that accelerates charged particles to ultra-relativistic energies in the vicinity of the BH. Along the BH rotation axis, these electrons/protons can reach energies of even thousands of PeV, so stellar-mass BHs in long gamma-ray bursts (GRBs) and supermassive BHs in active galactic nuclei (AGN) can contribute to the ultrahigh-energy cosmic rays (UHECRs) thorough this mechanism. At off-axis latitudes, the particles accelerate to energies of hundreds of GeV and emit synchrotron radiation at GeV energies. This process occurs within $60^\circ$ around the BH rotation axis, and due to the equatorial-symmetry, it forms a double-cone emission. We outline the theoretical framework describing these acceleration and radiation processes, how they extract the rotational energy of the Kerr BH and the consequences for the astrophysics of GRBs., Accepted for publication in the ApJ

Proceeding paper of the 4th European Conference on Plasma Diagnostics (ECPD2021) 7–11 June, 2021, A real-time control system is being developed for a magnetically driven Fast-Ion Loss Detector (FILD) at the ASDEX Upgrade tokamak. The insertion of the diagnostic head will be adjusted in real-time to react to changes in the graphite head temperature, plasma position and appearance of MHD instabilities. The graphite probe head of the detector is exposed to an intense heat flux (located ∼3–5 cm from separatrix). The control algorithm performance is constrained by: the graphite head sublimation temperature, the ultimate stress limit, the reaction time of the controller and the retraction time. In this work, the temperature and thermal induced stress distribution on the probe head are assessed to determine what temperature-related magnitude is the limiting factor. The heat flux at the probe head has been estimated using the time-averaged parallel heat flux measured at the divertor target via infrared thermography. A field line tracing algorithm determines which regions of the probe head receives a weighted heat flux due to shadowing (self-induced or from other structures) and the incidence angle of the field lines. A finite element model is used to simulate the temporal evolution of the graphite head temperature and to obtain the induced thermal stress. The temperature spatial distribution at the probe head is validated against measurements of the probe head for different FILD systems showing a good agreement. These measurements have been obtained from visible cameras with an infrared filter. The model concludes that the maximum stress (∼100 MPa) does not overcome the graphite mechanical limit (170 MPa) and that the probe head is not affected by fatigue. Therefore, the graphite sublimation temperature (2000 °C) is set as the limiting factor of the new control system., This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom Research and Training Programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053.

A new concept for velocity space thermal ion loss detection is presented. This diagnostic provides pitch angle resolved measurements that are unfeasible with current diagnostics. It uses the same detection principle as the Fast-Ion Loss Detector with a scintillator as the active component and includes a double slit configuration to measure simultaneously the escaping counter- and co-current ions. Simulations show a gyroradius range between 0.15 and 1.00 cm with a resolution below 0.15 cm (for a gyroradius of 1 cm) and a pitch angle range between 30° and 150° with a resolution below 8° for both counter- and co-current ions. The formation of a sheath in front of the detector and its associated electric field may impact the detection principle. Preliminary simulations with a homogeneous electric field show a decrease in the measurable velocity space range, whereas the gyroradius and pitch angle resolution barely change. The strike map is sensitive to the sheath electric field.

Authoritarian aggression, authoritarian submission, and conventionalism comprise beliefs or attitudes know as authoritarianism. In the present study, we report on the development and the test of the psychometric properties of a brief scale for the assessment of authoritarian tendencies, the Attitudes toward Authoritarianism Scale (ESCAUT). Participants in the study were 786 adults with ages ranging from 18 to 75 years, 70.7 % military. An initial pool of 42 items written to capture the core features of authoritarianism was evaluated by specialists, and then answered by the participants. Results from ordinal factor analysisindicated 20 items with moderately to highly discriminative (factor loadings > .50) of two latent factors: Moral and punitive authoritarianism (α = .88), and submissive authoritarianism (α = .89). Test information curves revealed a broad coverage of the latent trait in both subscales. Moreover, the instrument could discriminate military from non-military participants, with large size differences. The ESCAUT is a brief self-report scale recommended for the assessment of the main features of authoritarianism in the general Latin American population. Limitations of the study are addressed.

[Shortened] CONTEXT: [...] AIMS: To identify and verify the BdHNe I properties in the additional sources GRB160509A, GRB160625B and GRB1340427A, and compare and contrast the results with the ones of a BdHN II source GRB180728A. We have also identified in all four sources, following the analysis GRB 130427A in the companion paper, the GeV radiation during and following the UPE phase. Also in all the four sources, we describe the spectral properties of their afterglow emission, including the mass estimate of the $\nu$NS, following the results presented in the companion paper. METHODS: [...] RESULTS: The results of the spectral analysis have validated the common properties in all BdHNe I: the three Episodes as well as the self-similar structures and the associated power-laws in the UPE phase. The profound similarities of the results have made a significant step forward in the taxonomy of GRBs and in evidencing a standard composition of the BdHN I. This opens the opportunity of a vaster inquire of the astrophysical nature of their components in the population synthesis approach: e.g., the BH formation in all BdHN I occurs due to accretion of the SN ejecta in a tight binary system with a neutron star companion which reaches its critical mass, leading to the formation of the BH. The SN-rise in all five BdHNe are compare and contrasted. CONCLUSIONS: The most far reaching discovery of self-similarities and power-laws here extensively confirmed, thanks also to the conclusions presented in the companion papers, leads to the existence of a discrete quantized repetitive polarized emission, both in the GeV and MeV observed by {\it Fermi}-GBM and {\it Fermi}-LAT, on a timescale as short as $10^{-14}$s. These results open new paths in the discovery of fundamental physical laws.

Background Colonic neoplastic risk is increased in long-standing colitis. Chromoendoscopy (CE) is the recommended screening method. Narrow band imaging (NBI) is potentially a more convenient alternative. Few studies have explored the diagnostic yield of second generation NBI (Olympus 190 series) versus chromoendoscopy. Methods NBICromo (NCT04403997) is an ongoing prospective randomized controlled trial in which patients with clinical indication for CE (>8 years of disease, left-side or extensive colitis, colonic Crohn′s disease with >2 colonic segments affected or associated primary esclerosing cholangitis) are randomized on 1:1 ratio to CE with methylene blue 0,1% or NBI. All procedures are done with Olympus HQ190 endoscopes by endoscopists with experience in IBD. Biopsies are taken from all visible lesions. Primary objective is to compare the total number of neoplastic lesions detected in each group. Secondary objectives are to compare the procedure time, the number of biopsies taken,and the accuracy of optical characterization of the lesions. The study has been approved by the Hospital Ethics Committee and patient informed consents were obtained. Estimated sample size for the study is 175 patients, and recruitment is currently ongoing. An interim analysis was conducted with the first 75 randomized patients to exclude futility due to slowed recruitment caused by covid-19 pandemic. Results 75 patients were randomized, 34 to CE and 41 to NBI. 10 patients were excluded due to presence of inflammation or poor bowel preparation in the colonoscopy. 65 patients were analyzed per protocol, 31 in the CE arm and 34 in the NBI arm. Mean age was 57±13 years, 46.15% were male and 53.85% female. Mean disease duration was 17.1 ± 8.3 years. No significant differences were found between groups in basal characteristics. 123 lesions were detected. 77 with CE and 46 with NBI, of these 34 (27,6%) were neoplastic (14 neoplastic lesions were found in NBI group and 19 in CE group p=0.1. Neoplastic lesions were found in 13 patients in CE group (41,9%) and 7 patients with NBI (20,5%) p=0.06. Total withdrawal time (including staining and/or therapeutics) was significantly shorter in the NBI group (17.6 ±9.8 vs 30.5 ± 16.5 min p AE were 1 mild post resection bleeding and 1 mild fever, both in the CE group p=0.07. Conclusion In this interim analysis there are no significant differences in dysplasia detection between CE and NBI, although more sample size is needed. NBI could be a more convenient alternative to CE, with significant shorter and more simple procedures. The ongoing clinical trial will be completed.

On 2018 July 28, GRB 180728A triggered \textit{Swift} satellites and, soon after the determination of the redshift, we identified this source as a type II binary-driven hypernova (BdHN II) in our model. Consequently, we predicted the appearance time of its associated supernova (SN), which was later confirmed as SN 2018fip. A BdHN II originates in a binary composed of a carbon-oxygen core (CO$_{\rm core}$) undergoing SN, and the SN ejecta hypercritically accrete onto a companion neutron star (NS). From the time of the SN shock breakout to the time when the hypercritical accretion starts, we infer the binary separation $\simeq 3 \times 10^{10}$ cm. The accretion explains the prompt emission of isotropic energy $\simeq 3 \times 10^{51}$ erg, lasting $\sim 10$ s, and the accompanying observed blackbody emission from a thermal convective instability bubble. The new neutron star ($\nu$NS) originating from the SN powers the late afterglow from which a $\nu$NS initial spin of $2.5$ ms is inferred. We compare GRB 180728A with GRB 130427A, a type I binary-driven hypernova (BdHN I) with isotropic energy $> 10^{54}$ erg. For GRB 130427A we have inferred an initially closer binary separation of $\simeq 10^{10}$ cm, implying a higher accretion rate leading to the collapse of the NS companion with consequent black hole formation, and a faster, $1$ ms spinning $\nu$NS. In both cases, the optical spectra of the SNe are similar, and not correlated to the energy of the gamma-ray burst. We present three-dimensional smoothed-particle-hydrodynamic simulations and visualisations of the BdHNe I and II., Comment: 20 pages, 6 figures, 3 tables. Accepted for publication in ApJ

Objective: This paper presents an analysis of two regulatory proposals in response to the growing demand for kidney transplants in Colombia. The results can be useful in evaluating these possible policy interventions once they have been implemented. Methods: The proposed model uses System Dynamics as a tool to understand the behavior of this complex social system if two intervention projects are executed. The first is a bill of law seeking to expand the legal presumption of organ donation. The second one is to implement a Kidney Exchange Program. The analysis is made in two parts. Firstly, a causal loop diagram is proposed. Secondly, the simulation of the system using a stock and flow diagram is analyzed. Results: Results show that the projects can balance the system and encourage donations. Conclusion: The implementation of a KEP is recommended since it achieves stability of the system earlier than the amendment to the law, with a reduction in the waiting list size., Objetivo: Este artículo presenta un análisis de dos propuestas de regulación en respuesta a la creciente demanda de trasplantes de riñón en Colombia. Los resultados pueden ser útiles al evaluar esas posibles intervenciones en las políticas una vez han sido implementadas. Métodos: El modelo propuesto emplea la Dinámica de Sistemas como herramienta para entender el comportamiento de este complejo sistema social cuando se ejecutan dos proyectos de intervención. El primero es un proyecto de ley que buscan expandir la presunción legal de la donación del órgano. El segundo es la implementación de un Programa de intercambio de riñones (KEP). El análisis se realiza en dos partes: primero se propone un diagrama causal; en segundo lugar, se analiza la simulación del sistema usando un diagrama de existencias y flujos. Resultados: Los resultados muestran que los proyectos pueden equilibrar el sistema y motivar las donaciones. Conclusión: Se recomienda la implementación de un programa KEP dado que logra la estabilidad del sistema antes que la enmienda de las leyes, con una reducción en el tamaño de la lista de espera, Objetivo: Este artigo apresenta análise de duas propostas regulatórias em resposta à crescente demanda por transplantes renais na Colômbia. Os resultados podem ser úteis na avaliação das possíveis intervenções nas políticas, uma vez implementadas. Métodos: O modelo proposto usa a Dinâmica de Sistemas como uma ferramenta para compreender o comportamento desse complexo sistema social quando executados dois projetos de intervenção. O primeiro é um projeto de lei visando expandir a presunção legal da doação de órgãos. O segundo é a implementação de um Programa de troca de rins (KEP). A análise é realizada em duas partes: primeiro propõe-se diagrama causal; segundo, analisa-se a simulação do sistema usando um diagrama de estoque e fluxo. Resultados: Os resultados mostram que os projetos podem equilibrar o sistema e motivar as doações. Conclusão: Recomenda-se a implementação de um programa KEP uma vez que alcança a estabilidade do sistema antes da alteração das leis, com uma redução no tamanho da lista de espera., Corresponding author. E-mail: william.guerrero1@unisabana.edu.co

The aim of this study was to examine differences in performance of alternating attention test through variables of states and age. The participants were 3213 people who were going through the process of obtaining or renewing a Driver’s License in the states of Bahia , Mato Grosso do Sul, Paraná, Santa Catarina and São Paulo and age from 18 to 76 years. The instrument used was the Test of Alternating Attentio (TEALT). The findings about the differences among the five Brazilian states revealed that only the state of Bahia was differentiated from Paraná and Mato Grosso do Sul. The results about age group indicated that with increasing age decreases the performance in the attention test, corroborating previous researches.

This paper aims at designing a “Multifunctional device composed of load support and anti-theft lock for standard bicycles”. A previous study has been developed in order to justify and validate the final design of the unmet needs of people in their daily lives, with an emphasis on satisfying those that imply specific savings, whether economic, energy or time. As a result, the use of bicycles as a means of transport in Spain is promoted taking as a frame of reference countries such as the Netherlands or France. This means economic and energy savings (by replacing the car) and an improvement in people’s health and quality of life. Following the steps of the design methodology, once the need was detected, an information search was carried out in order to identify and prioritize the design specifications that meet the demands of potential customers. For this reason, various sources were used, Cyclelogistics (2013), a European project; a report “Food in Spain” by the Ministry of Agriculture, Food and Environment (2017), and the annual bicycle barometer developed by the DGT (Direccion General de Trafico, 2017) where the opinion, habits and use that the Spanish people make of the bicycle and the needs and demands they have in relation to it, is known. In addition to meeting the needs of the client, the design must comply with a set of reference regulations both, at the level of security devices and the transport of merchandise at retail. The result of the work has given rise to patent application with prior examination at a national level, in a first phase, and subsequently, at an international level.

Jose Luis López-Campos,1,2 Maria Abad Arranz,1 Carmen Calero-Acuña,1,2 Fernando Romero-Valero,3 Ruth Ayerbe-García,4 Antonio Hidalgo-Molina,3 Ricardo I Aguilar-Pérez-Grovas,4 Francisco García-Gil,5 Francisco Casas-Maldonado,6 Laura Caballero-Ballesteros,5 María Sánchez-Palop,6 Dolores Pérez-Tejero,7 Alejandro Segado Soriano,7 Jose Calvo-Bonachera,8 Bárbara Hernández-Sierra,8 Adolfo Doménech,9 Macarena Arroyo-Varela,9 Francisco González-Vargas,10 Juan J Cruz-Rueda10 1Unidad Médico-Quirúrgica de Enfermedades Respiratorias, Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/Universidad de Sevilla, Seville, 2CIBER de Enfermedades Respiratorias (CIBERES), Instituto de Salud Carlos III, Madrid, 3Sección de Neumología, Hospital Puerta del Mar, Cádiz, 4Servicio de Neumología, Hospital Juan Ramón Jiménez, Huelva, 5Servicio de Neumología, Hospital Universitario Reina Sofía, Córdoba, 6Servicio de Neumología, Hospital Universitario San Cecilio, Granada, 7Sección de Neumología, Hospital Infanta Margarita, Cabra, Córdoba, 8Servicio de Neumología, Hospital Torrecárdenas, Almería, 9Servicio de Neumología, Hospital Regional Universitario de Málaga, Málaga, 10Servicio de Neumología, Hospital Universitario Virgen de las Nieves, Granada,Spain Objectives: Clinical practice in chronic obstructive pulmonary disease (COPD) can be influenced by weather variability throughout the year. To explore the hypothesis of seasonal variability in clinical practice, the present study analyzes the results of the 2013–2014 Andalusian COPD audit with regard to changes in clinical practice according to the different seasons.Methods: The Andalusian COPD audit was a pilot clinical project conducted from October 2013 to September 2014 in outpatient respiratory clinics of hospitals in Andalusia, Spain (8provinces with more than 8 million inhabitants) with retrospective data gathering. For the present analysis, astronomical seasons in the Northern Hemisphere were used as reference. Bivariate associations between the different COPD guidelines and the clinical practice changes over the seasons were explored by using binomial multivariate logistic regression analysis with age, sex, Charlson comorbidity index, type of hospital, and COPD severity by forced expiratory volume in 1 second as covariates, and were expressed as odds ratio (OR) with 95% confidence intervals (CIs).Results: The Andalusian COPD audit included 621 clinical records from 9 hospitals. After adjusting for covariates, only inhaler device satisfaction evaluation was found to significantly differ according to the seasons with an increase in winter (OR, 3.460; 95% CI, 1.469–8.151), spring (OR, 4.215; 95% CI, 1.814–9.793), and summer (OR, 3.371; 95% CI, 1.391–8.169) compared to that in autumn. The rest of the observed differences were not significant after adjusting for covariates. However, compliance with evaluating inhaler satisfaction was low.Conclusion: The various aspects of clinical practice for COPD care were found to be quite homogeneous throughout the year for the variables evaluated. Inhaler satisfaction evaluation, however, presented some significant variation during the year. Inhaler device satisfaction should be evaluated during all clinical visits throughout the year for improved COPD management. Keywords: COPD, seasons, clinical practice, quality of care

[Objectives] Previous clinical audits of COPD have provided relevant information about medical intervention in exacerbation admissions. The present study aims to evaluate adherence to current guidelines in COPD through a clinical audit., [Methods] This is a pilot clinical audit performed in hospital outpatient respiratory clinics in Andalusia, Spain (eight provinces with more than 8 million inhabitants), including 9 centers (20% of the public centers in the area) between 2013 and 2014. Cases with an established diagnosis of COPD based on risk factors, clinical symptoms, and a post-bronchodilator FEV1/FVC ratio of less than 0.70 were deemed eligible. The performance of the outpatient clinics was benchmarked against three guidance documents available at the time of the audit. The appropriateness of the performance was categorized as excellent (>80%), good (60−80%), adequate (40−59%), inadequate (20−39%), and highly inadequate (, [Results] During the audit, 621 clinical records were audited. Adherence to the different guidelines presented a considerable variability among the different participating hospitals, with an excellent or good adherence for symptom recording, MRC or CAT use, smoking status evaluation, spirometry, or bronchodilation therapy. The most outstanding areas for improvement were the use of the BODE index, the monitoring of treatments, the determination of alpha1-antitrypsin, the performance of exercise testing, and vaccination recommendations., [Conclusions] The present study reflects the situation of clinical care for COPD patients in specialized secondary care outpatient clinics. Adherence to clinical guidelines shows considerable variability in outpatient clinics managing COPD patients, and some aspects of the clinical care can clearly be improved., This study was financially supported by an unrestricted grant from Laboratorios Menarini, SA (Barcelona, Spain).

We present the geometrical properties of the region where the vacuum polarization process occur in the Kerr‐Newman spacetime. We find that the shape of the region can be ellipsoid‐like or torus‐like depending on the charge of the black hole.