Energy exchange between relativistic fluids: the polytropic case

We present a simple, analytic and straightforward method to elucidate the effects produced by polytropic fluids on any other gravitational source, no matter its nature, for static and spherically symmetric spacetimes. As a direct application, we study the interaction between polytropes and perfect fluids coexisting inside a self-gravitating stellar objectComment: 10 pages, 12 figure

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).Comment: 6 pages, 4 figures, accepted by Astronomy & Astrophysic

Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes

We examine the electromagnetic properties of Kerr-anti-de Sitter (Kerr-AdS) black holes in four and higher spacetime dimensions. Assuming that the black holes may carry a test electric charge we show that the Killing one-form which represents the difference between the timelike generators in the spacetime and in the reference background can be used as a potential one-form for the associated electromagnetic field. In four dimensions the potential one-form and the Kerr-AdS metric with properly re-scaled mass parameter solve the Einstein-Maxwell equations, thereby resulting in the familiar Kerr-Newman-AdS solution. We solve the quartic equation governing the location of the event horizons of the Kerr-Newman-AdS black holes and present closed analytic expressions for the radii of the horizons. We also compute the gyromagnetic ratio for these black holes and show that it corresponds to g=2 just as for ordinary black holes in asymptotically flat spacetime. Next, we compute the gyromagnetic ratio for the Kerr-AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it tends to g=2 irrespective of the spacetime dimension. Finally, we consider the case of a five dimensional Kerr-AdS black hole with two angular momenta and show that it possesses two distinct gyromagnetic ratios in accordance with its two orthogonal 2-planes of rotation. In the special case of two equal angular momenta, the two gyromagnetic ratios merge into one leading to g=4 at the maximum angular velocities of rotation.Comment: Typos corrected; 31 pages, REVTe

Isotropization and change of complexity by gravitational decoupling

We employ the gravitational decoupling appro- ach for static and spherically symmetric systems to develop a simple and powerful method in order to (a) continuously isotropize any anisotropic solution of the Einstein field equa- tions, and (b) generate new solutions for self-gravitating dis- tributions with the same or vanishing complexity factor. A few working examples are given for illustrative purposes

Unstable fields in Kerr spacetimes

We show that both the interior region $r<M-\sqrt{M^2-a^2}$ of a Kerr black hole and the $a^2>M^2$ Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every harmonic number there is at least one axially symmetric mode that grows exponentially in time and decays properly in the radial directions. These can be used as Debye potentials to generate solutions for the scalar, Weyl spinor, Maxwell and linearized gravity field equations on these backgrounds, satisfying appropriate spatial boundary conditions and growing exponentially in time, as shown in detail for the Maxwell case. It is suggested that the existence of the unstable modes is related to the so called "time machine" region, where the axial Killing vector field is time-like, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic

Particle motion in the field of a five-dimensional charged black hole

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.Comment: 15 pages, accepted for publication in Astrophysics and Space Scienc

Hospital-Level Nicu Capacity, Utilization, and 30-Day Outcomes in Texas

IMPORTANCE: Risk-adjusted neonatal intensive care unit (NICU) utilization and outcomes vary markedly across regions and hospitals. The causes of this variation are poorly understood. OBJECTIVE: to assess the association of hospital-level NICU bed capacity with utilization and outcomes in newborn cohorts with differing levels of health risk. DESIGN, SETTING, AND PARTICIPANTS: This population-based retrospective cohort study included all Medicaid-insured live births in Texas from 2010 to 2014 using linked vital records and maternal and newborn claims data. Participants were Medicaid-insured singleton live births (LBs) with birth weights of at least 400 g and gestational ages between 22 and 44 weeks. Newborns were grouped into 3 cohorts: very low birth weight (VLBW; \u3c1500 \u3eg), late preterm (LPT; 34-36 weeks\u27 gestation), and nonpreterm newborns (NPT; ≥37 weeks\u27 gestation). Data analysis was conducted from January 2022 to October 2023. EXPOSURE: Hospital NICU capacity measured as reported NICU beds/100 LBs, adjusted (ie, allocated) for transfers. MAIN OUTCOMES AND MEASURES: NICU admissions and special care days; inpatient mortality and 30-day postdischarge adverse events (ie, mortality, emergency department visit, admission, observation stay). RESULTS: The overall cohort of 874 280 single LBs included 9938 VLBW (5054 [50.9%] female; mean [SD] birth weight, 1028.9 [289.6] g; mean [SD] gestational age, 27.6 [2.6] wk), 63 160 LPT (33 684 [53.3%] female; mean [SD] birth weight, 2664.0 [409.4] g; mean [SD] gestational age, 35.4 [0.8] wk), and 801 182 NPT (407 977 [50.9%] female; mean [SD] birth weight, 3318.7 [383.4] g; mean [SD] gestational age, 38.9 [1.0] wk) LBs. Median (IQR) NICU capacity was 0.84 (0.57-1.30) allocated beds/100 LB/year. For VLBW newborns, NICU capacity was not associated with the risk of NICU admission or number of special care days. For LPT newborns, birth in hospitals with the highest compared with the lowest category of capacity was associated with a 17% higher risk of NICU admission (adjusted risk ratio [aRR], 1.17; 95% CI, 1.01-1.33). For NPT newborns, risk of NICU admission was 55% higher (aRR, 1.55; 95% CI, 1.22-1.97) in the highest- vs the lowest-capacity hospitals. The number of special care days for LPT and NPT newborns was 21% (aRR, 1.21; 95% CI,1.08-1.36) and 37% (aRR, 1.37; 95% CI, 1.08-1.74) higher in the highest vs lowest capacity hospitals, respectively. Among LPT and NPT newborns, NICU capacity was associated with higher inpatient mortality and 30-day postdischarge adverse events. CONCLUSIONS AND RELEVANCE: In this cohort study of Medicaid-insured newborns in Texas, greater hospital NICU bed supply was associated with increased NICU utilization in newborns born LPT and NPT. Higher capacity was not associated with lower risk of adverse events. These findings raise important questions about how the NICU is used for newborns with lower risk

A two-mass expanding exact space-time solution

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space-time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space-time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski-Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.Comment: 15 pages, 5 figures. Replaced to match the published versio