Horizon Area Research Articles

An attempt to add Barrow entropy in f(R) gravity

In this work, a way to consider together two originally different corrections to the Friedmann equations is presented. The first is the Barrow entropy, which imposes a fractal structure on the black hole horizon area. While the second is the well-known f(R) gravity, which comes from a generalization of the Einstein-Hilbert action. Using the ideas of gravity-thermodynamics conjecture, these two models are combined. Then the modified Friedmann equation is obtained. Choosing a particular f(R) model, an application is investigated. The state parameter and the density parameters for matter and dark energy are calculated. With these results, the dynamic evolution of the universe is discussed.

Current morphological and hydroecological characteristics of the Berezan river

The article presents the results of two-year ecological, hydrological and hydrochemical studies of Berezan, one of the steppe rivers of Mykolaiv region, which begins the Berezan estuary in the lower part of the Tyligulo-Buzka confluence. The current state of the Berezan River is characterized by a significant level of anthropogenic transformation of the watercourse associated with the construction of cascade ponds. The independent existence of the flow rate and yearround water content of the Berezan River without its support by technical means of water supply is impossible. According to the hydrochemical composition of the river water, it belongs to the bicarbonate-calcium type with a high content of sulfates, chlorides, and sodium, differing in an extremely dynamic level of mineralization — from 760 mg/dm3 during the flood to 2900 mg/dm3 during the low tide. No less active influence on the state of this small steppe river and the Berezan estuary initiated by it are also exerted by natural factors such as increasing aridity of the climate, transgressive tendencies of the Black Sea, increasing environmental temperatures, increasing evaporation volumes and changes in the balance of surface-underground water exchange. Because of this, the Berezan River today is no longer able to independently maintain the water content, flowability and stability of the hydrochemical regime, showing a tendency to transform into a seasonally draining network of streams. The current nature of the water filling of the river is ensured by a cascade of reservoirs and maintenance of the flow rate due to water discharges from the South-Bug irrigation system fed from the South Bug. Despite the hydro-ecological problems, the river is still an important draining watercourse of the Tiligulo-Buzka interfluve, providing drainage, water regulation of the area and replenishment of underground horizons, with which the drinking water supply of 19 settlements is connected.

Thermodynamics of a quantum corrected Schwarzschild black hole in AdS spacetime

The thermodynamics for a quantum corrected Schwarzschild black hole with AdS background is investigated. First, the black hole metric is introduced and given when the spherical symmetric quantum fluctuations of spacetime are considered for Schwarzschild AdS black hole. Then, based on AdS background, we get the free energy for the quantum corrected black hole by AdS gravity renormalization and saddle-point approximation. By the spherical symmetric quantum fluctuation in AdS spacetime is considered, there are three main results found. Firstly, due to quantum fluctuation, there is a divergence term in the Euclidean action, which contributes to the energy of spacetime. Secondly, the entropy of the modified black hole is still proportional to the horizon area. But when the contribution of quantum fluctuations is deducted, the relationship between entropy and area is not so. It shows that, the area entropy theorem for the black hole is the both effect of quantum fluctuations and black hole. Thirdly, quantum fluctuation doesn't affect the temperature of Hawking-Page transition, but the radius of the black hole of Hawking-Page transition will be corrected.

Event horizon of a charged black hole binary merger

We analyze the formation and evolution of the event horizon of a black hole binary merger when the black holes are charged. We find that the presence of charge influences the properties of the merger and can be useful for investigating the validity of various theories of modified gravity and several proposals for dark matter candidates. It can moreover give insights into various aspects of astrophysical phenomena involving black holes, such as degeneracies in the gravitational wave parameter determination. We perform our analysis both analytically and numerically, in $D=4$ dimensions, in the extreme mass ratio (EMR) limit and compare the results. The development of analytical results in the EMR limit is of uttermost importance in view of the upcoming observations of the LISA interferometer. We then use our analysis to describe how the horizon evolves in time during the merger and to investigate the growth in the area of the event horizon and the duration of the merger. We moreover provide a numerical solution valid in arbitrary dimensions $D\ensuremath{\ge}4$ which could be of interest in the context of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence or for examining possible extensions of general relativity.

Resolving black-hole microstructure with new momentum carriers

All known horizonless black-hole microstate geometries correspond to brane sources that acquire a finite size, and hence break the spherical symmetry of the black hole. We construct, for the first time, solutions with zero horizon area that have the same charges as a three-charge F1-NS5-P Type-IIA black hole and preserve this spherical symmetry. The momentum of these solutions is carried by longitudinal D0-D4 density fluctuations inside the NS5-branes. We argue that these solutions should be interpreted as the long-throat limit of a family of smooth, horizonless microstate geometries, called superstrata, where such geometries degenerate. The existence of these geometries indicates that a finite-size horizon does not appear even in the singular corners of the moduli space of three-charge microstate geometries.

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar models in anti–de Sitter spacetime

The phenomenon of spontaneous scalarization of charged black holes has attracted a lot of attention. In this work, we study the dynamical process of the spontaneous scalarization of charged black hole in asymptotically anti-de Sitter spacetimes in Einstein-Maxwell-scalar models. Including various non-minimal couplings between the scalar field and Maxwell field, we observe that an initial scalar-free configuration suffers tachyonic instability and both the scalar field and the black hole irreducible mass grow exponentially at early times and saturate exponentially at late times. For fractional couplings, we find that though there is negative energy distribution near the black hole horizon, the black hole horizon area never decreases. But when the parameters are large, the evolution endpoints of linearly unstable bald black holes will be spacetimes with naked singularity and the cosmic censorship is violated. The effects of the black hole charge, cosmological constant and coupling strength on the dynamical scalarization process are studied in detail. We find that large enough cosmological constant can prevent the spontaneous scalarization.

Brown-York mass and positive scalar curvature I: First eigenvalue problem and its applications

In this article, we investigate the connection between scalar curvature and first eigenfunctions via positive mass theorem for Brown-York mass. For compact manifolds with nice boundary, we show that a sharp inequality holds for first eigenfunctions when posing appropriate assumptions on scalar curvature and first eigenvalue. This inequality implies that for a compact n n -dimensional manifold with boundary, its first eigenvalue is no less than n n , if its scalar curvature is at least n ( n − 1 ) n(n-1) with appropriate boundary conditions posed, where equality holds if and only the manifold is isometric to the canonical upper hemisphere. As an application, we derive an estimate for the area of event horizon in a vacuum static space with positive cosmological constant, which reveals an interesting connection between the area of event horizon and Brown-York mass. This estimate generalizes a similar result of Shen [Proc. Amer. Math. Soc. 125 (1997), pp. 901–905] for three dimensional vacuum static spaces and also improves the uniqueness result of de Sitter space-time due to Hizagi-Montiel-Raulot.

When null energy condition meets ADM mass

We give a conjecture on the lower bound of the ADM mass M by using the null energy condition. The conjecture includes a Penrose-like inequality and the Penrose inequality with the event horizon area and κ the surface gravity. Both the conjecture in the static spherically symmetric case and the Penrose inequality for a dynamical spacetime with spherical symmetry are proved by imposing the null energy condition. We then generalize the conjecture to a general dynamical spacetime. Our results raise a new challenge for the famous unsettled question in general relativity: in what general case can the null energy condition replace other energy conditions to ensure the Penrose inequality?

Constraining the topological Gauss-Bonnet coupling from GW150914

Recent gravitational wave observation based on the data from GW150914 has confirmed Hawking's area theorem and estimated the increase in total horizon area during a merger process of two Kerr black holes. We use this result and the validity of the second law to obtain the first observational bound on the 4D topological Gauss-Bonnet coupling as $\gamma \lesssim 2.804^{+7.946}_{-1.169} \times 10^{9}\, m^2$ with $95 \%$ credibility.

The irreducible mass and the horizon area of LIGO’s black holes

The mass of a Kerr black hole (BH) can be separated into irreducible and rotational components—the former is a lower limit to the energy that cannot be possibly extracted from the event horizon and is related to its area. Here we compute the irreducible masses of the stellar-mass BHs observed by gravitational-wave interferometers LIGO and Virgo. Using single-event data, we present a re-parameterization of the posterior distribution that explicitly highlights the irreducible and rotational contributions to the total energy. We exploit the area law to rank the black-hole mergers observed to date according to their irreversibility, thus providing a guide to selecting events for targeted tests of general relativity. Using population fits, we compute the rate by which the total area of black-hole horizons increases due to the observable mergers.

THE DESIGN PROFILE OF THE DIRECTIONAL WELL ON THE NORTHERN GOTURDEPE FIELD

When deciding to use the method of dual completion, the degree of depletion of reserves, the proximity of the oil-bearing contour to wells, the presence of resins and paraffin in the extracted oils, the thickness of productive layers and the non-permeable layers separating them, the state of the production column of wells, etc. are taken into account. The positive effect of applying the technology dual completion is expressed in a reduction in capital investments for the construction of wells for each of the operational facilities, in reducing operating costs and the development period of a multi-layer field, in increasing the production of hydrocarbons and the term of final oil recovery with cost-effective operation of wells. In addition, the use of this technology contributes to an increase in the utilization rate of downhole equipment and the reliability of the downhole installation. When two horizons are operated separately at the same time, the layers are separated from each other by a packer. One or two rows of pumping and compressor pipes descend into the well, which are lowered in parallel or concentrically. With dual completion of two or more horizons, reservoir development can be carried out according to the following schemes: fountain-fountain; fountain-pump; fountain-gas lift; fountain-injection; gas lift-pump; gas lift-gas lift, gas lift-injection; pump-pump; pump-injection; pump-injection. The article considers the experience of drilling a directional exploration well in Turkmenistan in order to trace and clarify the expansion of the area of productive horizons in the coastal zones of the coastal waters of the Caspian Sea. This work can be used for the development of fields in difficult-to-develop shallow waters and to reduce costs during their drilling, as well as to increase the volume of oil produced in order to develop the field using the method of dual completion (accelerated method), without increasing the oil recovery coefficient.

The first law for the Kerr-NUT spacetime

We show that the first law for the Kerr-NUT is straightforwardly established with the surface charge method. The entropy is explicitly found as a charge and its value is not proportional to the horizon area. We conclude that there are unavoidable contributions from the Misner strings to the charges, still the mass and angular momentum gets standard values. However, there are no independent charges associated with the Misner strings.

Global study of the scalar quasinormal modes of Kerr- AdS5 black holes: Stability, thermality, and horizon area quantization

We numerically explore the structure of quasi-normal (QN) frequencies of the five-dimensional small and large Kerr-anti de Sitter (Kerr-AdS${}_5$) black hole with equal and unequal rotations. Our investigation also covers low and high Hawking temperatures. We then study the stability of the Kerr-AdS${}_5$ black hole and the structure of highly damped QN modes, which would reflect the thermodynamic property of the Kerr-AdS${}_5$ black hole. We find that the highly damped complex QN frequencies of a nearly maximally spinning Kerr-AdS${}_5$ black hole have the periodic separation of the surface gravity at the horizon in the imaginary part while the real part converges to the superradiant frequency, which may be relevant to the pole structure of the thermal Green's function in the corresponding conformal field theory on the Kerr-AdS${}_5$ boundary. Finally, we discuss a relation between the QN modes of the Kerr-AdS${}_5$ black hole and the Hod's conjecture on the horizon area quantization along with the analysis of the horizon topology of the Kerr-AdS${}_5$ black hole. We show that in general, an ultra-spinning Kerr-AdS${}_5$ black hole, whose spin parameter is infinitesimally close to the AdS curvature radius, has its non-compact horizon, and based on the Hod's conjecture, we argue that the horizon area may be continuous, that is, the unit area of the horizon vanishes in the ultra-spinning regime.

Domain collisions

We use holography to study collisions of phase domains formed in a four-dimensional, strongly-coupled gauge theory with a first-order, thermal phase transition. We find three qualitatively different dynamical regimes depending on the collision velocity. For low velocities the domains slow down before the collision and subsequently merge and relax to equilibrium. For intermediate velocities no slow down is present before the merger. For high enough velocities the domains can collide and break apart several times before they finally merge. These features leave an imprint on the time evolution of the entropy of the system, which we compute from the area of the dual horizon on the gravity side.

Running Newton coupling, scale identification, and black hole thermodynamics

We discuss the quantum improvement of black hole solutions in the context of asymptotic safety. The Newton coupling in this formulation depends on an energy scale, which must be identified with some length scale in order to study physical consequences to black holes. However, no physical principle has so far been known for the identification. Here we propose that the consistency of the first law of thermodynamics is the principle that should determine physically sensible scale identification, at least close to the horizon. We show that this leads to a natural solution that the Newton coupling should be a function of the horizon area and find a universal formula for the quantum entropy, which agrees with the standard Bekenstein-Hawking entropy for constant Newton coupling, for Kerr black holes and other higher-dimensional black holes. This suggests that the Newton coupling is a function of the area near the horizon, and also away to infinity, where the quantum effects may not be so important.

Barrow black holes and the minimal length

Following Barrow's idea of fractal black hole horizon, we re-derive black hole entropy of static spherically symmetric black holes. When a black hole absorbs matter its horizon area will increase. Given the spherically fractal structure, we conjecture that the minimal increase of the horizon area should be the area of the smallest bubble sphere. From this, we find the black hole entropy has a logarithmic form, which is similar to that of Boltzmann entropy if we consider A/Apl as the number of microscopic states. We further calculate temperatures and heat capacities of Schwarzschild, Reissner-Nordström (RN), and RN-AdS black holes. It is found that their temperatures are all monotonically increasing and the heat capacities are all positive, which means these black holes are thermodynamically stable. Besides, for RN-AdS black hole we find its heat capacity has Schottky anomaly-like behavior, which may reflect the existence of the discrete energy level and restricted microscopical degree of freedom.

On light surfaces in black hole thermodynamics

We discuss the fundamentals of classical black hole (BH) thermodynamics in a new framework determined by light surfaces and their frequencies. This new approach allows us to study BH transitions inside the Kerr geometry. In the case of BHs, we introduce a new parametrization of the metric in terms of the maximum extractable rotational energy or, correspondingly, the irreducible mass, which is an alternative to the spin parametrization. It turns out that BH spacetimes with spins a/M= sqrt{8/9} and a/M=1/sqrt{2} show anomalies in the rotational energy extraction and surface gravity whereas the case a/M=sqrt{3}/2 is of particular relevance to study the variations of the horizon area. We find the general conditions under which BH transitions can occur and express them in terms of the masses of the initial and final states. This shows that BH transitions in the Kerr geometry are not arbitrary but depend on the relationship between the mass and spin of the initial and final states. From an observational point of view, we argue that near the BH poles it is possible to detect photon orbits with frequencies that characterize the light surfaces analyzed in this work.

Quantum black hole–white hole entangled states

We investigate the quantum deformation of the Wheeler–DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg–Weyl Uq(h4) group. We show that the event horizon area and the mass are quantized, degenerate, and bounded. The degeneracy of states indicates entangled quantum black hole/white hole states. Accordingly, quantum deformation provides a new framework to examine Einstein–Rosen wormhole solutions. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Schwarzschild black hole. We find an upper bound on the mass of a black hole/white hole pair. Also, at the quantum deformation level, the entropy of the black hole contains three parts: the usual Bekenstein–Hawking entropy, the logarithmic term, and a Cube of usual black hole entropy.

Constructions of entropy and modified Friedmann equations in gravity theories

The FRW universe is considered a thermodynamical system. We assume that the universe filled in a perfect fluid. So, we obtain apparent horizon radius, surface gravity, and temperature. Using the unified first law as well as the first law of thermodynamics and Friedmann equations, we obtain the entropy-area relation on the apparent horizon in Einstein’s gravity. In Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories, using corresponding Friedmann equations, we obtain the corresponding entropies in integration forms. Next, for a power law, future singularity, and de Sitter expansions, we obtain the general entropy function F(A) in terms of horizon area A on different IR cutoffs like Hubble, apparent, particle, event, (m, n)-type event, conformal age, and Ricci horizons. Moreover, by considering general entropy, we determine the modified Friedmann equations for Horava–Lifshitz gravity, scalar–tensor gravity, f(R) gravity and f(T) gravity theories.

The averaged null energy condition on holographic evaporating black holes

We examine the averaged null energy condition (ANEC) for strongly coupled fields, along the event horizon of an evaporating black hole by using the AdS/CFT duality. First, we consider a holographic model of a 3-dimensional evaporating black hole with a perturbed 4-dimensional black droplet geometry as the bulk dual, and investigate how negative energy flux going into the boundary black hole horizon appears. We show that the ingoing negative energy flux always appears at the boundary black hole horizon when the horizon area decreases. Second, we test the ANEC in a holographic model whose boundary geometry is a 4-dimensional asymptotically flat spacetime, describing the formation and subsequent evaporation of a spherically symmetric black hole. By applying the “bulk-no-shortcut principle”, we show that the ANEC is always satisfied when the local null energy is averaged with a weight function along the incomplete null geodesic on the event horizon from beginning of the formation to the final instant of the black hole evaporation. Our results indicate that the total ingoing negative energy flux is compensated by a large amount of positive energy flux in the early stage of the black hole formation.