Black Hole Area Research Articles

Spectral Lines of Quantized, Spinning Black Holes and their Astrophysical Relevance.

In this Letter, we study black hole area quantization in the context of gravitational wave physics. It was recently argued that black hole area quantization could be a mechanism to produce so-called echoes as well as characteristic absorption lines in gravitational wave observations of merging black holes. One can match the spontaneous decay of these quantum black holes to Hawking radiation calculations. Using some assumptions, one can then estimate the natural widths of these states. As can be seen from a classical paper by Bekenstein and Mukhanov, the ratio between width and spacing of nonspinning black hole states approaches a small constant, which seems to confirm the claim. However, we find that, including the effect of black hole spin, the natural widths increase. To properly address any claim about astrophysical black holes, one should examine the spinning case, as real black holes spin. Thus, the word "spinning" is key to the question of whether or not black holes should have an observable spectrum in nature. Our results suggest that it should be possible to distinguish between any scenarios for which the answer to this question is yes. However, for all of the commonly discussed scenarios, our answer is "almost certainly no."

Black holes quasinormal modes, Loop Quantum Gravity Immirzi parameter and nonextensive statistics

It is argued that, using the black hole area entropy law together with the Boltzmann-Gibbs statistical mechanics and the quasinormal modes of the black holes, it is possible to determine univocally the lowest possible value for the spin j in the context of the Loop Quantum Gravity theory which is jmin=1. Consequently, the value of Immirzi parameter is given by γ=ln⁡3/(2π2). In this paper, we have shown that if we use Tsallis microcanonical entropy rather than Boltzmann-Gibbs framework then the minimum value of the label j depends on the nonextensive q-parameter and may have values other than jmin=1.

Dyon-Like Black Hole Solutions in the Model with Two Abelian Gauge Fields

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter e = ±1 before the scalar field kinetic term. Here e = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $$\lambda_i^2 \neq 1/2$$ for e = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented.

Gravitational wave echoes from black hole area quantization

Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave “echoes” in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization.

Area and entropy quantization of quantum-corrected Schwarzschild black hole surrounded by quintessence

In this paper, the minimal change in the area and the entropy of quantum-corrected Schwarzschild black hole immersed in the quintessence matter is investigated. Utilizing two different approaches, namely, the periodicity of the outgoing wave and the black hole adiabatic property, the area spectrum is derived, which is independent of both the length scale coming from quantum deformation of the Schwarzschild black hole, and the quintessential state parameter, and which is in agreement with the uniform area spacing originally found by Bekenstein.

Black hole entropy without microstates

I argue that black hole area should be thought of as an ‘entropy-like quantity’ rather than an entropy. This precludes the need for a statistical mechanical description of black hole thermodynamics in terms of microstates.

Spectroscopy of quantum-corrected Schwarzschild black hole

The quantization of black hole parameters is a long-standing topic in physics. Adiabatic invariance, periodicity of outgoing waves, quantum tunneling, and quasi-normal modes are the typical tools via which the area and the entropy of a black hole are quantized. In this paper, the quantum spectra of area and entropy of quantum-corrected Schwarzschild black hole are investigated. The deformation in the space–time of Schwarzschild black hole was perused by Kazakov and Solodukhin. Here the deformed Schwarzschild metric is taken into account, and the effect of the space–time modification on the minimal area and entropy increment for the Schwarzschild black hole is scrutinized, utilizing two different procedure: Jiang-Han's method of the adiabatic invariant integral and Zeng et al.'s approach of the periodic property of outgoing waves. The analyses of this paper draw the conclusion that the quantum correction to the space–time does not alter the quantum characteristics of the Schwarzschild black hole.

Observational tests of the black hole area increase law

The black hole area theorem implies that when two black holes merge, the area of the final black hole should be greater than the sum of the areas of the two original black holes. We examine how this prediction can be tested with gravitational-wave observations of binary black holes. By separately fitting the early inspiral and final ringdown stages, we calculate the posterior distributions for the masses and spins of the two initial and the final black holes. This yields posterior distributions for the change in the area and thus a statistical test of the validity of the area increase law. We illustrate this method with a GW150914-like binary black hole waveform calculated using numerical relativity, and detector sensitivities representative of both the first observing run and the design configuration of Advanced LIGO. We obtain a $\sim74.6\%$ probability that the simulated signal is consistent with the area theorem with current sensitivity, improving to $\sim99.9\%$ when Advanced LIGO reaches design sensitivity. An important ingredient in our test is a method of estimating when the post-merger signal is well-fit by a damped sinusoid ringdown waveform.

Entropy spectrum and area spectrum of Kerr black hole in gravity's rianbow

Black hole spectroscopy is an important content in the quantum properties of black holes. In this paper, we use the adiabatic invariants of black holes to investigate the entropy spectrum and area spectrum of the Kerr black hole in gravity's rainbow. Firstly, by considering the particles passing through the event horizon, the adiabatic invariance action for the modified Kerr black hole is calculated. Here, the Euclidean coordinate and the period of the Euclidean time of a loop about the event horizon are used. Combined the obtained adiabatic invariants with the Bohr-Sommerfen quantization condition, the equally spaced entropy spectra that are the same as the original Beckenstein spectra are derived. The entropy spectrum of the gravity's rainbow is independent of the test particle energy. Next, using the first law of the black hole thermodynamics and the black hole entropy spectrum, the area spectrum of the modified Kerr black hole is studied. Due to the quantum gravity effect of the gravity's rainbow, the obtained area spectrum is different from the original Beckenstein spectrum. The present area spectrum is non-equidistant and dependent on the horizon area of the black hole. With the decrease of black hole area, the area space gradually turns smaller. When the black hole reaches the minimum area on a Planck scale, the area quantum is zero. Thus the black hole area no longer decrease and a remnant of the black hole radiation appears. In the case of a large black hole, the correction of the area spectrum to the equally spaced spectra can be ignored, and the area spectrum of the Kerr black hole in gravity's rainbow can return to the original Beckenstein spectrum. It is also shown that like the entropy spectrum, the area spectrum of the gravity's rainbow does not depend on the energy of the test particles either. In addition, the entropy of the modified Kerr black hole in gravity's rainbow is discussed by using the first law of the black hole thermodynamics. The black hole entropy with quantum correction items as the area reciprocal to the Beckenstein-Hawking entropy is derived and the relation between the quantum correction items and the area is discussed. In addition, the consistency between the entropy correction and the area correction for the modified black hole is analyzed. The current research supports that in different spacetimes including quantum corrected spacetimes, the black hole entropy spectrum has the universality, but the black hole area spectrum is dependent on the area due to the spacetime quantum properties.

Dilatonic dyon-like black hole solutions in the model with two Abelian gauge fields

Dilatonic black hole dyon-like solutions in the gravitational 4d model with a scalar field, two 2-forms, two dilatonic coupling constants lambda _i ne 0, i =1,2, obeying lambda _1 ne - lambda _2 and the sign parameter varepsilon = pm 1 for scalar field kinetic term are considered. Here varepsilon = - 1 corresponds to a ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when lambda ^2_i ne 1/2 for varepsilon = - 1. Some physical parameters of the solutions are obtained: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters beta and gamma . The PPN parameters do not depend on the couplings lambda _i and varepsilon . A set of bounds on the gravitational mass and scalar charge are found by using a certain conjecture on the parameters of solutions, when 1 +2 lambda _i^2 varepsilon > 0, i =1,2.

Universality of DC electrical conductivity from holography

We propose a universal formula of dc electrical conductivity in rotational- and translational- symmetries breaking systems via the holographic duality. This formula states that the ratio of the determinant of the dc electrical conductivities along any spatial directions to the black hole area density in zero-charge limit has a universal value. As explicit illustrations, we give several examples elucidating the validation of this formula: We construct an anisotropic black brane solution, which yields linear in temperature for the in-plane resistivity and insulating behavior for the out-of-plane resistivity; We also construct a spatially isotropic black brane solution that both the linear-T and quadratic-T contributions to the resistivity can be realized.

Goldstone origin of black hole hair from supertranslations and criticality

Degrees of freedom that carry black hole entropy and hair can be described in the language of Goldstone phenomenon. They represent the pseudo-Goldstone bosons of certain supertranslations, called [Formula: see text]-transformations, that are spontaneously broken by the black hole metric. This breaking gives rise to a tower of Goldstone bosons created by the spontaneously-broken generators that can be labeled by spherical harmonics. Classically, the number of charges is infinite, they have vanishing vacuum expectation values (VEVs) and the corresponding Goldstone modes are gapless. The resulting hair and entropy are infinite, but unresolvable. In quantum theory, the two things happen. The number of legitimate Goldstone modes restricted by requirement of weak-coupling, becomes finite and scales as black hole area in Planck units. The Goldstones generate a tiny gap, controlled by their gravitational coupling. The gap turns out to be equal to the inverse of black hole half-life, [Formula: see text]. Correspondingly, in quantum theory the charges are neither conserved nor vanish, but non-conservation time is set by [Formula: see text]. This picture nicely matches with the idea of a black hole as critical system is composed of many soft gravitons. The [Formula: see text]-Goldstones of geometric picture represent the near-gapless Bogoliubov–Goldstone modes of critical soft-graviton system.

Black hole collapse and democratic models

We study the evolution of black hole entropy and temperature in collapse scenarios, finding three generic lessons. First, entropy evolution is extensive. Second, at large times, entropy and temperature ring with twice the frequency of the lowest quasinormal mode. Third, the entropy oscillations saturate black hole area theorems in general relativity. The first two features are characteristic of entanglement dynamics in `democratic' models. Solely based on general relativity and Bekenstein-Hawking entropy formula, our results point to democratic models as microscopic theories of black holes. The third feature can be taken as a prediction for democratic models coming from black hole physics.

A QOS Parameter based Solution for Black hole Denial of Service Attack in Wireless Sensor Networks

Background/Objectives: A typical Wireless Sensor Network (WSN) is a collection of Sensor nodes with limited charge that get deployed in a range enabling different applications. Enormous potential is there for deployment of WSN in consumer centric applications, industry sector and defence. Method: WSNs are vulnerable to various types of attack, upon which black-hole, a type of Denial of Service (DoS) pose enormous challenge in detection and defence. The primary characteristic of the attack is that reprogramming done by attackers in the captured nodes block the packets received than forwarding to the base station. This results in information entering the black hole area not getting routed to the destination and degradation of QoS factors of delay and final throughput. In this study a comparative performance weighing of Star and tree topology setup of WSN nodes is carried out under the black hole scenario. In case, the parameter of delay is vital Mesh setup is chosen and in the requirement of throughput efficiency and fault tolerance Star topology is chosen. A methodology for choosing the topology depending on the required service parameter under black hole scenario is also devised. Findings: The vital parameters considered for the simulation study are delay in transmission of packets and throughput efficiency among the sensor nodes. The results prove a considerable reduction of the parameter of delay in transmission of packets if hybrid topology is followed and a reasonable increase in the QoS parameter of throughput as mesh topology is adopted during transmission in a black hole vulnerable network. Improvements: The vital parameters of negligible delay and throughput efficiency that contribute effective cooperation among the sensor nodes are taken into account while choosing the appropriate topology, and the results show the distribution of the parameter values for the particular topology chosen.

On the Penrose inequality along null hypersurfaces

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a functional on surfaces and studying its properties along a null hypersurface Ω extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawking energy along a specific class of geodesic foliations called Geodesic Asymptotically Bondi (GAB), which are shown to always exist. Whenever this foliation approaches large spheres, this inequality becomes the null Penrose inequality and we recover the results of Ludvigsen–Vickers (1983 J. Phys. A: Math. Gen. 16 3349–53) and Bergqvist (1997 Class. Quantum Grav. 14 2577–83). By exploiting further properties of the functional along general geodesic foliations, we introduce an approach to the null Penrose inequality called the Renormalized Area Method and find a set of two conditions which imply the validity of the null Penrose inequality. One of the conditions involves a limit at infinity and the other a restriction on the spacetime curvature along the flow. We investigate their range of applicability in two particular but interesting cases, namely the shear-free and vacuum case, where the null Penrose inequality is known to hold from the results by Sauter (2008 PhD Thesis Zürich ETH), and the case of null shells propagating in the Minkowski spacetime. Finally, a general inequality bounding the area of the quasi-local black hole in terms of an asymptotic quantity intrinsic of Ω is derived.

The hot attractor mechanism: decoupling without deep throats

Non-extremal black holes in $\mathcal{N}=2$ supergravity have two horizons, the geometric mean of whose areas recovers the horizon area of the extremal black hole obtained from taking a smooth zero temperature limit. In prior work (arxiv:1410.3478), using the attractor mechanism, we deduced the existence of several moduli independent invariant quantities obtained from averaging over a decoupled inter-horizon region. We establish that non-extremal geometries at the Reissner--Nordstr\"om point, where the scalar moduli are held fixed, can be lifted to solutions in supergravity with a near-horizon AdS$_3\times$S$^2$. These solutions have the same entropy and temperature as the original black hole and therefore allow an interpretation of the underlying gravitational degrees of freedom in terms of CFT$_2$. Symmetries of the moduli space enable us to explicate the origin of entropy in the extremal limit.

Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor

We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein–Hawking term in the black hole entropy. The corrected classical Bekenstein–Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein–Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.

Dilatonic dyon black hole solutions

Dilatonic black hole dyon solutions with an arbitrary dilatonic coupling constant and canonical sign for the scalar field kynetic term are considered. These solutions are defined up to solutions of two master equations for moduli functions. For the solutions are extended to = ±1, where corresponds to a ghost (phantom) scalar field. Some physical parameters of the solutions: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters β and γ are obtained. It is shown that PPN parameters do not depend on scalar field coupling λ and ϵ. Two groups of bounds on gravitational mass and scalar charge (for a fixed and arbitrary extremality parameter ) are found by using a certain conjecture on parameters of solutions when . These bounds are verified numerically for certain examples. Using the product we are led to the well-known lower bound on mass which was obtained earlier by Gibbons, Kastor, London, Townsend and Traschen by using spinor techniques.

Shadow banking system in china after the global financial crisis

This article first examines the composition of the shadow banking system in China and then critically analyses its interconnectivity with the traditional banking system and global capital markets. It argues that whilst shadow bank lending in China contributes to the country's economic growth, the normal functionality of capital markets could be impaired if shadow banks continue to operate on a high-risk/high-yield business model which could potentially pose a systemic risk. It also addresses the concerns arising from high-leverage shadow bank lending practice and cautions against shadow banks operating in a black hole area that enables them to escape from regulatory purview. The article suggests that future regulatory (law) reform should guide shadow banks towards consumer protection by establishing an effective internal control system, enabling sufficient risk controls and requiring material information disclosure; towards safeguarding capital markets; and towards reducing their high levels of leverage.

Area spectrum from quasinormal modes of a Lifshitz black hole in 2+1 dimensions

In this paper, we have studied the area and mass spectrum of a Lifshitz black hole in 2+1 dimensions. This black hole is obtained for conformal gravity in 2+1 dimensions and is asymptotic to z = 0 Lifshitz spacetime. Quasinormal modes (QNM) frequencies of the conformally coupled scalar field perturbations are employed for the purpose of analyzing the area spectrum of the black hole. We have used two methods: modified Hod's conjecture and Kunsttater's method. In both methods, the area and the mass spectrum is shown to be equally spaced. We compared our results with the area spectrum of the BTZ black hole and the z = 3 black hole and made suggestions to extend this work in the future.