Hadassah Institute

West Jerusalem, Israel

Hadassah Institute

West Jerusalem, Israel
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Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review Letters | Year: 2010

Motivated by novel results in the theory of network synchronization, we analyze the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. We determine analytically the fundamental limit of synchronization efficiency in a noisy environment with uniform time delays. We show that the optimal efficiency of the network is achieved for λτ=π3/22√π+4≈0. 738, where λ is the coupling strength (relaxation coefficient) and τ is the characteristic time delay in the communication between pairs of nodes. Our analysis reveals the underlying mechanism responsible for the trade-off phenomena observed in recent numerical simulations of network synchronization problems. © 2010 The American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

A charged scalar field impinging upon a charged Reissner-Nordström black hole can be amplified as it scatters off the hole, a phenomenon known as super-radiant scattering. This scattering process in the super-radiant regime ω


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Classical and Quantum Gravity | Year: 2015

The interplay between black holes and fundamental fields has attracted much attention over the years from both physicists and mathematicians. In this paper we study analytically a physical system that is composed of massive scalar fields linearly coupled to a rapidly rotating Kerr black hole. Using simple arguments, we first show that the coupled black hole-scalar field system may possess stationary bound-state resonances (stationary scalar 'clouds') in the bounded regime 1 < μ/mΩH < √2, where μ and m are respectively the mass and azimuthal harmonic index of the field, and ΩH is the angular velocity of the black-hole horizon. We then show explicitly that these two bounds on the dimensionless ratio μ/mΩH can be saturated in the asymptotic m → ∞ limit. In particular, we derive a remarkably simple analytical formula for the resonance mass spectrum of the stationary bound-state scalar clouds in the regime Mμ 蠑 of large field masses: μn = √2mΩH [ 1 - m | ln τ |/π(R + n) ], where τ is the dimensionless temperature of the rapidly rotating (near extremal) black hole, R < 1 is a constant, and n = 0, 1, 2, ... is the resonance parameter. In addition, it is shown that, contrary to the flat-space intuition, the effective lengths of the scalar field configurations in the curved black-hole spacetime approach a finite asymptotic value in the large mass Mμ 蠑 1 limit. In particular, we prove that in the large mass limit, the characteristic length scale of the scalar clouds scales linearly with the black-hole temperature. © 2015 IOP Publishing Ltd.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

A corotating bosonic field interacting with a spinning Kerr black hole can extract rotational energy and angular momentum from the hole. This intriguing phenomenon is known as superradiant scattering. As pointed out by Press and Teukolsky, the black-hole-field system can be made unstable (explosive) by placing a reflecting mirror around the black hole, which prevents the extracted energy from escaping to infinity. This composed black-hole-mirror-field bomb has been studied extensively by many researchers. It is worth noting, however, that most former studies of the black-hole bomb phenomenon have focused on the specific case of confined scalar (spin-0) fields. In the present study we explore the physical properties of the higher-spin (electromagnetic and gravitational) black-hole bombs. It is shown that this composed system is amenable to an analytic treatment in the physically interesting regime of rapidly rotating black holes. In particular, we prove that the composed black-hole-mirror-field bomb is characterized by the unstable resonance frequency ω=mΩH+is·2πTBH (here s and m are, respectively, the spin parameter and the azimuthal harmonic index of the field, and ΩH and TBH are, respectively, the angular-velocity and the temperature of the rapidly spinning black hole). Our results provide evidence that the higher-spin (electromagnetic and gravitational) black-hole-mirror bombs are much more explosive than the extensively studied scalar black-hole-mirror bomb. In particular, it is shown here that the instability growth rates that characterize the higher-spin black-hole bombs are 2 orders of magnitude larger than the instability growth rate of the scalar black-hole bomb. © 2013 American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

The weak cosmic censorship conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside of black holes, invisible to distant observers. This conjecture, put forward by Penrose more than four decades ago, is widely believed to be one of the basic principles of nature. However, a complete proof of this hypothesis is still lacking and the validity of the conjecture has therefore remained one of the most important open questions in general relativity. In this study we analyze a gedanken experiment that is designed to challenge cosmic censorship by trying to overcharge a Reissner-Nordström black hole: a charged shell is lowered adiabatically into the charged black hole. The mass energy delivered to the black hole can be redshifted by letting the dropping point of the shell approach the black-hole horizon. On the other hand, the electric charge of the shell is not redshifted by the gravitational field of the black hole. It therefore seems, at first sight, that the charged shell is not hindered from entering the black hole, overcharging it and removing its horizon. However, in the present study we prove that the exposure of a naked singularity to distant observers is actually excluded due to the formation of a new (and larger) horizon around the original black hole. Moreover, we shall prove that this new horizon is already formed before the charged shell crosses the original black-hole horizon. This result, which seems to have been previously overlooked, guarantees the validity of the weak cosmic censorship conjecture in this type of gedanken experiments. © 2013 American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

Motivated by novel results in the theory of wave dynamics in black-hole spacetimes, we analyze the dynamics of a massive scalar field surrounding a rapidly rotating Kerr black hole. In particular, we report on the existence of stationary (infinitely long-lived) regular field configurations in the background of maximally rotating black holes. The effective height of these scalar "clouds" above the central black hole is determined analytically. Our results support the possible existence of stationary scalar field dark matter distributions surrounding rapidly rotating black holes. © 2012 American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2011

Einstein-matter theories in which hairy black-hole configurations have been found are studied. We prove that the nontrivial behavior of the hair must extend beyond the null circular orbit (the photonsphere) of the corresponding spacetime. We further conjecture that the region above the photonsphere contains at least 50% of the total hair's mass. We support this conjecture with analytical and numerical results. © 2011 American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2014

It is shown that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. To that end, we solve analytically the Klein-Gordon wave equation for a stationary charged massive scalar field in the background of a near-extremal Kerr-Newman black hole. In particular, we derive a simple analytical formula which describes the physical properties of these stationary bound-state resonances of the charged massive scalar fields in the Kerr-Newman black-hole spacetime. © 2014 American Physical Society.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2012

The stability of Reissner-Nordström black holes to neutral (gravitational and electromagnetic) perturbations was established almost four decades ago. However, the stability of these charged black holes under charged perturbations has remained an open question due to the well-known phenomena of superradiant scattering: A charged scalar field impinging on a charged Reissner-Nordström black hole can be amplified as it scatters off the hole. If the incident field has a non-zero rest mass, then the mass term effectively works as a mirror, preventing the energy extracted from the hole from escaping to infinity. One may suspect that such superradiant amplification of charged fields in Reissner-Nordström spacetimes may lead to an instability of these charged black holes (in as much the same way that rotating Kerr black holes are unstable under rotating scalar perturbations). However, we show here that, for extremal Reissner-Nordström black holes, the two conditions which are required in order to trigger a possible superradiant instability [namely: (1) the existence of a trapping potential well outside the black hole, and (2) superradiant amplification of the trapped modes] cannot be satisfied simultaneously. Our results thus support the stability of extremal Reissner-Nordström black holes to charged scalar perturbations. © 2012 Elsevier B.V.


Hod S.,Ruppin Academic Center | Hod S.,Hadassah Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2011

The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived analytically. We show that there exists a critical mass parameter, μc, below which increasing the mass μ of the field increases the oscillation frequency (ω) of the resonance. On the other hand, above the critical field mass increasing the mass μ increases the damping rate (ω) of the mode. We confirm our analytical results by numerical computations. © 2011 American Physical Society.

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