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Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2014

The elegant 'no short hair' theorem states that, if a spherically-symmetric static black hole has hair, then this hair must extend beyond 3/2 the horizon radius. In the present paper we provide evidence for the failure of this theorem beyond the regime of spherically-symmetric static black holes. In particular, we show that rotating black holes can support extremely short-range stationary scalar configurations (linearized scalar 'clouds') in their exterior regions. To that end, we solve analytically the Klein-Gordon-Kerr-Newman wave equation for a linearized massive scalar field in the regime of large scalar masses. © 2014 The Author.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2014

It was first pointed out by Press and Teukolsky that a system composed of a spinning Kerr black hole surrounded by a reflecting mirror may develop instabilities. The physical mechanism responsible for the development of these exponentially growing instabilities is the superradiant amplification of bosonic fields confined between the black hole and the mirror. A remarkable feature of this composed black-hole-mirror-field system is the existence of a critical mirror radius, rmstat, which supports stationary (marginally-stable) field configurations. This critical ('stationary') mirror radius marks the boundary between stable and unstable black-hole-mirror-field configurations: composed systems whose confining mirror is situated in the region rmrmstat are unstable (that is, there are confined field modes which grow exponentially over time). In the present paper we explore this critical (marginally-stable) boundary between stable and explosive black-hole-mirror-field configurations. It is shown that the innermost (smallest) radius of the confining mirror which allows the extraction of rotational energy from a spinning Kerr black hole approaches the black-hole horizon radius in the extremal limit of rapidly-rotating black holes. We find, in particular, that this critical mirror radius (which marks the onset of superradiant instabilities in the composed system) scales linearly with the black-hole temperature. © 2014 The Author.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2013

The fundamental role played by black holes in many areas of physics makes it highly important to explore the nature of their stability. The stability of charged 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 complexity introduced by 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 the superradiant amplification of charged fields by the charged black hole may lead to an instability of the Reissner-Nordström spacetime (in as much the same way that rotating Kerr black holes are unstable under rotating scalar perturbations). However, in this Letter we show that, for charged Reissner-Nordström black holes in the regime (Q/M)2≤8/9, 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 charged Reissner-Nordström black holes under charged scalar perturbations in the regime (Q/M)2≤8/9. © 2012 Elsevier B.V.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

Perfect black-body emitters in a flat three-dimensional space are characterized by the well-known relation S ˙flat3D=(32π2AP3/1215h{stroke}3)1/4, where S ˙flat and P are respectively the entropy and energy emission rates out of the 3-D hot body, and A is the 2-D surface area of the emitting body. However, Bekenstein and Mayo have pointed out that three-dimensional Schwarzschild black holes are characterized by a qualitatively different relation: S ˙BH3D=CBH3D×(P/h{stroke})1/2, where CBH3D is a numerically computed proportionality coefficient. Thus, in their entropy emission properties, these three-dimensional black holes effectively behave as one-dimensional entropy emitters: in particular, they respect Pendry's upper bound S ˙flat1D=Cflat1D×(P/h{stroke})1/2 on the entropy emission rate out of one-dimensional flat-space thermal bodies, where Cflat1D=(π/3)1/2. One naturally wonders whether this intriguing property of the three-dimensional black holes is a generic feature of all D-dimensional Schwarzschild black holes? In this paper we shall show that the answer to this question (and to the question raised in the title) is 'Yes and No'. 'Yes', because we shall prove that all D-dimensional Schwarzschild black holes are characterized by the one-dimensional functional relation S ˙BHD=CBHD×(P/h{stroke})1/2. 'No', because we shall show that, in the large-D limit, the analytically calculated coefficients CBHD are larger than Cflat1D=(π/3)1/2, implying that higher-dimensional black holes may violate Pendry's upper bound on the entropy emission rate of one-dimensional physical systems. © 2015 The Author.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

The spheroidal harmonics Slm(θ;c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm(c)} of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m→∞ with a fixed value of c, or to the complementary regime |c|→∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m→∞ and |c|→∞ with a fixed m/c ratio. © 2015 The Author.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit α. ≡. Mμ. ≪. 1 (here μ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: ωR/μ=1-α2/2n-02, where the integer n-0(l,n;α→0)=l+n+1 is the principal quantum number of the bound-state resonance (here the integers l=. 1, 2, 3, . . . and n=. 0, 1, 2, . . . are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter n-0, this small-mass (α. ≪. 1) hydrogenic spectrum is obviously degenerate. In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime α. =. O(1). In particular, we derive the non-hydrogenic (and, in general, non-degenerate) resonance oscillation spectrum ωR/μ=1-(α/n-)2, where n-(l,n;α)=(l+1/2)2-2mα+2α2+1/2+n is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances. © 2015 The Author.


Hod S.,Ruppin Academic Center | Hod S.,The Hadassah Institute
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015

The recently proved 'no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: rfield>rnull. In this paper we provide compelling evidence that the bound can be violated by non-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes - charged rotating black holes which support linearized stationary charged scalar configurations in their exterior regions. In particular, for given parameters {M, Q, J} of the central black hole, we find the dimensionless ratio q/μ of the field parameters which minimizes the effective lengths (radii) of the exterior stationary charged scalar configurations (here {M, Q, J} are respectively the mass, charge, and angular momentum of the black hole, and {μ, q} are respectively the mass and charge coupling constant of the linearized scalar field). This allows us to prove explicitly that (non-spherically symmetric non-static) composed Kerr-Newman-charged-scalar-field configurations can violate the no-short-hair lower bound. In particular, it is shown that extremely compact stationary charged scalar 'clouds', made of linearized charged massive scalar fields with the property rfield→rH, can be supported in the exterior spacetime regions of extremal Kerr-Newman black holes (here rfield is the peak location of the stationary scalar configuration and rH is the black-hole horizon radius). Furthermore, we prove that these remarkably compact stationary field configurations exist in the entire range s≡J/M2∈(0, 1) of the dimensionless black-hole angular momentum. In particular, in the large-mass limit they are characterized by the simple dimensionless ratio q/μ=(1-2s2)/(1-s2). © 2015 The Author.


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

The fundamental resonances of rapidly rotating Kerr black holes in the eikonal limit are derived analytically. We show that there exists a critical value, μ c for the dimensionless ratio μm/l between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode, above which the perturbations become long lived. In particular, it is proved that above μ c the imaginary parts of the quasinormal frequencies scale like the black-hole temperature: ωI(n;μ>μc)=2πTBH(n+12). This implies that for perturbations modes in the interval μ c<μ≤1, the relaxation period τ~1/ω I of the black hole becomes extremely long as the extremal limit T BH→0 is approached. A generalization of the results to the case of scalar quasinormal resonances of near-extremal Kerr-Newman black holes is also provided. In particular, we prove that only black holes that rotate fast enough (with MΩ≥25, where M and Ω are the black-hole mass and angular velocity, respectively) possess this family of remarkably long-lived perturbation modes. © 2012 Elsevier B.V.


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

The fundamental quasinormal resonances of charged Reissner-Nordström black holes due to charged scalar perturbations are derived analytically. In the WKB regime, qq>ℏ, we obtain a simple expression for the fundamental quasinormal resonances: ω=qQ/r +-i2πT BH(n+12), where T BH and Q are the temperature and electric charge of the black hole and q is the electric charge of the field. Remarkably, our results show that the relaxation dynamics of a perturbed Reissner-Nordström black hole may saturate the recently proposed universal relaxation bound. © 2012 Elsevier B.V.


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

The instability of rotating Kerr black holes due to massive scalar perturbations is investigated. It is well known that a bosonic field impinging on a Kerr black hole can be amplified as it scatters off the hole. This superradiant scattering occurs for frequencies in the range ω < mΩ, where Ω is the angular frequency of the black hole and m is the azimuthal harmonic index of the mode. If the incident field has a non-zero rest mass, μ, then the mass term effectively works as a mirror, reflecting the scattered wave back towards the black hole. The wave may bounce back and forth between the black hole and some turning point amplifying itself each time. This may lead to a dynamical instability of the system, a phenomena known as a "black-hole bomb". In this work we provide a bound on the instability regime of rotating Kerr spacetimes. In particular, we show that Kerr black holes are stable to massive perturbations in the regime μ≥2mΩ. © 2012 Elsevier B.V.

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