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Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 145 records · Page 8Linked to original sources
arXiv2015

Numerical evidence for universality in the excited instability spectrum of magnetically charged Reissner-Nordström black holes

It is well-known that the SU(2) Reissner-Nordström black-hole solutions of the Einstein-Yang-Mills theory are characterized by an infinite set of unstable (imaginary) eigenvalues $\{ω_n(T_{\text{BH}})\}_{n=0}^{n=\infty}$ (here $T_{\text{BH}}$ is the black-hole temperature). In this paper we analyze the excited instability spectrum of these magnetically charged black holes. The numerical results suggest the existence of a universal behavior for these black-hole excited eigenvalues. In particular, we show that unstable eigenvalues in the regime $ω_n\ll T_{\text{BH}}$ are characterized, to a very good degree of accuracy, by the simple universal relation $ω_n(r_+-r_-)={\text{constant}}$, where $r_{\pm}$ are the horizon radii of the black hole.

gr-qc↗
arXiv2014

Onset of superradiant instabilities in the composed Kerr-black-hole-mirror bomb

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, $r^{\text{stat}}_{\text{m}}$, which supports {\it 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 $r_{\text{m}} r^{\text{stat}}_{\text{m}}$ 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 ({\it 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.

gr-qc↗
arXiv2014

Self-gravitating field configurations: The role of the energy-momentum trace

Static spherically-symmetric matter distributions whose energy-momentum tensor is characterized by a non-negative trace are studied analytically within the framework of general relativity. We prove that such field configurations are necessarily highly relativistic objects. In particular, for matter fields with $T\geqα\cdotρ\geq0$ (here $T$ and $ρ$ are respectively the trace of the energy-momentum tensor and the energy density of the fields, and $α$ is a non-negative constant), we obtain the lower bound $\text{max}_r\{2m(r)/r\}>(2+2α)/(3+2α)$ on the compactness (mass-to-radius ratio) of regular field configurations. In addition, we prove that these compact objects necessarily possess (at least) {\it two} photon-spheres, one of which exhibits {\it stable} trapping of null geodesics. The presence of stable photon-spheres in the corresponding curved spacetimes indicates that these compact objects may be nonlinearly unstable. We therefore conjecture that a negative trace of the energy-momentum tensor is a {\it necessary} condition for the existence of stable, soliton-like (regular) field configurations in general relativity.

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arXiv2014

Rotating black holes can have short bristles

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.

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arXiv2014

The instability spectrum of weakly-magnetized SU(2) Reissner-Nordström black holes

It is well known that the U(1) Reissner-Nordström black hole is stable within the framework of the Einstein-Maxwell theory. However, the SU(2) Reissner-Nordström black-hole solution of the coupled Einstein-Yang-Mills equations is known to be unstable. In fact, this magnetically charged black hole is characterized by an infinite set of unstable (growing in time) perturbation modes. In the present paper we study {\it analytically} the instability resonance spectrum of weakly-magnetized SU(2) Reissner-Nordström black holes. In particular, we obtain explicit analytical expressions for the infinite set $\{ω_n\}_{n=0}^{n=\infty}$ of imaginary eigenvalues that characterize the instability growth rates of the perturbation modes. We discuss the role played by these unstable eigenvalues as critical exponents in the gravitational collapse of the Yang-Mills field. Finally, it is shown that our analytical formulas for the characteristic black-hole instability spectrum agree with new numerical data that recently appeared in the literature.

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arXiv2014

Resonance spectra of caged black holes

Recent numerical studies of the coupled Einstein-Klein-Gordon system in a cavity have provided compelling evidence that {\it confined} scalar fields generically collapse to form black holes. Motivated by this intriguing discovery, we here use analytical tools in order to study the characteristic resonance spectra of the confined fields. These discrete resonant frequencies are expected to dominate the late-time dynamics of the coupled black-hole-field-cage system. We consider caged Reissner-Nordström black holes whose confining mirrors are placed in the near-horizon region $x_{\text{m}}\equiv (r_{\text{m}}-r_+)/r_+\llτ\equiv (r_+-r_-)/r_+$ (here $r_{\text{m}}$ is the radius of the confining mirror and $r_{\pm}$ are the radii of the black-hole horizons). We obtain a simple analytical expression for the fundamental quasinormal resonances of the coupled black-hole-field-cage system: $ω_n=-i2πT_{\text{BH}}\cdot n[1+O(x^n_{\text{m}}/τ^n)]$, where $T_{\text{BH}}$ is the temperature of the caged black hole and $n=1,2,3,...$ is the resonance parameter.

gr-qc↗
arXiv2014

A short remark (with a long title) on the universality of the quasinormal spectrum of near-extremal Kerr-Newman black holes

In a recent paper (arXiv:1410.0694) Zilhão, Cardoso, Herdeiro, Lehner, and Sperhake have studied the nonlinear stability of Kerr-Newman black holes. We show that their numerical results for the time evolutions of the spacetime deformations of near-extremal Kerr-Newman black holes are described extremely well by a {\it universal} formula for the quasinormal resonances of the black holes. This formula is expressed in terms of the black-hole physical parameters: the horizon angular velocity $Ω_{\text{H}}$ and the Bekenstein-Hawking temperature $T_{\text{BH}}$.

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arXiv2014

Kerr-Newman black holes with stationary charged scalar clouds

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.

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arXiv2014

Onset of superradiant instabilities in the hydrodynamic vortex model

The hydrodynamic vortex, an effective spacetime geometry for propagating sound waves, is studied analytically. In contrast with the familiar Kerr black-hole spacetime, the hydrodynamic vortex model is described by an effective acoustic geometry which has no horizons. However, this acoustic spacetime possesses an ergoregion, a property which it shares with the rotating Kerr spacetime. It has recently been shown numerically that this physical system is linearly unstable due to the superradiant scattering of sound waves in the ergoregion of the effective spacetime. In the present study we use analytical tools in order to explore the onset of these superradiant instabilities which characterize the effective spacetime geometry. In particular, we derive a simple analytical formula which describes the physical properties of the hydrodynamic vortex system in its critical (marginally-stable) state, the state which marks the boundary between stable and unstable fluid configurations. The analytically derived formula is shown to agree with the recently published numerical data for the hydrodynamic vortex system.

gr-qc↗
arXiv2014

Algebraically special resonances of the Kerr-black-hole-mirror bomb

A co-rotating 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 $ω=mΩ_{\text{H}}+is\cdot 2πT_{\text{BH}}$ (here $s$ and $m$ are respectively the spin-parameter and the azimuthal harmonic index of the field, and $Ω_{\text{H}}$ and $T_{\text{BH}}$ 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 which characterize the higher-spin black-hole bombs are two orders of magnitudes larger than the instability growth rate of the scalar black-hole bomb.

gr-qc↗
arXiv2014

Self-gravitating ring of matter in orbit around a black hole: The innermost stable circular orbit

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$. In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$, the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(μ\ln(M/r))$, where $μ\equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.

gr-qc↗
arXiv2014

Asymptotic late-time tails of massive spin-2 fields

The late-time dynamics of massive spin-2 fields in flat and curved spacetimes are studied analytically. We find that the time evolutions of the massive fields are characterized by oscillatory power-law decaying tails at asymptotically late times. In a flat spacetime the decaying exponent depends on the multipole number and the parity of the mode. In the curved Schwarzschild black-hole spacetime the decaying exponent is found to be universal.

gr-qc↗
arXiv2013

The gravitational two-body problem in the vicinity of the light ring: Insights from the black-hole-ring toy model

The physical properties of an axisymmetric black-hole-ring system are studied analytically within the framework of general relativity to second order in the dimensionless mass ratio $μ\equiv m/M$. In particular, we analyze the asymptotic behaviors of the binding-energy and the total angular-momentum of the two-body system in the vicinity of the light ring at $R=3M$, where the circular orbit becomes null. We find that both quantities diverge {\it quadratically} in $μ(1-3M/R)^{-1}$ at the light ring. The reported divergent behavior of the physical quantities stems from the second order spin-orbit interaction between the black hole and the orbiting object (the dragging of inertial frames by the orbiting ring). It is shown that this composed black-hole-ring toy model captures some of the essential features of the conservative dynamics of the (astrophysically more interesting) black-hole-particle system. In particular, we show that both systems share the {\it same} quadratic divergent behavior of the physical quantities near the light ring. Moreover, we prove that both systems are characterized by the {\it same} ratio ${{E^{(2)}(R\to 3M)}\over{J^{(2)}(R\to 3M)}}={{1}\over{3\sqrt{3}}}$, where $E^{(2)}$ and $J^{(2)}$ are the divergent second order (self-interaction) expansion coefficients of the binding-energies and the angular-momenta of the systems, respectively.

gr-qc↗
arXiv2013

Stationary resonances of rapidly-rotating Kerr black holes

The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field in the black-hole spacetime. The analytically derived formula is shown to agree with direct numerical computations of the resonances. Our results provide an upper bound on the instability regime of rapidly-rotating Kerr black holes to massive scalar perturbations.

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arXiv2013

Purely imaginary polar resonances of rapidly-rotating Kerr black holes

We prove the existence of a unique family of non-oscillatory (purely-imaginary) polar quasinormal resonances of rapidly-rotating Kerr black holes. These purely imaginary resonances can be expressed in the compact form: w_n=-i2*pi*T_{BH}*(l+1+n), where T_{BH} is the black-hole temperature, l is the spheroidal harmonic index of the mode, and n=0,1,2,... is the resonance parameter. It is shown that our analytical results for the black-hole resonance spectrum agree with new numerical data that recently appeared in the literature.

gr-qc↗
arXiv2013

Analytic toy-model for the ISCO shift

A simple black-hole-ring system is proposed as a toy model for the two-body problem in general relativity. This toy-model yields the fractional shift $ΔΩ_{\text{isco}}/Ω_{\text{isco}}={{29}\over{81\sqrt{2}}}η$ in the Schwarzschild ISCO (innermost stable circular orbit) frequency, where $η\equiv m/M_{\text{ir}}\ll 1$ is the dimensionless ratio between the mass of the particle and the irreducible mass of the black hole. Our model suggests that the second-order spin-orbit interaction between the black hole and the orbiting particle (the dragging of inertial frames) is the main element determining the observed value of the ISCO shift.

gr-qc↗
arXiv2013

Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime

A charged scalar field impinging upon a charged Reissner-Nordstrom black hole can be amplified as it scatters off the hole, a phenomenon known as superradiant scattering. This scattering process in the superradiant regime w >1 and for mirror radii r_m in the near-horizon region x_m=(r_m-r_+)/r_+< >(tau/x_m)^2>>1 regime, which implies that the instability timescale 1/w_I of the system can be made arbitrarily short in the qQ-->infinity limit. The short instability timescale found in the linear regime along with the spherical symmetry of the system, make the charged bomb a convenient toy model for future numerical studies aimed to investigate the non-linear end-state of superradiant instabilities.

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