arXiv subjects

Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 127 records · Page 7Linked to original sources

arXiv2016

Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime

We determine the characteristic timescales associated with the linearized relaxation dynamics of the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system. To that end, the quasinormal resonant frequencies $\{ω_n(μ,q,M,Q)\}_{n=0}^{n=\infty}$ which characterize the dynamics of a charged scalar field of mass $μ$ and charge coupling constant $q$ in the charged Reissner-Nordström black-hole spacetime of mass $M$ and electric charge $Q$ are determined {\it analytically} in the eikonal regime $1\ll Mμ<qQ$. Interestingly, we find that, for a given value of the dimensionless black-hole electric charge $Q/M$, the imaginary part of the resonant oscillation frequency is a monotonically {\it decreasing} function of the dimensionless ratio $μ/q$. In particular, it is shown that the quasinormal resonance spectrum is characterized by the asymptotic behavior $\Imω\to0$ in the limiting case $Mμ\to qQ$. This intriguing finding implies that the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system is characterized by extremely long relaxation times $τ_{\text{relax}}\equiv 1/\Imω\to\infty$ in the $Mμ/qQ\to 1^-$ limit.

gr-qc↗

arXiv2016

A quantum bound on the thermodynamic description of gravity

The seminal works of Bekenstein and Hawking have revealed that black holes have a well-defined thermodynamic description. In particular, it is often stated in the physical literature that black holes, like mundane physical systems, obey the first law of thermodynamics: $ΔS=ΔE/T_{\text{BH}}$, where $T_{\text{BH}}$ is the Bekenstein-Hawking temperature of the black hole. In the present work we test the regime of validity of the thermodynamic description of gravity. In particular, we provide compelling evidence that, due to quantum effects, the first law of thermodynamics breaks down in the low-temperature regime $T_{\text{BH}}\times r_{\text{H}}\lesssim ({{\hbar}/{r_{\text{H}}}})^2$ of near-extremal black holes (here $r_{\text{H}}$ is the radius of the black-hole horizon).

hep-th↗

arXiv2016

Hawking radiation and the Stefan-Boltzmann law: The effective radius of the black-hole quantum atmosphere

It has recently been suggested [S. B. Giddings, Phys. Lett. B {\bf 754}, 39 (2016)] that the Hawking black-hole radiation spectrum originates from an effective quantum "atmosphere" which extends well outside the black-hole horizon. In particular, comparing the Hawking radiation power of a $(3+1)$-dimensional Schwarzschild black hole of horizon radius $r_{\text{H}}$ with the familiar Stefan-Boltzmann radiation power of a $(3+1)$-dimensional flat space perfect blackbody emitter, Giddings concluded that the source of the Hawking semi-classical black-hole radiation is a quantum region outside the Schwarzschild black-hole horizon whose effective radius $r_{\text{A}}$ is characterized by the relation $Δr\equiv r_{\text{A}}-r_{\text{H}}\sim r_{\text{H}}$. It is of considerable physical interest to test the general validity of Giddings's intriguing conclusion. To this end, we study the Hawking radiation of $(D+1)$-dimensional Schwarzschild black holes. We find that the dimensionless radii $r_{\text{A}}/r_{\text{H}}$ which characterize the black-hole quantum atmospheres, as determined from the Hawking black-hole radiation power and the $(D+1)$-dimensional Stefan-Boltzmann radiation law, are a decreasing function of the number $D+1$ of spacetime dimensions. In particular, it is shown that radiating $(D+1)$-dimensional Schwarzschild black holes are characterized by the relation $(r_{\text{A}}-r_{\text{H}})/r_{\text{H}}\ll1$ in the large $D\gg1$ regime. Our results therefore suggest that, at least in some physical cases, the Hawking emission spectrum originates from quantum excitations very near the black-hole horizon.

gr-qc↗

arXiv2016

The large-mass limit of cloudy black holes

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 {\it analytically} a physical system which 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 $1<μ/mΩ_{\text{H}}<\sqrt{2}$, where $μ$ and $m$ are respectively the mass and azimuthal harmonic index of the field, and $Ω_{\text{H}}$ is the angular velocity of the black-hole horizon. We then show explicitly that these two bounds on the dimensionless ratio $μ/mΩ_{\text{H}}$ can be saturated in the asymptotic $m\to\infty$ 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 $Mμ\gg1$ of large field masses: $μ_n = \sqrt{2}m Ω_{\text{H}} \big[1-{{π({\cal R}+n)} \over {m|\lnτ|}}\big]$, where $τ$ is the dimensionless temperature of the rapidly-rotating (near-extremal) black hole, ${\cal R}<1$ 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 {\it finite} asymptotic value in the large mass $Mμ\gg1$ 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.

gr-qc↗

arXiv2016

The entropy emission properties of near-extremal Reissner-Nordström black holes

Bekenstein and Mayo have revealed an interesting property of evaporating $(3+1)$-dimensional Schwarzschild black holes: their entropy emission rates $\dot S_{\text{Sch}}$ are related to their energy emission rates $P$ by the simple relation $\dot S_{\text{Sch}}=C_{\text{Sch}}\times (P/\hbar)^{1/2}$. Remembering that $(1+1)$-dimensional perfect black-body emitters are characterized by the same functional relation, $\dot S^{1+1}=C^{1+1}\times(P/\hbar)^{1/2}$, Bekenstein and Mayo have concluded that, in their entropy emission properties, $(3+1)$-dimensional Schwarzschild black holes behave effectively as $(1+1)$-dimensional entropy emitters. One naturally wonders whether all black holes behave as simple $(1+1)$-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner-Nordström black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of these black holes can be studied {\it analytically} in the near-extremal $T_{\text{BH}}\to0$ regime. We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the non-trivial entropy-energy relations $\dot S^{\text{Scalar}}_{\text{RN}} = -C^{\text{Scalar}}_{\text{RN}} \times (AP^3/\hbar^3)^{1/4} \ln(AP/\hbar)$ and $\dot S^{\text{Elec-Grav}}_{\text{RN}} = -C^{\text{Elec-Grav}}_{\text{RN}} \times (A^4P^9/\hbar^9)^{1/10} \ln(AP/\hbar)$ in the near-extremal $T_{\text{BH}}\to0$ limit (here $A$ is the surface area of the Reissner-Nordström black hole). Our analytical results therefore indicate that {\it not} all black holes behave as simple $(1+1)$-dimensional entropy emitters.

gr-qc↗

arXiv2016

The superradiant instability regime of the spinning Kerr black hole

Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $Mμ< m \cdot \sqrt{{{2(1+γ) (1-\sqrt{1-γ^2}) - γ^2} \over {4γ^2}}}$, where $\{μ,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $γ\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superradiant instability regime of the spinning Kerr black hole agrees with recent {\it numerical} computations of the instability resonance spectrum.

gr-qc↗

arXiv2016

The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field

The well-known superradiant amplification mechanism allows a charged scalar field of proper mass $μ$ and electric charge $q$ to extract the Coulomb energy of a charged Reissner-Nordström black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the {\it charged black-hole bomb}. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequality $q/μ>1$ provides a necessary condition for the development of the superradiant instability. In the present paper we use analytical techniques to study the instability properties of the charged black-hole bomb in the regime of linearized scalar fields. In particular, we prove that the lower bound ${{q}\overμ}>\sqrt{{r_{\text{m}/r_--1}\over{r_{\text{m}}/r_+-1}}}$ provides a necessary condition for the development of the superradiant instability in this composed physical system (here $r_{\pm}$ are the horizon radii of the charged Reissner-Nordström black hole and $r_{\text{m}}$ is the radius of the confining mirror). This {\it analytically} derived lower bound on the superradiant instability regime of the composed black-hole-charged-scalar-field-mirror system is shown to agree with direct {\it numerical} computations of the instability spectrum.

gr-qc↗

arXiv2016

The Hawking cascades of gravitons from higher-dimensional Schwarzschild black holes

It has recently been shown that the Hawking evaporation process of $(3+1)$-dimensional Schwarzschild black holes is characterized by the dimensionless ratio $η\equivτ_{\text{gap}}/τ_{\text{emission}}\gg1$, where $τ_{\text{gap}}$ is the characteristic time gap between the emissions of successive Hawking quanta and $τ_{\text{emission}}$ is the characteristic timescale required for an individual Hawking quantum to be emitted from the Schwarzschild black hole. This strong inequality implies that the Hawking cascade of gravitons from a $(3+1)$-dimensional Schwarzschild black hole is extremely {\it sparse}. In the present paper we explore the semi-classical Hawking evaporation rates of {\it higher}-dimensional Schwarzschild black holes. We find that the dimensionless ratio $η(D)\equiv{τ_{\text{gap}}/{τ_{\text{emission}}}}$, which characterizes the Hawking emission of gravitons from the $(D+1)$-dimensional Schwarzschild black holes, is a {\it decreasing} function of the spacetime dimension. In particular, we show that higher-dimensional Schwarzschild black holes with $D\gtrsim 10$ are characterized by the relation $η(D)<1$. Our results thus imply that, contrary to the $(3+1)$-dimensional case, the characteristic Hawking cascades of gravitons from these higher-dimensional black holes have a {\it continuous} character.

gr-qc↗

arXiv2015

Ten shades of black

The holographic principle has taught us that, as far as their entropy content is concerned, black holes in $(3+1)$-dimensional curved spacetimes behave as ordinary thermodynamic systems in flat $(2+1)$-dimensional spacetimes. In this essay we point out that the opposite behavior can also be observed in black-hole physics. To show this we study the quantum Hawking evaporation of near-extremal Reissner-Nordström black holes. We first point out that the black-hole radiation spectrum departs from the familiar radiation spectrum of genuine $(3+1)$-dimensional perfect black-body emitters. In particular, the would be black-body thermal spectrum is distorted by the curvature potential which surrounds the black hole and effectively blocks the emission of low-energy quanta. Taking into account the energy-dependent gray-body factors which quantify the imprint of passage of the emitted radiation quanta through the black-hole curvature potential, we reveal that the $(3+1)$-dimensional black holes effectively behave as perfect black-body emitters in a flat $(9+1)$-dimensional spacetime.

gr-qc↗

arXiv2015

Numerical evidence for universality in the relaxation dynamics of near-extremal Kerr-Newman black holes

The coupled gravitational-electromagnetic quasinormal resonances of charged rotating Kerr-Newman black holes are explored. In particular, using the recently published numerical data of Dias, Godazgar, and Santos [Phys. Rev. Lett. 114, 151101 (2015)], we show that the characteristic relaxation times $τ\equiv 1/\Imω_0$ of near-extremal Kerr-Newman black holes in the regime $Q/r_+\leq 0.9$ are described, to a very good degree of accuracy, by the simple universal relation $τ\times T_{\text{BH}}=π^{-1}$ (here $Q, r_+$, and $T_{\text{BH}}$ are respectively the electric charge, horizon radius, and temperature of the Kerr-Newman black hole, and $ω_0$ is the fundamental quasinormal resonance of the perturbed black-hole spacetime).

hep-th↗

arXiv2015

Bekenstein's generalized second law of thermodynamics: The role of the hoop conjecture

Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, $S_{\text{BH}}=Ac^3/4\hbar G$ (here $A$ is the black-hole surface area), and the ordinary entropy of matter and radiation fields in the black-hole exterior region never decreases. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. In this historical gedanken experiment an entropy-bearing box is lowered into a charged Reissner-Nordström black hole. For the GSL to work, the resulting increase in the black-hole surface area (entropy) must compensate for the loss of the box's entropy. We show that if the box can be lowered adiabatically all the way down to the black-hole horizon, as previously assumed in the literature, then for near-extremal black holes the resulting increase in black-hole surface-area (due to the assimilation of the box by the black hole) may become too small to compensate for the loss of the box's entropy. In order to resolve this apparent violation of the GSL, we here suggest to use a generalized version of the hoop conjecture. In particular, assuming that a physical system of mass $M$ and electric charge $Q$ forms a black hole if its circumference radius $r_{\text{c}}$ is equal to (or smaller than) the corresponding Reissner-Nordström black-hole radius $r_{\text{RN}}=M+\sqrt{M^2-Q^2}$, we prove that a new (and larger) horizon is already formed before the entropy-bearing box reaches the horizon of the original near-extremal black hole. This result, which seems to have been overlooked in previous analyzes of the composed black-hole-box system, ensures the validity of Bekenstein's GSL in this famous gedanken experiment.

gr-qc↗

arXiv2015

Dragging of inertial frames in the composed black-hole-ring system

A well-established phenomenon in general relativity is the dragging of inertial frames by a spinning object. In particular, due to the dragging of inertial frames by a ring orbiting a central black hole, the angular-velocity of the black-hole horizon in the composed black-hole-ring system is no longer related to the black-hole angular-momentum by the simple Kerr-like (vacuum) relation $Ω^{\text{Kerr}}_{\text{H}}(J_{\text{H}})=J_{\text{H}}/2M^2R_{\text{H}}$. Will has performed a perturbative treatment of the composed black-hole-ring system in the regime of slowly rotating black holes and found the explicit relation $Ω^{\text{BH-ring}}_{\text{H}}(J_{\text{H}}=0,J_{\text{R}},R)=2J_{\text{R}}/R^3$ for the angular-velocity of a central black hole with zero angular-momentum. Analyzing a sequence of black-hole-ring configurations with adiabatically varying (decreasing) circumferential radii, we show that the expression found by Will implies a smooth transition of the central black-hole angular-velocity from its asymptotic near-horizon value $Ω^{\text{BH-ring}}_{\text{H}}(J_{\text{H}}=0,J_{\text{R}},R\to R^{+}_{\text{H}})$ to its final Kerr (vacuum) value $Ω^{\text{Kerr}}_{\text{H}}(J^{\text{new}}_{\text{H}})$. We use this important observation in order to generalize the result of Will to the regime of black-hole-ring configurations in which the central black holes possess non-zero angular momenta. Remarkably, we find the simple universal relation $ΔΩ_{\text{H}}\equivΩ^{\text{BH-ring}}_{\text{H}}(J_{\text{H}},J_{\text{R}},R\to R^{+}_{\text{H}})-Ω^{\text{Kerr}}_{\text{H}}(J_{\text{H}})={J_{\text{R}}/{4M^3}}$ for the asymptotic deviation of the black-hole angular-velocity in the composed black-hole-ring system from the corresponding angular-velocity of the unperturbed (vacuum) Kerr black hole with the same angular-momentum.

gr-qc↗

arXiv2015

On the branching of the quasinormal resonances of near-extremal Kerr black holes

It has recently been shown by Yang. et. al. [Phys. Rev. D {\bf 87}, 041502(R) (2013)] that rotating Kerr black holes are characterized by two distinct sets of quasinormal resonances. These two families of quasinormal resonances display qualitatively different asymptotic behaviors in the extremal ($a/M\to 1$) black-hole limit: The zero-damping modes (ZDMs) are characterized by relaxation times which tend to infinity in the extremal black-hole limit ($\Imω\to 0$ as $a/M\to 1$), whereas the damped modes (DMs) are characterized by non-zero damping rates ($\Imω\to$ finite-values as $a/M\to 1$). In this paper we refute the claim made by Yang et. al. that co-rotating DMs of near-extremal black holes are restricted to the limited range $0\leq μ\lesssimμ_{\text{c}}\approx 0.74$, where $μ\equiv m/l$ is the dimensionless ratio between the azimuthal harmonic index $m$ and the spheroidal harmonic index $l$ of the perturbation mode. In particular, we use an analytical formula originally derived by Detweiler in order to prove the existence of DMs (damped quasinormal resonances which are characterized by finite $\Imω$ values in the $a/M\to 1$ limit) of near-extremal black holes in the $μ>μ_{\text{c}}$ regime, the regime which was claimed by Yang et. al. not to contain damped modes. We show that these co-rotating DMs (in the regime $μ>μ_{\text{c}}$) are expected to characterize the resonance spectra of rapidly-rotating (near-extremal) black holes with $a/M\gtrsim 1-10^{-9}$.

gr-qc↗

arXiv2015

Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation

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 $α\equiv Mμ\ll1$ (here $μ$ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: $ω_{\text{R}}/μ=1-α^2/2{\bar n}^2_0$, where the integer $\bar n_0(l,n;α\to0)=l+n+1$ 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 $\bar n_0$, this small-mass ($α\ll1$) 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 ${ω_{\text{R}}/μ}=\sqrt{1-(α/{\bar n})^2}$, where $\bar n(l,n;α)=\sqrt{(l+1/2)^2-2mα+2α^2}+1/2+n$ 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.

gr-qc↗

arXiv2015

Universality in the relaxation dynamics of the composed black-hole-charged-massive-scalar-field system: The role of quantum Schwinger discharge

The quasinormal resonance spectrum $\{ω_n(μ,q,M,Q)\}_{n=0}^{n=\infty}$ of charged massive scalar fields in the charged Reissner-Nordström black-hole spacetime is studied {\it analytically} in the large-coupling regime $qQ\gg Mμ$ (here $\{μ, q\}$ are respectively the mass and charge coupling constant of the field, and $\{M,Q\}$ are respectively the mass and electric charge of the black hole). This physical system provides a striking illustration for the validity of the universal relaxation bound $τ\times T \geq \hbar/π$ in black-hole physics (here $τ\equiv 1/\Imω_0$ is the characteristic relaxation time of the composed black-hole-scalar-field system, and $T$ is the Bekenstein-Hawking temperature of the black hole). In particular, it is shown that the relaxation dynamics of charged massive scalar fields in the charged Reissner-Nordström black-hole spacetime may {\it saturate} this quantum time-times-temperature inequality. Interestingly, we prove that potential violations of the bound by light scalar fields are excluded by the Schwinger-type pair-production mechanism (a vacuum polarization effect), a {\it quantum} phenomenon which restricts the physical parameters of the composed black-hole-charged-field system to the regime $qQ\ll M^2μ^2/\hbar$.

gr-qc↗

arXiv2015

The Hawking evaporation process of rapidly-rotating black holes: An almost continuous cascade of gravitons

It is shown that rapidly-rotating Kerr black holes are characterized by the dimensionless ratio $τ_{\text{gap}}/τ_{\text{emission}}=O(1)$, where $τ_{\text{gap}}$ is the average time gap between the emission of successive Hawking quanta and $τ_{\text{emission}}$ is the characteristic timescale required for an individual Hawking quantum to be emitted from the black hole. This relation implies that the Hawking cascade from rapidly-rotating black holes has an almost continuous character. Our results correct some inaccurate claims that recently appeared in the literature regarding the nature of the Hawking black-hole evaporation process.

gr-qc↗

arXiv2015

Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

The spheroidal harmonics $S_{lm}(θ;c)$ 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 $\{A_{lm}(c)\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\to\infty$ with a fixed value of $c$, or to the complementary regime $|c|\to\infty$ 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 $m\to\infty$ and $|c|\to\infty$ with a fixed $m/c$ ratio.

gr-qc↗

arXiv2015

Quantum-Gravity Fluctuations and the Black-Hole Temperature

Bekenstein has put forward the idea that, in a quantum theory of gravity, a black hole should have a discrete energy spectrum with concomitant discrete line emission. The quantized black-hole radiation spectrum is expected to be very different from Hawking's semi-classical prediction of a thermal black-hole radiation spectrum. One naturally wonders: Is it possible to reconcile the {\it discrete} quantum spectrum suggested by Bekenstein with the {\it continuous} semi-classical spectrum suggested by Hawking ? In order to address this fundamental question, in this essay we shall consider the zero-point quantum-gravity fluctuations of the black-hole spacetime. In a quantum theory of gravity, these spacetime fluctuations are closely related to the characteristic gravitational resonances of the corresponding black-hole spacetime. Assuming that the energy of the black-hole radiation stems from these zero-point quantum-gravity fluctuations of the black-hole spacetime, we derive the effective temperature of the quantized black-hole radiation spectrum. Remarkably, it is shown that this characteristic temperature of the {\it discrete} (quantized) black-hole radiation agrees with the well-known Hawking temperature of the {\it continuous} (semi-classical) black-hole spectrum.

gr-qc↗