arXiv subjects

Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 91 records · Page 5Linked to original sources

arXiv2018

The Hawking paradox and the Bekenstein resolution in higher-dimensional spacetimes

The black-hole information puzzle has attracted much attention over the years from both physicists and mathematicians. One of the most intriguing suggestions to resolve the information paradox is due to Bekenstein, who has stressed the fact that the low-energy part of the semi-classical black-hole emission spectrum is partly blocked by the curvature potential that surrounds the black hole. As explicitly shown by Bekenstein, this fact implies that the grey-body emission spectrum of a (3+1)-dimensional black hole is considerably less entropic than the corresponding radiation spectrum of a perfectly thermal black-body emitter. Using standard ideas from quantum information theory, it was shown by Bekenstein that, in principle, the filtered Hawking radiation emitted by a (3+1)-dimensional Schwarzschild black hole may carry with it a substantial amount of information, the information which was suspected to be lost. It is of physical interest to test the general validity of the "information leak" scenario suggested by Bekenstein as a possible resolution to the Hawking information puzzle. In the present paper we analyze the semi-classical entropy emission properties of higher-dimensional black holes. In particular, we provide evidence that the characteristic Hawking quanta of $(D+1)$-dimensional Schwarzschild black holes in the large $D\gg1$ regime are almost unaffected by the spacetime curvature outside the black-hole horizon. This fact implies that, in the large-$D$ regime, the Hawking black-hole radiation spectra are almost purely thermal, thus suggesting that the emitted quanta cannot carry the amount of information which is required in order to resolve the information paradox. Our analysis therefore suggests that the elegant information leak scenario suggested by Bekenstein cannot provide a generic resolution to the intriguing Hawking information paradox.

gr-qc↗

arXiv2018

Upper bound on the energies of the emitted Hawking quanta

Using Thorne's hoop conjecture, it is argued that the energies of the Hawking quanta emitted from canonical Schwarzschild black holes are bounded from above by the simple quantum relation ${\cal E}<{\cal E}_{\text{max}}={\hbar^{2/3}}/M^{1/3}$. In particular, it is shown that, due to non-linear (self-gravity) effects of the tunneling quanta, higher energy field modes are re-absorbed (rather than escape to infinity) by the black hole.

hep-th↗

arXiv2018

Comment on arXiv:1810.00886: "Strong Cosmic Censorship: the nonlinear story"

A very interesting work that has recently appeared in the physics literature [arXiv:1810.00886] claims that the strong cosmic censorship conjecture, a fundamental cornerstone of black-hole physics, may be violated in asymptotically de Sitter charged spacetimes. In this short Comment I would like to point out that this conclusion cannot be self-consistently deduced from the numerical simulations presented in arXiv:1810.00886.

gr-qc↗

arXiv2018

Lower bound on the compactness of isotropic ultra-compact objects

Horizonless spacetimes describing spatially regular ultra-compact objects which, like black-hole spacetimes, possess closed null circular geodesics (light rings) have recently attracted much attention from physicists and mathematicians. In the present paper we raise the following physically intriguing question: How compact is an ultra-compact object? Using analytical techniques, we prove that ultra-compact isotropic matter configurations with light rings are characterized by the dimensionless lower bound $\text{max}_r\{2m(r)/r\}>7/12$ on their global compactness parameter.

gr-qc↗

arXiv2018

Black-hole evaporation, cosmic censorship, and a quantum lower bound on the Bekenstein-Hawking temperature

The semi-classical Hawking evaporation process of Reissner-Nordström black holes is analyzed. It is shown that this quantum mechanism may turn a near-extremal black-hole spacetime with $T_{\text{BH}}\lesssim \hbar^2/G^2M^3$ into an horizonless naked singularity, thus violating the Penrose cosmic censorship conjecture. It is therefore conjectured that, within the framework of a self-consistent quantum theory of gravity, the Bekenstein-Hawking temperature should be bounded from below by the simple relation $T_{\text{BH}}\gtrsim \hbar^2/G^2M^3$.

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arXiv2018

Natural broadening in the quantum emission spectra of higher-dimensional Schwarzschild black holes

Following an intriguing heuristic argument of Bekenstein, many researches have suggested during the last four decades that quantized black holes may be characterized by discrete radiation spectra. Bekenstein and Mukhanov (BM) have further argued that the emission spectra of quantized $(3+1)$-dimensional Schwarzschild black holes are expected to be sharp in the sense that the characteristic natural broadening $δω$ of the black-hole radiation lines, as deduced from the quantum time-energy uncertainty principle, is expected to be much smaller than the characteristic frequency spacing $Δω=O(T_{\text{BH}}/\hbar)$ between adjacent black-hole quantum emission lines. It is of considerable physical interest to test the general validity of the interesting conclusion reached by BM regarding the sharpness of the Schwarzschild black-hole quantum radiation spectra. To this end, in the present paper we explore the physical properties of the expected radiation spectra of quantized $(D+1)$-dimensional Schwarzschild black holes. In particular, we analyze the functional dependence of the characteristic dimensionless ratio $ζ(D)\equivδω/Δω$ on the number $D+1$ of spacetime dimensions. Interestingly, it is proved that the dimensionless physical parameter $ζ(D)$, which characterizes the sharpness of the black-hole quantum emission spectra, is an increasing function of $D$. In particular, we prove that the quantum emission lines of $(D+1)$-dimensional Schwarzschild black holes in the regime $D\gtrsim 10$ are characterized by the dimensionless ratio $ζ(D)\gtrsim1$ and are therefore effectively blended together.

gr-qc↗

arXiv2018

Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these {\it horizonless} compact objects cannot support spatially regular {\it static} matter configurations made of scalar (spin-0) fields, vector (spin-1) fields, and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support {\it stationary} (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass $μ$ and proper frequency $ω$ in the curved background of a spherically symmetric compact reflecting star of mass $M$ and radius $R_{\text{s}}$. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities $1-2M/R_{\text{s}}<(ω/μ)^2<1$. Interestingly, in the regime $M/R_{\text{s}}\ll1$ of weakly self-gravitating stars we derive a remarkably compact {\it analytical} formula for the discrete spectrum $\{ω(M,R_{\text{s}},μ)\}^{n=\infty}_{n=1}$ of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations.

gr-qc↗

arXiv2018

The holographic entropy bound in higher-dimensional spacetimes: As strong as ever

The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove that this composed physical system, which at first sight seems to violate the holographic entropy bound, actually conforms to the entropy-area inequality $S\leq {\cal A}/4{\ell^2_P}$. In particular, we shall explicitly show that the homogeneity property of the confined thermal fields sets an upper bound on the entropy content of the system. The present analysis therefore resolves the apparent violation of the holographic entropy bound by confined thermal fields in higher-dimensional spacetimes.

hep-th↗

arXiv2018

Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell

We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the Klein-Gordon wave equation for the composed charged-shell-charged-massive-scalar-field system. Interestingly, it is proved that the resonant oscillation frequencies of this composed physical system are determined by the characteristic zeroes of the confluent hypergeometric function. Following this observation, we derive a remarkably compact analytical formula for the resonant oscillation frequencies which characterize the marginally-bound charged massive scalar field configurations. The analytically derived resonance spectrum is confirmed by numerical computations.

gr-qc↗

arXiv2018

Bekenstein, I, and the quantum of black-hole surface area

Professor Jacob Bekenstein was known not only for his brilliant and original physical ideas, but also for their clear presentation in his lectures and seminal research papers. I here provide a short review of Bekenstein's pioneering ideas about the quantization of black holes. I also describe my attempt, as a young and extremely naive student, to prove him wrong and how I got convinced in the correctness and utility of his deep physical intuition. Finally, my personal contribution to the ongoing attempts to understand the evenly spaced (discrete) area spectrum of quantized black holes, as originally suggested by Bekenstein in the early days of his scientific career, is described.

gr-qc↗

arXiv2018

Stationary bound-state scalar configurations supported by rapidly-spinning exotic compact objects

Some quantum-gravity theories suggest that the absorbing horizon of a classical black hole should be replaced by a reflective surface which is located a microscopic distance above the would-be classical horizon. Instead of an absorbing black hole, the resulting horizonless spacetime describes a reflective exotic compact object. Motivated by this intriguing prediction, in the present paper we explore the physical properties of exotic compact objects which are linearly coupled to stationary bound-state massive scalar field configurations. In particular, solving the Klein-Gordon wave equation for a stationary scalar field of proper mass $μ$ and spheroidal harmonic indices $(l,m)$ in the background of a rapidly-rotating exotic compact object of mass $M$ and angular momentum $J=Ma$, we derive a compact analytical formula for the {\it discrete} radii $\{r_{\text{c}}(μ,l,m,M,a;n)\}$ of the exotic compact objects which can support the stationary bound-state massive scalar field configurations. We confirm our analytical results by direct numerical computations.

gr-qc↗

arXiv2018

Quasinormal modes and strong cosmic censorship in near-extremal Kerr-Newman-de Sitter black-hole spacetimes

The quasinormal resonant modes of massless neutral fields in near-extremal Kerr-Newman-de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime ${\bar a}> \sqrt{{1-2{\barΛ}\over{4+{\barΛ}/3}}}$, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula $\Imω(n)=κ_+\cdot(n+{1\over2})$ [here the physical parameters $\{{\bar a},κ_+,{\barΛ},n\}$ are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensionless cosmological constant of the spacetime, and the integer resonance parameter]. Our results support the validity of the Penrose strong cosmic censorship conjecture in these black-hole spacetimes.

gr-qc↗

arXiv2018

Viscosity bound versus the universal relaxation bound

For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, $η/s=1/4π$. The holographic calculations have motivated the formulation of the celebrated KSS conjecture, according to which all fluids conform to the lower bound $η/s \geq 1/4π$. The bound on $η/s$ may be regarded as a lower bound on the {\it relaxation} properties of perturbed fluids and it has been the focus of much recent attention. In particular, it was argued that for a class of field theories with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, $η/s$, could violate the conjectured KSS bound. In the present paper we argue that the proposed violations of the KSS bound are strongly constrained by Bekenstein's generalized second law (GSL) of thermodynamics. In particular, it is shown that physical consistency of the Gauss-Bonnet theory with the GSL requires its coupling constant to be bounded by $λ_{GB}\lesssim 0.063$. We further argue that the genuine physical bound on the relaxation properties of physically consistent fluids is $\Imω(k>2πT)>πT$, where $ω$ and $k$ are respectively the proper frequency and the wavenumber of a perturbation mode in the fluid.

hep-th↗

arXiv2018

Charged reflecting stars supporting charged massive scalar field configurations

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars {\it cannot} support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars {\it can} support {\it charged} massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein-Gordon wave equation for a linearized charged scalar field of mass $μ$, charge coupling constant $q$, and spherical harmonic index $l$ in the background of a spherically symmetric compact reflecting star of mass $M$, electric charge $Q$, and radius $R_{\text{s}}\gg M,Q$. Interestingly, it is proved that the discrete set $\{R_{\text{s}}(M,Q,μ,q,l;n)\}^{n=\infty}_{n=1}$ of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime $M\ll R_{\text{s}}\ll 1/μ$. The analytically derived resonance spectrum is confirmed by direct numerical computations.

hep-th↗

arXiv2018

Strong cosmic censorship in charged black-hole spacetimes: As strong as ever

It is proved that dynamically formed Reissner-Nordström-de Sitter (RNdS) black holes, which have recently been claimed to provide counter-examples to the Penrose strong cosmic censorship conjecture, are characterized by unstable (singular) inner Cauchy horizons. The proof is based on analytical techniques which explicitly reveal the fact that {\it charged} massive scalar fields in the charged RNdS black-hole spacetime are characterized, in the large-coupling regime, by quasinormal resonant frequencies with $\Imω^{\text{min}}<{1\over2}κ_+$, where $κ_+$ is the surface gravity of the black-hole event horizon. This result implies that the corresponding relaxation rate $ψ\sim e^{-\Imω^{\text{min}}t}$ of the collapsed charged fields is slow enough to guarantee, through the mass-inflation mechanism, the instability of the dynamically formed inner Cauchy horizons. Our results reveal the physically important fact that, taking into account the unavoidable presence of {\it charged} matter fields in dynamically formed {\it charged} spacetimes, non-asymptotically flat RNdS black holes are globally hyperbolic and therefore respect the fundamental strong cosmic censorship conjecture.

gr-qc↗

arXiv2017

On the number of light rings in curved spacetimes of ultra-compact objects

In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least {\it two} (and, in general, an even number of) light rings, of which the inner one is {\it stable}. In the present compact paper we explicitly prove that, while this intriguing theorem is generally true, there is an important exception in the presence of degenerate light rings which, in the spherically symmetric static case, are characterized by the simple dimensionless relation $8πr^2_γ(ρ+p_{\text{T}})=1$ [here $r_γ$ is the radius of the light ring and $\{ρ,p_{\text{T}}\}$ are respectively the energy density and tangential pressure of the matter fields]. Ultra-compact objects which belong to this unique family can have an {\it odd} number of light rings. As a concrete example, we show that spherically symmetric constant density stars with dimensionless compactness $M/R=1/3$ possess only {\it one} light ring which, interestingly, is shown to be {\it unstable}.

gr-qc↗

arXiv2017

Ultra-spinning exotic compact objects supporting static massless scalar field configurations

Horizonless spacetimes describing highly compact exotic objects with reflecting (instead of absorbing) surfaces have recently attracted much attention from physicists and mathematicians as possible quantum-gravity alternatives to canonical classical black-hole spacetimes. Interestingly, it has recently been proved that spinning compact objects with angular momenta in the sub-critical regime ${\bar a}\equiv J/M^2\leq1$ are characterized by an infinite countable set of surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=\infty}_{n=1}$, that can support asymptotically flat static configurations made of massless scalar fields. In the present paper we study analytically the physical properties of ultra-spinning exotic compact objects with dimensionless angular momenta in the complementary regime ${\bar a}>1$. It is proved that ultra-spinning reflecting compact objects with dimensionless angular momenta in the super-critical regime $\sqrt{1-[{{m}/{(l+2)}}]^2}\leq|{\bar a}|^{-1}<1$ are characterized by a finite discrete family of surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=N_{\text{r}}}_{n=1}$, distributed symmetrically around $r=M$, that can support spatially regular static configurations of massless scalar fields (here the integers $\{l,m\}$ are the harmonic indices of the supported static scalar field modes). Interestingly, the largest supporting surface radius $r^{\text{max}}_{\text{c}}({\bar a})\equiv \text{max}_n\{r_{\text{c}}({\bar a};n)\}$ marks the onset of superradiant instabilities in the composed ultra-spinning-exotic-compact-object-massless-scalar-field system.

hep-th↗

arXiv2017

Marginally stable resonant modes of the polytropic hydrodynamic vortex

The polytropic hydrodynamic vortex describes an effective $(2+1)$-dimensional acoustic spacetime with an inner reflecting boundary at $r=r_{\text{c}}$. This physical system, like the spinning Kerr black hole, possesses an ergoregion of radius $r_{\text{e}}$ and an inner non-pointlike curvature singularity of radius $r_{\text{s}}$. Interestingly, the fundamental ratio $r_{\text{e}}/r_{\text{s}}$ which characterizes the effective geometry is determined solely by the dimensionless polytropic index $N_{\text{p}}$ of the circulating fluid. It has recently been proved that, in the $N_{\text{p}}=0$ case, the effective acoustic spacetime is characterized by an {\it infinite} countable set of reflecting surface radii, $\{r_{\text{c}}(N_{\text{p}};n)\}^{n=\infty}_{n=1}$, that can support static (marginally-stable) sound modes. In the present paper we use {\it analytical} techniques in order to explore the physical properties of the polytropic hydrodynamic vortex in the $N_{\text{p}}>0$ regime. In particular, we prove that in this physical regime, the effective acoustic spacetime is characterized by a {\it finite} discrete set of reflecting surface radii, $\{r_{\text{c}}(N_{\text{p}},m;n)\}^{n=N_{\text{max}}}_{n=1}$, that can support the marginally-stable static sound modes (here $m$ is the azimuthal harmonic index of the acoustic perturbation field). Interestingly, it is proved analytically that the dimensionless outermost supporting radius $r^{\text{max}}_{\text{c}}/r_{\text{e}}$, which marks the onset of superradiant instabilities in the polytropic hydrodynamic vortex, increases monotonically with increasing values of the integer harmonic index $m$ and decreasing values of the dimensionless polytropic index $N_{\text{p}}$.

gr-qc↗