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Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 73 records · Page 4Linked to original sources
arXiv2020

Lower bound on the radii of black-hole photonspheres

The existence of closed null circular geodesics around black holes is one of the most intriguing predictions of general relativity. It has recently been conjectured that the radii of black-hole photonspheres are bounded from below by the simple relation $r_{\text{ph}}\geq {3\over2}r_{\text{H}}$, where $r_{\text{H}}$ is the radius of the outer black-hole horizon. We here prove the validity of this conjecture for spherically symmetric hairy black-hole configurations whose radial pressure function $P\equiv |r^3p|$ decreases monotonically.

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arXiv2020

A proof of the strong cosmic censorship conjecture

The Penrose strong cosmic censorship conjecture asserts that Cauchy horizons inside dynamically formed black holes are unstable to remnant matter fields that fall into the black holes. The physical importance of this conjecture stems from the fact that it provides a necessary condition for general relativity to be a truly deterministic theory of gravity. Determining the fate of the Penrose conjecture in non-asymptotically flat black-hole spacetimes has been the focus of intense research efforts in recent years. In the present essay we provide a remarkably compact proof, which is based on Bekenstein's generalized second law of thermodynamics, for the validity of the intriguing Penrose conjecture in physically realistic (dynamically formed) curved black-hole spacetimes.

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arXiv2020

No-go theorem for spatially regular boson stars made of static nonminimally coupled massive scalar fields

We present a compact theorem which reveals the fact that static spatially regular massive scalar fields with nonminimal coupling to gravity cannot form spherically symmetric asymptotically flat horizonless matter configurations. In particular, the no-go theorem rules out the existence of boson stars made of static scalar fields with generic values of the physical parameter $ξ$ which quantifies the coupling between the spacetime curvature and the massive bosonic fields.

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arXiv2020

Onset of spontaneous scalarization in spinning Gauss-Bonnet black holes

It has recently been proved numerically that spinning black holes in Einstein-scalar theories which are characterized by a non-minimal negative coupling of the scalar field to the Gauss-Bonnet invariant of the curved spacetime may develop exponentially growing instabilities. Intriguingly, it has been demonstrated that this tachyonic instability, which marks the onset of the spontaneous scalarization phenomenon in the Einstein-Gauss-Bonnet-scalar theory, characterizes spinning black holes whose dimensionless angular momentum parameter ${\bar a}\equiv a/M$ is larger than some critical value ${\bar a}_{\text{crit}}\simeq0.505$. In the present paper we prove, using {\it analytical} techniques, that the critical rotation parameter which marks the boundary between bald Kerr black holes and hairy (scalarized) spinning black holes in the Einstein-Gauss-Bonnet-scalar theory is given by the exact dimensionless relation ${\bar a}_{\text{crit}}={1\over 2}$.

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arXiv2020

Reissner-Nordström black holes supporting non-minimally coupled massive scalar field configurations

It has recently been demonstrated that static spatially regular scalar fields, which are non-minimally coupled to the electromagnetic field of a charged central black hole, can be supported in the exterior regions of the black-hole spacetime. In the present paper we use {\it analytical} techniques in order to study the physical and mathematical properties of the externally supported linearized scalar field configurations (scalar 'clouds') in the dimensionless large-mass regime $μr_+\gg1$ (here $μ$ and $r_+$ are respectively the proper mass of the supported scalar field and the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum $\{α_n(μ;Q/M)\}_{n=0}^{n=\infty}$ which characterizes the dimensionless coupling parameter of the composed black-hole-non-minimally-coupled-linearized-massive-scalar-field configurations. The physical significance of this resonant spectrum stems from the fact that, for a given value of the dimensionless black-hole electric charge $Q/M$, the fundamental (smallest) eigenvalue $α_0(μ)$ determines the critical existence-line of the composed black-hole-massive-field system, a boundary line which separates non-linearly coupled hairy charged-black-hole-massive-scalar-field configurations from bald Reissner-Nordström black holes. The analytical results derived in this paper are confirmed by direct numerical computations.

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arXiv2020

No hair for spherically symmetric neutral reflecting stars: nonminimally coupled massive scalar fields

Recent no-hair theorems have revealed the intriguing fact that horizonless stars with compact reflecting surfaces {\it cannot} support non-linear matter configurations made of scalar, vector, and tensor fields. In the present paper we extend the regime of validity of these no-hair theorems by explicitly proving that spherically symmetric compact reflecting stars cannot support static configurations made of {\it massive} scalar fields with {\it non}-minimal coupling to gravity. Interestingly, our no-hair theorem is valid for {\it generic} values of the dimensionless field-curvature coupling parameter $ξ$.

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arXiv2020

No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields

It is proved that spherically symmetric asymptotically flat neutral black holes cannot support spatially regular static configurations made of massive scalar fields with non-minimal coupling to gravity. Interestingly, our compact no-hair theorem is valid for generic values of the dimensionless physical parameter $ξ$ which quantifies the strength of coupling between the scalar field and the spacetime curvature.

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arXiv2020

Spontaneous scalarization of charged Reissner-Nordström black holes: Analytic treatment along the existence line

It has recently been demonstrated that charged black holes can support spatially regular matter configurations made of massless scalar fields which are non-minimally coupled to the electromagnetic field of the charged spacetime. Intriguingly, using numerical techniques, it has been revealed that the resonant spectra of the composed charged-black-hole-nonminimally-coupled-scalar-field configurations are characterized by charge-dependent discrete scalarization bands $α\in\{[α^{-}_{n}({\bar Q}),α^{+}_{n}({\bar Q}]\}_{n=0}^{n=\infty}$, where $α$ is the dimensionless coupling constant of the theory and ${\bar Q}\equiv Q/M$ is the dimensionless charge-to-mass ratio of the central supporting black hole. In the present paper we use {\it analytical} techniques in order to study the physical and mathematical properties of the spatially regular non-minimally coupled scalar field configurations (linearized scalar clouds) which are supported by the central charged Reissner-Nordström black holes. In particular, we derive a remarkably compact formula for the discrete resonant spectrum $\{α^-_n({\bar Q})\}_{n=0}^{n=\infty}$ which characterizes the composed black-hole-linearized-field configurations along the {\it existence-line} of the system, the critical line which separates bare Reissner-Nordström black holes from hairy scalarized black-hole configurations. The analytical results are confirmed by direct numerical computations.

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arXiv2019

Spontaneous scalarization of Gauss-Bonnet black holes: Analytic treatment in the linearized regime

It has recently been proved that nontrivial couplings between scalar fields and the Gauss-Bonnet invariant of a curved spacetime may allow a central black hole to support spatially regular scalar hairy configurations. Interestingly, former numerical studies of the intriguing black-hole spontaneous scalarization phenomenon have demonstrated that the composed hairy black-hole-scalar-field configurations exist if and only if the dimensionless coupling parameter $\barη$ of the theory belongs to a discrete set $\{[\barη^{-}_{n},\barη^{+}_{n}]\}_{n=0}^{n=\infty}$ of scalarization bands. We have examined the numerical data that are available in the physics literature and found that the newly discovered hairy black-hole-linearized-massless-scalar-field configurations are characterized by the asymptotic universal behavior $Δ_n\equiv \sqrt{\barη^{+}_{n+1}}-\sqrt{\barη^{+}_{n}}\simeq 2.72$. Motivated by this intriguing observation, in the present paper we study {\it analytically} the physical and mathematical properties of the spontaneously scalarized Schwarzschild black holes in the linearized (weak-field) regime. In particular, we provide a remarkably compact analytical explanation for the numerically observed universal behavior $Δ_n\simeq 2.72$ which characterizes the discrete resonant spectrum $\{\barη^{+}_{n}\}_{n=0}^{n=\infty}$ of the composed hairy black-hole-linearized-scalar-field configurations.

gr-qc↗
arXiv2019

Strong Cosmic Censorship and the Universal Relaxation Bound

The strong cosmic censorship conjecture, introduced by Penrose five decades ago, asserts that, in self-consistent theories of gravity, Cauchy horizons inside dynamically formed black holes should be unstable to remnant perturbation fields that fall into the newly born black holes. The question of the (in)validity of this intriguing conjecture in non-asymptotically flat charged black-hole spacetimes has recently attracted much attention from physicists and mathematicians. We here provide a general proof, which is based on Bekenstein's generalized second law of thermodynamics, for the validity of this fundamental conjecture in non-asymptotically flat de Sitter black-hole spacetimes.

gr-qc↗
arXiv2019

The quantum emission spectra of rapidly-rotating Kerr black holes: discrete or continuous?

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of gravity, black holes may have discrete emission spectra. Using the time-energy uncertainty principle they have also shown that, for a (non-rotating) Schwarzschild black hole, the natural broadening $δω$ of the black-hole emission lines is expected to be small on the scale set by the characteristic frequency spacing $Δω$ of the spectral lines: $ζ^{\text{Sch}}\equivδω/Δω\ll1$. BM have therefore concluded that the expected discrete emission lines of the quantized Schwarzschild black hole are unlikely to overlap. In this paper we calculate the characteristic dimensionless ratio $ζ(\bar a)\equivδω/Δω$ for the predicted BM emission spectra of rapidly-rotating Kerr black holes (here $\bar a\equiv J/M^2$ is the dimensionless angular momentum of the black hole). It is shown that $ζ(\bar a)$ is an increasing function of the black-hole angular momentum. In particular, we find that the quantum emission lines of Kerr black holes in the regime $\bar a\gtrsim 0.9$ are characterized by the dimensionless ratio $ζ(\bar a)\gtrsim1$ and are therefore effectively blended together. Our results thus suggest that, even if the underlying mass (energy) spectrum of these rapidly-rotating Kerr black holes is fundamentally discrete as suggested by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with the time-energy uncertainty principle) is expected to smear the black-hole radiation spectrum into a continuum.

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arXiv2019

Upper bound on the gravitational masses of stable spatially regular charged compact objects

In a very interesting paper, Andréasson has recently proved that the gravitational mass of a spherically symmetric compact object of radius $R$ and electric charge $Q$ is bounded from above by the relation $\sqrt{M}\leq{\sqrt{R}\over{3}}+\sqrt{{{R}\over{9}}+{{Q^2}\over{3R}}}$. In the present paper we prove that, in the dimensionless regime ${{Q}/{M}}<\sqrt{9/8}$, a stronger upper bound can be derived on the masses of physically realistic ({\it stable}) self-gravitating horizonless compact objects: $M<{{R}\over{3}}+{{2Q^2}\over{3R}}$.

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arXiv2019

No-go theorem for static boson stars

It is proved that self-gravitating static scalar fields whose self-interaction potential $V(ψ^2)$ is a monotonically increasing function of its argument cannot form spherically symmetric asymptotically flat bound matter configurations. Our compact theorem rules out, in particular, the existence of spatially regular static boson stars made of nonlinear massive scalar fields.

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arXiv2018

The instability spectra of near-extremal Reissner-Nordström-de Sitter black holes

The linearized dynamics of charged massive scalar fields in the near-extremal charged Reissner-Nordström-de Sitter (RNdS) black-hole spacetime is studied analytically. Interestingly, it is proved that the non-asymptotically flat charged black-hole-field system is characterized by {\it unstable} (exponentially growing in time) complex resonant modes. Using a WKB analysis in the eikonal large-mass regime $Mμ\gg1$, we provide a remarkably compact analytical formula for the quasinormal resonant spectrum $\{ω_n(M,Q,Λ,μ,q)\}_{n=0}^{n=\infty}$ which characterizes the unstable modes of the composed RNdS-black-hole-charged-massive-scalar-field system [here $\{M,Q,Λ\}$ are respectively the mass, electric charge, and cosmological constant of the black-hole spacetime, and $\{μ,q\}$ are the proper mass and charge coupling constant of the linearized field].

gr-qc↗
arXiv2018

The Reissner-Nordström black hole with the fastest relaxation rate

Numerous {\it numerical} investigations of the quasinormal resonant spectra of Kerr-Newman black holes have revealed the interesting fact that the characteristic relaxation times $τ({\bar a},{\bar Q})$ of these canonical black-hole spacetimes can be described by a two-dimensional function ${\bar τ}\equiv τ/M$ which increases monotonically with increasing values of the dimensionless angular-momentum parameter ${\bar a}\equiv J/M^2$ and, in addition, is characterized by a non-trivial ({\it non}-monotonic) functional dependence on the dimensionless charge parameter ${\bar Q}\equiv Q/M$. In particular, previous numerical investigations have indicated that, within the family of spherically symmetric charged Reissner-Nordström spacetimes, the black hole with ${\bar Q}\simeq 0.7$ has the {\it fastest} relaxation rate. In the present paper we use {\it analytical} techniques in order to investigate this intriguing non-monotonic functional dependence of the Reissner-Nordström black-hole relaxation rates on the dimensionless physical parameter ${\bar Q}$. In particular, it is proved that, in the eikonal (geometric-optics) regime, the black hole with ${\bar Q}={\sqrt{51-3\sqrt{33}}\over{8}}\simeq 0.73$ is characterized by the {\it fastest} relaxation rate (the smallest dimensionless relaxation time ${\bar τ}$) within the family of charged Reissner-Nordström black-hole spacetimes.

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arXiv2018

Analytic study of self-gravitating polytropic spheres with light rings

Ultra-compact objects describe horizonless solutions of the Einstein field equations which, like black-hole spacetimes, possess null circular geodesics (closed light rings). We study {\it analytically} the physical properties of spherically symmetric ultra-compact isotropic fluid spheres with a polytropic equation of state. It is shown that these spatially regular horizonless spacetimes are generally characterized by two light rings $\{r^{\text{inner}}_γ,r^{\text{outer}}_γ\}$ with the property ${\cal C}(r^{\text{inner}}_γ)\leq{\cal C}(r^{\text{outer}}_γ)$, where ${\cal C}\equiv m(r)/r$ is the dimensionless compactness parameter of the self-gravitating matter configurations. In particular, we prove that, while black-hole spacetimes are characterized by the lower bound ${\cal C}(r^{\text{inner}}_γ)\geq1/3$, horizonless ultra-compact objects may be characterized by the opposite dimensionless relation ${\cal C}(r^{\text{inner}}_γ)\leq1/4$. Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotný, Hladík, and Stuchlík [Phys. Rev. D 95, 043009 (2017)].

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