arXiv subjects
Publications and source records attributed to Shahar Hod.
It has recently been proposed [M. P. Hertzberg and A. Loeb, arXiv:2302.09090] that the observed value of the cosmological constant can be related to the physical parameters of the Standard Model. In the present compact note we point out that the derivation of the claimed cosmological-constant-standard-model relation presented in \cite{HL} is, unfortunately, erroneous.
It is proved that spherically symmetric extermal black holes possess at least one external light ring. Our remarkably compact proof is based on the dominant energy condition which characterizes the external matter fields in the non-vacuum extremal black-hole spacetimes.
It is by now well established that charged rotating Kerr-Newman black holes can support bound-state charged matter configurations which are made of minimally coupled massive scalar fields. We here prove that the externally supported stationary charged scalar configurations {\it cannot} be arbitrarily compact. In particular, for linearized charged massive scalar fields supported by charged rotating near-extremal Kerr-Newman black holes, we derive the remarkably compact lower bound $(r_{\text{field}}-r_+)/(r_+-r_-)>1/s^2$ on the effective lengths of the external charged scalar `clouds' [here $r_{\text{field}}$ is the radial peak location of the stationary scalar configuration, and $\{s\equiv J/M^2, r_{\pm}\}$ are respectively the dimensionless angular momentum and the horizon radii of the central supporting Kerr-Newman black hole]. Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass, electric charge, and angular momentum) of the supported charged scalar fields.
It has recently been demonstrated that Reissner-Nordström black holes in composed Einstein-Maxwell-scalar field theories can support static scalar field configurations with a non-minimal negative coupling to the Maxwell electromagnetic invariant of the charged spacetime. We here reveal the physically interesting fact that scalar field configurations with a non-minimal {\it positive} coupling to the spatially-dependent Maxwell electromagnetic invariant ${\cal F}\equiv F_{μν}F^{μν}$ can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling black-hole spontaneous scalarization phenomenon is induced by a non-zero combination $a\cdot Q\neq0$ of {\it both} the spin $a\equiv J/M$ and the electric charge $Q$ of the central supporting black hole. Using analytical techniques we prove that the regime of existence of the positive-coupling spontaneous scalarization phenomenon of Kerr-Newman black holes with horizon radius $r_+(M,a,Q)$ and a non-zero electric charge $Q$ (which, in principle, may be arbitrarily small) is determined by the {\it critical onset line} $(a/r_+)_{\text{critical}}=\sqrt{2}-1$. In particular, spinning and charged Kerr-Newman black holes in the composed Einstein-Maxwell-scalar field theory are spontaneously scalarized by the positively coupled fields in the dimensionless charge regime $0<{{Q}\over{M}}\leq\sqrt{2\sqrt{2}-2}$ if their dimensionless spin parameters lie above the critical onset line ${{a(Q)}\over{M}}\geq \big[{{a(Q)}\over{M}}\big]_{\text{critical}}={{1+\sqrt{1-2(2-\sqrt{2}){(Q/M)}^2}}\over{2\sqrt{2}}}$.
The Gauss-Bonnet curvature invariant has attracted the attention of physicists and mathematicians over the years. In particular, it has recently been proved that black holes can support external matter configurations that are non-minimally coupled to the Gauss-Bonnet invariant of the curved spacetime. Motivated by this physically interesting behavior of black holes in Einstein-Gauss-Bonnet theories, we present a detailed {\it analytical} study of the physical and mathematical properties of the Gauss-Bonnet curvature invariant ${\cal G}_{\text{Kerr}}(r,\cosθ;a/M)$ of spinning Kerr black holes in the spacetime region outside the horizon. Interestingly, we prove that, for all spinning Kerr spacetimes in the physically allowed regime $a/M\in[0,1]$, the spin-dependent maximum curvature of the Gauss-Bonnet invariant is attained at the equator of the black-hole surface. Intriguingly, we reveal that the location of the global minimum of the Gauss-Bonnet invariant has a highly non-trivial functional dependence on the black-hole rotation parameter: (i) For Kerr black holes in the dimensionless slow-rotation $a/M<(a/M)^{-}_{\text{crit}}=1/2$ regime, the Gauss-Bonnet curvature invariant attains its global minimum asymptotically at spatial infinity, (ii) for black holes in the intermediate spin regime $1/2=(a/M)^{-}_{\text{crit}}\leq a/M\leq(a/M)^{+}_{\text{crit}}= \sqrt{\Big\{{{7+\sqrt{7}\cos\Big[3^{-1}\arctan\big(3\sqrt{3}\big)\Big]- \sqrt{21}\sin\Big[3^{-1}\arctan\big(3\sqrt{3}\big)\Big]\Big\}}/12}}$, the global minima are located at the black-hole poles, and (iii) Kerr black holes in the super-critical regime $a/M>(a/M)^{+}_{\text{crit}}$ are characterized by a non-trivial functional behavior of the Gauss-Bonnet curvature invariant along the black-hole horizon with a spin-dependent polar angle for the global minimum point.
It has recently been demonstrated that magnetized black holes in composed Einstein-Maxwell-scalar-Gauss-Bonnet field theories with a non-minimal negative coupling of the scalar field to the Gauss-Bonnet curvature invariant may support spatially regular scalar hairy configurations. In particular, it has been revealed that, for Schwarzschild-Melvin black-hole spacetimes, the onset of the near-horizon spontaneous scalarization phenomenon is marked by the numerically computed dimensionless critical relation $(BM)_{\text{crit}}\simeq0.971$, where $\{M,B\}$ are respectively the mass and the magnetic field of the spacetime. In the present paper we prove, using analytical techniques, that the boundary between bald Schwarzschild-Melvin black-hole spacetimes and hairy (scalarized) black-hole solutions of the composed Einstein-Maxwell-scalar-Gauss-Bonnet theory is characterized by the exact dimensionless relation $(BM)_{\text{crit}}=\sqrt{{{\sqrt{6}-2}\over{2\sqrt{6}}}+\sqrt{{{\sqrt{6}-1}\over{2}}}}$ for the critical magnetic strength. Intriguingly, we prove that the critical dimensionless magnetic parameter $(BM)_{\text{crit}}$ corresponds to magnetized black holes that support a pair of linearized non-minimally coupled thin scalar rings that are characterized by the non-equatorial polar angular relation $(\sin^2θ)_{\text{scalar-ring}}={{690-72\sqrt{6}+4\sqrt{3258\sqrt{6}-7158}}\over{789}}<1$. It is also proved that the classically allowed angular region for the negative-coupling near-horizon spontaneous scalarization phenomenon of magnetized Schwarzschild-Melvin spacetimes is restricted to the black-hole poles, $\sin^2θ_{\text{scalar}}\to0$, in the asymptotic large-strength magnetic regime $BM\gg1$.
We reveal the existence of a new form of spontaneously scalarized black-hole configurations. In particular, it is proved that Reissner-Nordström black holes in the highly charged regime $Q/M>(Q/M)_{\text{crit}}=\sqrt{21}/5$ can support {\it thin} matter shells that are made of massive scalar fields with a non-minimal coupling to the Gauss-Bonnet invariant of the curved spacetime. These static scalar shells, which become infinitesimally thin in the dimensionless large-mass $Mμ\gg1$ regime, hover a finite proper distance above the black-hole horizon [here $\{M,Q\}$ are respectively the mass and electric charge of the central supporting black hole, and $μ$ is the proper mass of the supported scalar field]. In addition, we derive a remarkably compact analytical formula for the discrete resonance spectrum $\{η(Q/M,Mμ;n)\}_{n=0}^{n=\infty}$ of the non-trivial coupling parameter which characterizes the bound-state charged-black-hole-thin-massive-scalar-shell cloudy configurations of the composed Einstein-Maxwell-scalar field theory.
The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation $τ\times T\geq {{\hbar}\overπ}$. It is known that some perturbation modes of near-extremal Kerr black holes in the regime $MT_{\text{BH}}/\hbar\ll m^{-2}$ are characterized by normalized relaxation times $πτ\times T_{\text{BH}}/\hbar$ which, in the approach to the limit $MT_{\text{BH}}/\hbar\to0$, make infinitely many oscillations with a tiny constant amplitude around $1$ and therefore cannot be used directly to verify the validity of the TTT bound in the entire parameter space of the black-hole spacetime (Here $\{T_{\text{BH}},M\}$ are respectively the Bekenstein-Hawking temperature and the mass of the black hole, and $m$ is the azimuthal harmonic index of the linearized perturbation mode). In the present compact paper we explicitly prove that all rapidly-spinning Kerr black holes respect the TTT relaxation bound. In particular, using analytical techniques, it is proved that all black-hole perturbation modes in the complementary regime $m^{-1}\ll MT_{\text{BH}}/\hbar\ll1$ are characterized by relaxation times with the simple dimensionless property $πτ\times T_{\text{BH}}/\hbar\geq1$.
It has recently been revealed that spinning black holes of the photon-fluid model can support acoustic `clouds', stationary density fluctuations whose spatially regular radial eigenfunctions are determined by the $(2+1)$-dimensional Klein-Gordon equation of an effective massive scalar field. Motivated by this intriguing observation, we use {\it analytical} techniques in order to prove a no-short hair theorem for the composed acoustic-black-hole-scalar-clouds configurations. In particular, it is proved that the effective lengths of the stationary bound-state co-rotating acoustic scalar clouds are bounded from below by the series of inequalities $r_{\text{hair}}>{1+\sqrt{5}\over{2}}\cdot r_{\text{H}}>r_{\text{null}}$, where $r_{\text{H}}$ and $r_{\text{null}}$ are respectively the horizon radius of the supporting black hole and the radius of the co-rotating null circular geodesic that characterizes the acoustic spinning black-hole spacetime.
Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a {\it finite} mass gap above the corresponding zero-temperature (extremal) black-hole configuration. In the present compact paper we explicitly prove that the minimum energy gap ${\cal E}_{\text{gap}}=\hbar^2/M^3$, which characterizes the mass spectra of near-extremal charged Reissner-Nordström black holes, can be inferred from a simple semi-classical analysis.
We study {\it analytically} the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum $\{R_{\text{s}}(Q,α,l;n)\}^{n=\infty}_{n=1}$ of charged shell radii that can support the non-minimally coupled massless scalar fields can be expressed in a remarkably compact form in terms of the characteristic zeros of the Bessel function (here $Q$, $α$, and $l$ are respectively the electric charge of the central supporting shell, the dimensionless non-minimal coupling parameter of the Maxwell-scalar theory, and the angular harmonic index of the supported scalar configuration).
We analyze the Hawking evaporation process of Reissner-Nordström black holes. It is shown that the characteristic radiation quanta emitted by the charged black holes may turn near-extremal black-hole spacetimes into horizonless naked singularities. The present analysis therefore reveals the intriguing possibility that the semi-classical Hawking evaporation process of black holes may violate the fundamental Penrose cosmic censorship conjecture.
It has recently been proved that, in the presence of vortex flows, the fluctuation dynamics of a rotating photon-fluid model is governed by the Klein-Gordon equation of an effective massive scalar field in a $(2+1)$-dimensional acoustic black-hole spacetime. Interestingly, it has been demonstrated numerically that the rotating acoustic black hole, like the familiar Kerr black-hole spacetime, may support spatially regular stationary density fluctuations (linearized acoustic scalar `clouds') in its exterior regions. In particular, it has been shown that the composed rotating-acoustic-black-hole-stationary-scalar-field configurations of the photon-fluid model exist in the narrow dimensionless regime $α\equivΩ_0/mΩ_{\text{H}}\in(1,α_{\text{max}})$ with $α_{\text{max}}\simeq 1.08$ [here $Ω_{\text{H}}$ is the angular velocity of the black-hole horizon and $\{Ω_0,m\}$ are respectively the effective proper mass and the azimuthal harmonic index of the acoustic scalar field]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the acoustic scalar clouds of the photon-fluid model in the regime $Ω_{\text{H}}r_{\text{H}}\gg1$ of rapidly-spinning central supporting acoustic black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum $\{Ω_0(Ω_{\text{H}},m;n)\}$ which characterizes the stationary bound-state acoustic scalar clouds of the photon-fluid model. Interestingly, it is proved that the critical (maximal) mass parameter $α_{\text{max}}$, which determines the regime of existence of the composed acoustic-black-hole-stationary-bound-state-massive-scalar-field configurations, is given by the exact dimensionless relation $α_{\text{max}}=\sqrt{{{32}\over{27}}}$.
The physical and mathematical properties of the non-linearly coupled black-hole-orbiting-ring system are studied analytically to second order in the dimensionless angular velocity $M_{\text{ir}}ω_{\text{H}}$ of the black-hole horizon (here $M_{\text{ir}}$ is the irreducible mass of the slowly rotating central black hole). In particular, we determine analytically, to first order in the dimensionless ring-to-black-hole mass ratio $m/M_{\text{ir}}$, the shift $ΔΩ_{\text{mb}}/Ω_{\text{mb}}$ in the orbital frequency of the {\it marginally bound} circular geodesic that characterizes the composed curved spacetime. Interestingly, our analytical results for the frequency shift $ΔΩ_{\text{mb}}$ in the composed black-hole-orbiting-ring toy model agree qualitatively with the recently published numerical results for the corresponding frequency shift in the physically related (and mathematically much more complex) black-hole-orbiting-particle system. In particular, the present analysis provides evidence that, at order $O(m/M_{\text{ir}})$, the recently observed positive shift in the angular frequency of the marginally bound circular orbit is directly related to the physically intriguing phenomenon of dragging of inertial frames by orbiting masses in general relativity.
Black-hole spacetimes are known to possess closed light rings. We here present a remarkably compact theorem which reveals the physically intriguing fact that these unique null circular geodesics provide the {\it fastest} way, as measured by asymptotic observers, to circle around spinning Kerr black holes.
It is conjectured that stationary black holes are characterized by the inverse hoop relation ${\cal A}\leq {\cal C}^2/π$, where ${\cal A}$ and ${\cal C}$ are respectively the black-hole surface area and the circumference length of the smallest ring that can engulf the black-hole horizon in every direction. We explicitly prove that generic Kerr-Newman-(anti)-de Sitter black holes conform to this conjectured area-circumference relation.
It has recently been demonstrated that black holes with spatially regular horizons can support external scalar fields (scalar hairy configurations) which are non-minimally coupled to the Gauss-Bonnet invariant of the curved spacetime. The composed black-hole-scalar-field system is characterized by a critical existence line $α=α(μr_{\text{H}})$ which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here $\{α,μ,r_{\text{H}}\}$ are respectively the dimensionless non-minimal coupling parameter of the field theory, the proper mass of the scalar field, and the horizon radius of the central supporting black hole]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the marginally-stable composed black-hole-linearized-scalar-field configurations in the eikonal regime $μr_{\text{H}}\gg1$ of large field masses. In particular, we derive a remarkably compact analytical formula for the critical existence-line $α=α(μr_{\text{H}})$ of the system which separates bare Schwarzschild black-hole spacetimes from composed hairy (scalarized) black-hole-field configurations.
The hoop conjecture, introduced by Thorne almost five decades ago, asserts that black holes are characterized by the mass-to-circumference relation $4π{\cal M}/{\cal C}\geq1$, whereas horizonless compact objects are characterized by the opposite inequality $4π{\cal M}/{\cal C}<1$ (here ${\cal C}$ is the circumference of the smallest ring that can engulf the self-gravitating compact object in all azimuthal directions). It has recently been proved that a necessary condition for the validity of this conjecture in horizonless spacetimes of spatially regular charged compact objects is that the mass ${\cal M}$ be interpreted as the mass contained within the engulfing sphere (and not as the asymptotically measured total ADM mass). In the present paper we raise the following physically intriguing question: Is it possible to formulate a unified version of the hoop conjecture which is valid for both black holes and horizonless compact objects? In order to address this important question, we analyze the behavior of the mass-to-circumference ratio of Kerr-Newman black holes. We explicitly prove that if the mass ${\cal M}$ in the hoop relation is interpreted as the quasilocal Einstein-Landau-Lifshitz-Papapetrou and Weinberg mass contained within the black-hole horizon, then these charged and spinning black holes are characterized by the sub-critical mass-to-circumference ratio $4π{\cal M}/{\cal C}<1$. Our results provide evidence for the non-existence of a unified version of the hoop conjecture which is valid for both black-hole spacetimes and spatially regular horizonless compact objects.