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Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 37 records · Page 2Linked to original sources
arXiv2025

Survival probabilities in biased random walks: To restart or not to restart? that is the question

The time-dependent survival probability function $S(t;x_0,q)$ of biased Sisyphus random walkers, who at each time step have a finite probability $q$ to step towards an absorbing trap at the origin and a complementary probability $1-q$ to return to their initial position $x_0$, is derived {\it analytically}. In particular, we explicitly prove that the survival probability function of the walkers decays exponentially at asymptotically late times. Interestingly, our analysis reveals the fact that, for a given value $q$ of the biased jumping probability, the survival probability function $S(t;x_0,q)$ is characterized by a {\it critical} (marginal) value $x^{\text{crit}}_0(q)$ of the initial gap between the walkers and the trap, above which the late-time survival probability of the biased Sisyphus random walkers is {\it larger} than the corresponding survival probability of standard random walkers.

cond-mat.stat-mech↗
arXiv2025

A Compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields

Self-gravitating horizonless ultra-compact objects that possess light rings have attracted the attention of physicists and mathematicians in recent years. In the present compact paper we raise the following physically interesting question: Is there a lower bound on the global compactness parameters ${\cal C}\equiv\text{max}_r\{2m(r)/r\}$ of spherically symmetric ultra-compact objects? Using the non-linearly coupled Einstein-matter field equations we explicitly prove that spatially regular ultra-compact objects with monotonically decreasing density functions (or monotonically decreasing radial pressure functions) are characterized by the lower bound ${\cal C}\geq1/3$ on their dimensionless compactness parameters.

gr-qc↗
arXiv2025

Electroweak clouds supported by magnetically charged black holes: Analytic treatment along the existence-line

It has recently been revealed [R. Gervalle and M. S. Volkov, Phys. Rev. Lett. (2024)] that magnetically charged black holes of the composed Einstein-Weinberg-Salam field theory can support bound-state hairy configurations of electroweak fields. In the present paper we study, using {\it analytical} techniques, the physical and mathematical properties of the supported linearized electroweak fields (spatially regular electroweak 'clouds') in the dimensionless large-mass $μ\equiv m_{\text{w}} r_+\gg1$ regime of the composed black-hole-field system (here $m_{\text{w}}$ is the mass of the supported W-boson field and $r_+$ is the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact formula for the discrete resonance spectrum $\{μ_k(n)\}_{k=0}^{k=\infty}$ that characterizes the composed black-hole-linearized-field configurations, where the integer $n\equiv 2Pe\in\mathbb{Z}$ characterizes the discrete charge parameter $P$ of the central magnetic Reissner-Nordström black hole and $e$ is the electron charge. The physical significance of the analytically derived resonant spectrum stems from the fact that, in the dimensionless large-charge $n\gg1$ regime, the fundamental (largest) eigenvalue $μ_0(n)$ determines the critical existence-line of the composed Einstein-Weinberg-Salam theory, a boundary line that separates hairy magnetic-black-hole-electroweak-field bound-state configurations from bald magnetic Reissner-Nordström black holes.

gr-qc↗
arXiv2025

A sufficient condition for the development of superradiant instabilities in charged black-hole spacetimes

The physical and mathematical properties of charged black holes that are linearly coupled to charged massive scalar fields are studied analytically. In particular, we prove that, in the eikonal large-mass regime $Mμ\gg1$, the compact dimensionless inequality $Φ_{\text{H}}>Q/M$ provides a sufficient condition for the development of superradiant instabilities in the curved black-hole spacetime [here $\{M,Q,Φ_{\text{H}}\}$ are respectively the mass, the electric charge, and the horizon electrostatic potential of the central black hole and $μ$ is the proper mass of the field]. The familiar charged Reissner-Nordström black hole does not satisfy this inequality. On the other hand, we explicitly prove that all charged Ayón-Beato-García (ABG) black-hole spacetimes satisfy this analytically derived sufficient condition and may therefore become superradiantly unstable to perturbations of charged massive scalar fields.

gr-qc↗
arXiv2025

Maximum force conjecture in curved spacetimes of stable self-gravitating matter configurations

Gibbons and Schiller have raised the physically interesting conjecture that forces in general relativity are bounded from above by the mathematically compact relation ${\cal F}\leq c^4/4G$. In the present compact paper we explicitly prove, using the non-linearly coupled Einstein-matter field equations, that the force function ${\cal F}\equiv 4πr^2 p(r)$ in {\it stable} self-gravitating horizonless matter configurations is characterized by the upper bound ${\cal F}\leq c^4/G$ [here $p(r)$ is the radial pressure inside the self-gravitating matter configuration].

gr-qc↗
arXiv2024

Non-equatorial scalar rings supported by rapidly spinning Gauss-Bonnet black holes

Black-hole spacetimes that possess stationary equatorial matter rings are known to exist in general relativity. We here reveal the existence of black-hole spacetimes that support {\it non}-equatorial matter rings. In particular, it is proved that rapidly-rotating Kerr black holes in the dimensionless large-spin regime ${\bar a}>{\bar a}_{\text{crit}}= \sqrt{\big\{{{7+\sqrt{7}\cos\big[{1\over3}\arctan\big(3\sqrt{3}\big)\big]- \sqrt{21}\sin\big[{1\over3}\arctan\big(3\sqrt{3}\big)\big]}\big\}/12}}\simeq0.78$ can support a pair of non-equatorial massive scalar rings which are negatively coupled to the Gauss-Bonnet curvature invariant of the spinning spacetime (here ${\bar a}\equiv J/M^2$ is the dimensionless angular momentum of the central supporting black hole). We explicitly prove that these non-equatorial scalar rings are characterized by the dimensionless functional relation $-{{57+28\sqrt{21}\cos\big[{1\over3}\arctan\big({{1}\over{3\sqrt{3}}}\big)\big]} \over{8(1+\sqrt{1-{\bar a}^2})^6}} \cdot{{\barη}\over{{\barμ}^2}}\to 1^{+}$ in the large-mass ${\barμ}\equiv Mμ\gg1$ regime (here $\{{\barη}<0,μ\}$ are respectively the non-trivial coupling parameter of the composed Einstein-Gauss-Bonnet-massive-scalar field theory and the proper mass of the supported non-minimally coupled scalar field).

gr-qc↗
arXiv2024

A test of the conjectured critical black-hole formation -- null geodesic correspondence: The case of self-gravitating scalar fields

It has recently been conjectured [A. Ianniccari {\it et al.}, Phys. Rev. Lett. {\bf 133}, 081401 (2024)] that there exists a correspondence between the critical threshold of black-hole formation and the stability properties of null circular geodesics in the curved spacetime of the collapsing matter configuration. In the present compact paper we provide a non-trivial test of this intriguing conjecture. In particular, using analytical techniques we study the physical and mathematical properties of self-gravitating scalar field configurations that possess marginally-stable (degenerate) null circular geodesics. We reveal the interesting fact that the {\it analytically} calculated critical compactness parameter ${\cal C}^{\text{analytical}}\equiv{\text{max}_r}\{m(r)/r\}=6/25$, which signals the appearance of the first (marginally-stable) null circular geodesic in the curved spacetime of the self-gravitating scalar fields, agrees quite well (to within $\sim10\%$) with the exact compactness parameter ${\cal C}^{\text{numerical}}\equiv\text{max}_t\{\text{max}_r\{m(r)/r\}\}\simeq0.265$ which is computed {\it numerically} using fully non-linear numerical simulations of the gravitational collapse of scalar fields at the threshold of black-hole formation [here $m(r)$ is the gravitational mass contained within a sphere of radius $r$].

gr-qc↗
arXiv2024

Survival probabilities in the Sisyphus random walk model with absorbing traps

We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position $x_0$. In particular, we present a remarkably compact derivation of the time-dependent survival probability function $S(t;x_0)$ which characterizes the random walkers in the presence of an absorbing trap at the origin. The survival probabilities are expressed in a compact mathematical form in terms of the $x_0$-generalized Fibonacci-like numbers $G^{(x_0)}_t$. Interestingly, it is proved that, as opposed to the standard random walk model in which the survival probabilities depend linearly on the initial distance $x_0$ of the walkers from the trap and decay asymptotically as an inverse power of the time, in the Sisyphus random walk model the asymptotic survival probabilities decay exponentially in time and are characterized by a non-trivial (non-linear) dependence on the initial gap $x_0$ from the absorbing trap. We use the analytically derived results in order to analyze the underlying dynamics of the `survival-game', a highly risky investment strategy in which non-absorbed agents receive a reward $P(t)$ which gradually increases in time.

cond-mat.stat-mech↗
arXiv2024

Super-extremal black holes in the quasitopological electromagnetic field theory

It has recently been proved that a simple generalization of electromagnetism, referred to as quasitopological electromagnetic field theory, is characterized by the presence of dyonic black-hole solutions of the Einstein field equations that, in certain parameter regions, are characterized by four horizons. In the present compact paper we reveal the existence, in this non-linear electrodynamic field theory, of super-extremal black-hole spacetimes that are characterized by the four degenerate functional relations $[g_{00}(r)]_{r=r_{\text{H}}}=[dg_{00}(r)/dr]_{r=r_{\text{H}}}=[d^2g_{00}(r)/dr^2]_ {r=r_{\text{H}}}=[d^3g_{00}(r)/dr^3]_{r=r_{\text{H}}}=0$, where $g_{00}(r)$ is the $tt$-component of the curved line element and $r_{\text{H}}$ is the black-hole horizon radius. In particular, using analytical techniques we prove that the quartically degenerate super-extremal black holes are characterized by the universal (parameter-{\it independent}) dimensionless compactness parameter $M/r_{\text{H}}={2\over3}(2γ+1)$, where $γ\equiv{_2F_1}(1/4,1;5/4;-3)$.

gr-qc↗
arXiv2024

Spatially regular charged black holes supporting charged massive scalar clouds

We prove that, as opposed to the familiar charged Reissner-Nordström black-hole spacetime, the spatially regular charged Ayón-Beato-García (ABG) black-hole spacetime can support charged scalar clouds, spatially regular stationary matter configurations which are made of linearized charged massive scalar fields. Interestingly, we reveal the fact that the composed black-hole-field system is amenable to an analytical treatment in the regime $Q/M\ll1\ll Mμ$ of weakly charged black holes and large-mass fields, in which case it is proved that the dimensionless physical parameter $α\equiv{{qQ}\over{Mμ}}$ must lie in the narrow interval $α\in\big(\sqrt{{{3240}\over{6859}}},{{16}\over{23}}\big)$ [here $\{M,Q\}$ are the mass and electric charge of the central black hole and $\{μ,q\}$ are the proper mass and charge coupling constant of the supported scalar field]. In particular, we explicitly prove that, for weakly charged black holes, the discrete resonance spectrum $\{α(M,Q,μ,q;n\}^{n=\infty}_{n=0}$ of the composed charged-ABG-black-hole-charged-massive-scalar-field cloudy configurations can be determined {\it analytically} in the eikonal large-mass regime.

gr-qc↗
arXiv2023

Lower bound on the radii of light rings in traceless black-hole spacetimes

Photonspheres, curved hypersurfaces on which massless particles can perform closed geodesic motions around highly compact objects, are an integral part of generic black-hole spacetimes. In the present compact paper we prove, using analytical techniques, that the innermost light rings of spherically symmetric hairy black-hole spacetimes whose external matter fields are characterized by a traceless energy-momentum tensor cannot be located arbitrarily close to the central black hole. In particular, we reveal the physically interesting fact that the non-linearly coupled Einstein-matter field equations set the lower bound $r_γ\geq {6\over5}r_{\text{H}}$ on the radii of traceless black-hole photonspheres, where $r_{\text{H}}$ is the radius of the outermost black-hole horizon.

gr-qc↗
arXiv2023

Compact stars: To cross or go around? That is the question

The travel times of light signals between two antipodal points on the surface of a compact star are calculated for two different trajectories: a straight line that passes through the center of the star and a semi-circular trajectory that connects the antipodal points along the surface of the star. Interestingly, it is explicitly proved that, for highly dense stars, the longer trajectory (the one that goes along the surface of the star) may be characterized by the {\it shorter} travel time as measured by asymptotic observers. In particular, for constant density stars we determine {\it analytically} the critical value of the dimensionless density-area parameter $Λ\equiv 4πR^2ρ$ that marks the boundary between situations in which a direct crossing of the star through its center has the shorter travel time and situations in which the semi-circular trajectory along the surface of the star is characterized by the shorter travel time as measured by asymptotic observers [here $\{R,ρ\}$ are respectively the radius of the star and its density].

gr-qc↗
arXiv2023

The superradiant instability spectrum of the hydrodynamic vortex model

We study analytically the superradiant instability properties of the hydrodynamic vortex model, an asymptotically flat acoustic geometry which, like the spinning Kerr black-hole spacetime, possesses an effective ergoregion. In particular, we derive a compact analytical formula for the complex resonant frequencies that characterize the long-wavelength dynamics of sound modes in this physically interesting acoustic spacetime.

gr-qc↗
arXiv2023

Analytic study of the Maxwell electromagnetic invariant in spinning and charged Kerr-Newman black-hole spacetimes

The Maxwell invariant plays a fundamental role in the mathematical description of electromagnetic fields in charged spacetimes. We present a detailed {\it analytical} study of the physical and mathematical properties of the Maxwell electromagnetic invariant ${\cal F}_{\text{KN}}(r,θ;M,a,Q)$ which characterizes the Kerr-Newman black-hole spacetime. It is proved that, for all Kerr-Newman black-hole spacetimes, the spin and charge dependent minimum value of the Maxwell electromagnetic invariant is attained on the equator of the black-hole surface. Interestingly, we reveal the physically important fact that Kerr-Newman spacetimes are characterized by two critical values of the dimensionless rotation parameter ${\hat a}\equiv a/r_+$, ${\hat a}^{-}_{\text{crit}}=\sqrt{3-2\sqrt{2}}$ and ${\hat a}^{+}_{\text{crit}}= \sqrt{5-2\sqrt{5}}$, which mark the boundaries between three qualitatively different spatial functional behaviors of the Maxwell electromagnetic invariant: (i) Kerr-Newman black holes in the slow-rotation ${\hat a}<{\hat a}^{-}_{\text{crit}}$ regime are characterized by negative definite Maxwell electromagnetic invariants that increase monotonically towards spatial infinity, (ii) for black holes in the intermediate spin regime ${\hat a}^{-}_{\text{crit}}\leq {\hat a}\leq{\hat a}^{+}_{\text{crit}}$, the positive global maximum of the Kerr-Newman Maxwell electromagnetic invariant is located at the black-hole poles, and (iii) Kerr-Newman black holes in the super-critical regime ${\hat a}>{\hat a}^{+}_{\text{crit}}$ are characterized by a non-monotonic spatial behavior of the Maxwell electromagnetic invariant along the black-hole horizon with a spin and charge dependent global maximum whose polar angular location is characterized by the dimensionless functional relation ${\hat a}^2\cdot(\cos^2θ)_{\text{max}}=5-2\sqrt{5}$.

gr-qc↗
arXiv2023

Black holes that are too cold to respect cosmic censorship

In this essay it is proved that there are black holes that are dangerously cold. In particular, by analyzing the emission spectra of highly charged black holes we reveal the fact that near-extremal black holes whose Bekenstein-Hawking temperatures lie in the regime $T_{\text{BH}}\lesssim m^6_e/e^3$ may turn into horizonless naked singularities, thus violating the cosmic censorship principle, if they emit a photon with the characteristic thermal energy $ω=O(T_{\text{BH}})$ [here $\{m_e,e\}$ are respectively the proper mass and the electric charge of the electron, the lightest charged particle]. We therefore raise here the conjecture that, in the yet unknown quantum theory of gravity, the temperatures of well behaved black-hole spacetimes are fundamentally bounded from below by the relation $T_{\text{BH}}\gtrsim m^6_e/e^3$.

gr-qc↗
arXiv2023

Universal lower bound on orbital periods around central compact objects

It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods $T_{\infty}$ of test particles around central compact objects as measured by flat-space asymptotic observers are fundamentally bounded from below. The lower bound on orbital periods becomes universal (independent of the mass $M$ of the central compact object) in the dimensionless $ME_{\text{c}}\gg1$ regime, in which case it can be expressed in terms of the electric charge $e$ and the proper mass $m_{e}$ of the lightest charged particle in nature: $T_{\infty}>{{2πe\hbar}\over{\sqrt{G}c^2 m^2_{e}}}$ (here $E_{\text{c}}=m^2_{e}/e\hbar$ is the critical electric field for pair production). The explicit dependence of the bound on the fundamental constants of nature $\{G,c,\hbar\}$ suggests that it may reflect a fundamental physical property of the elusive quantum theory of gravity.

gr-qc↗
arXiv2023

What can a detected photon with a given gravitational redshift tell us about the maximum density of a compact star?

Far away observers can in principle bound from below the dimensionless maximum-density parameter $Λ\equiv4πR^2ρ_{\text{max}}$ of a compact star by measuring the gravitational redshift factor $z\equivν_{\text{e}}/ν_{\infty}-1$ of photons that were emitted from the {\it surface} of the star: $Λ\geq{3\over2}[1-(1+z)^{-2}]$ [here $R$ is the radius of the star and $\{ν_{\text{e}},ν_{\infty}\}$ are respectively the frequency of the emitted light as measured at the location of the emission and by asymptotic observers]. However, if photons that were created somewhere {\it inside} the star can make their way out and reach the asymptotic observers, then the measured redshift parameter $z$ may not determine uniquely the surface properties of the star, thus making the above bound unreliable. In the present compact paper we prove that in these cases, in which the creation depth of a detected photon is not known to the far away observers, the empirically measured redshift parameter can still be used to set a (weaker) lower bound on the dimensionless density parameter of the observed star: $Λ\geq{3\over2}[1-(1+z)^{-2/3}]$.

gr-qc↗
arXiv2023

Charged Gauss-Bonnet black holes supporting non-minimally coupled scalar clouds: Analytic treatment in the near-critical regime

Recent numerical studies have revealed the physically intriguing fact that charged black holes whose charge-to-mass ratios are larger than the critical value $(Q/M)_{\text{crit}}=\sqrt{2(9+\sqrt{6})}/5$ can support hairy matter configurations which are made of scalar fields with a non-minimal negative coupling to the Gauss-Bonnet invariant of the curved spacetime. Using {\it analytical} techniques, we explore the physical and mathematical properties of the composed charged-black-hole-nonminimally-coupled-linearized-massless-scalar-field configurations in the near-critical $Q/M\gtrsim (Q/M)_{\text{crit}}$ regime. In particular, we derive an analytical resonance formula that describes the charge-dependence of the dimensionless coupling parameter $\barη_{\text{crit}}=\barη_{\text{crit}}(Q/M)$ of the composed Einstein-Maxwell-nonminimally-coupled-scalar-field system along the {\it existence-line} of the theory, a critical border that separates bald Reissner-Nordström black holes from hairy charged-black-hole-scalar-field configurations. In addition, it is explicitly shown that the large-coupling $-\barη_{\text{crit}}(Q/M)\gg1$ analytical results derived in the present paper for the composed Einstein-Maxwell-scalar theory agree remarkably well with direct numerical computations of the corresponding black-hole-field resonance spectrum.

gr-qc↗