arXiv subjects

Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 109 records · Page 6Linked to original sources

arXiv2017

Highly excited bound-state resonances of short-range inverse power-law potentials

We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form $V(r)=-β_n r^{-n}$ with $n>2$. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius $R$, we derive a compact {\it analytical} formula for the threshold energy $E^{\text{max}}_l=E^{\text{max}}_l(n,β_n,R)$ which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.

quant-ph↗

arXiv2017

No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars

It has recently been proved that horizonless compact stars with reflecting boundary conditions {\it cannot} support spatially regular matter configurations made of minimally coupled scalar fields, vector fields, and tensor fields. In the present paper we extend this intriguing no-hair property to the physically interesting regime of scalar fields with {\it nonminimal} coupling to gravity. In particular, we prove that static spherically symmetric configurations made of nonminimally coupled massless scalar fields cannot be supported by compact reflecting stars.

gr-qc↗

arXiv2017

Extremal Kerr-Newman black holes with extremely short charged scalar hair

The recently proved `no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: $r_{\text{field}}>r_{\text{null}}$. In this paper we provide compelling evidence that the bound can be {\it violated} by {\it non}-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes -- charged rotating black holes which support linearized stationary charged scalar configurations in their exterior regions.

gr-qc↗

arXiv2017

Marginally bound (critical) geodesics of rapidly rotating black holes

One of the most important geodesics in a black-hole spacetime is the marginally bound spherical orbit. This critical geodesic represents the innermost spherical orbit which is bound to the central black hole. The radii $r_{\text{mb}}({\bar a})$ of the marginally bound {\it equatorial} circular geodesics of rotating Kerr black holes were found analytically by Bardeen {\it et. al.} more than four decades ago (here $\bar a\equiv J/M^2$ is the dimensionless angular-momentum of the black hole). On the other hand, no closed-form formula exists in the literature for the radii of generic ({\it non}-equatorial) marginally bound geodesics of the rotating Kerr spacetime. In the present study we analyze the critical (marginally bound) orbits of rapidly rotating Kerr black holes. In particular, we derive a simple {\it analytical} formula for the radii $r_{\text{mb}}(\bar a\simeq 1;\cos i)$ of the marginally bound spherical orbits, where $\cos i$ is an effective inclination angle (with respect to the black-hole equatorial plane) of the geodesic. We find that the marginally bound spherical orbits of rapidly-rotating black holes are characterized by a critical inclination angle, $\cos i=\sqrt{2/3}$, above which the coordinate radii of the geodesics approach the black-hole radius in the extremal $\bar a\to1$ limit. It is shown that this critical inclination angle signals a transition in the physical properties of the orbits: in particular, it separates marginally bound spherical geodesics which lie a finite proper distance from the black-hole horizon from marginally bound geodesics which lie an infinite proper distance from the horizon.

gr-qc↗

arXiv2017

A no-short scalar hair theorem for rotating Kerr black holes

If a black hole has hair, how short can this hair be? A partial answer to this intriguing question was recently provided by the 'no-short hair' theorem which asserts that the external fields of a spherically-symmetric electrically neutral hairy black-hole configuration must extend beyond the null circular geodesic which characterizes the corresponding black-hole spacetime. One naturally wonders whether the no-short hair inequality $r_{\text{hair}}>r_{\text{null}}$ is a generic property of all electrically neutral hairy black-hole spacetimes? In this paper we provide evidence that the answer to this interesting question may be positive. In particular, we prove that the recently discovered cloudy Kerr black-hole spacetimes -- non-spherically symmetric non-static black holes which support linearized massive scalar fields in their exterior regions -- also respect this no-short hair lower bound. Specifically, we analytically derive the lower bound $r_{\text{field}}/r_+>r_+/r_-$ on the effective lengths of the external bound-state massive scalar clouds (here $r_{\text{field}}$ is the peak location of the stationary bound-state scalar fields and $r_{\pm}$ are the horizon radii of the black hole). Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass and angular harmonic indices) of the exterior scalar fields. Our results suggest that the lower bound $r_{\text{hair}}>r_{\text{null}}$ may be a general property of asymptotically flat electrically neutral hairy black-hole configurations.

gr-qc↗

arXiv2017

A proof of the weak gravity conjecture

The weak gravity conjecture suggests that, in a self-consistent theory of quantum gravity, the strength of gravity is bounded from above by the strengths of the various gauge forces in the theory. In particular, this intriguing conjecture asserts that in a theory describing a U(1) gauge field coupled consistently to gravity, there must exist a particle whose proper mass is bounded (in Planck units) by its charge: $m/m_{\text{P}}<q$. This beautiful and remarkably compact conjecture has attracted the attention of physicists and mathematicians over the last decade. It should be emphasized, however, that despite the fact that there are numerous examples from field theory and string theory that support the conjecture, we still lack a general proof of its validity. In the present Letter we prove that the weak gravity conjecture (and, in particular, the mass-charge upper bound $m/m_{\text{P}}<q$) can be inferred directly from Bekenstein's generalized second law of thermodynamics, a law which is widely believed to reflect a fundamental aspect of the elusive theory of quantum gravity.

gr-qc↗

arXiv2017

Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner-Nordström black-hole spacetime

The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner-Nordström black-hole spacetime are studied {\it analytically}. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein-Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system.

hep-th↗

arXiv2017

Onset of superradiant instabilities in rotating spacetimes of exotic compact objects

Exotic compact objects, horizonless spacetimes with reflective properties, have intriguingly been suggested by some quantum-gravity models as alternatives to classical black-hole spacetimes. A remarkable feature of spinning horizonless compact objects with reflective boundary conditions is the existence of a {\it discrete} set of critical surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=\infty}_{n=1}$, which can support spatially regular static ({\it marginally-stable}) scalar field configurations (here ${\bar a}\equiv J/M^2$ is the dimensionless angular momentum of the exotic compact object). Interestingly, the outermost critical radius $r^{\text{max}}_{\text{c}}\equiv \text{max}_n\{r_{\text{c}}({\bar a};n)\}$ marks the boundary between stable and unstable exotic compact objects: spinning objects whose reflecting surfaces are situated in the region $r_{\text{c}}>r^{\text{max}}_{\text{c}}({\bar a})$ are stable, whereas spinning objects whose reflecting surfaces are situated in the region $r_{\text{c}}<r^{\text{max}}_{\text{c}}({\bar a})$ are superradiantly unstable to scalar perturbation modes. In the present paper we use analytical techniques in order to explore the physical properties of the critical (marginally-stable) spinning exotic compact objects. In particular, we derive a remarkably compact {\it analytical} formula for the discrete spectrum $\{r^{\text{max}}_{\text{c}}({\bar a})\}$ of critical radii which characterize the marginally-stable exotic compact objects. We explicitly demonstrate that the analytically derived resonance spectrum agrees remarkably well with numerical results that recently appeared in the physics literature.

hep-th↗

arXiv2017

Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell

The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied {\it analytically}. To that end, we solve the Klein-Gordon wave equation for a static scalar field of proper mass $μ$, charge coupling constant $q$, and spherical harmonic index $l$ in the background of a charged shell of radius $R$ and electric charge $Q$. It is proved that the dimensionless inequality $μR<\sqrt{(qQ)^2-(l+1/2)^2}$ provides an upper bound on the regime of existence of the composed charged-spherical-shell-charged-massive-scalar-field configurations. Interestingly, we explicitly show that the {\it discrete} spectrum of shell radii $\{R_n(μ,qQ,l)\}_{n=0}^{n=\infty}$ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.

gr-qc↗

arXiv2017

Upper bound on the radii of black-hole photonspheres

One of the most remarkable predictions of the general theory of relativity is the existence of black-hole "photonspheres", compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by $r_γ \leq 3M$, where $M$ is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound.

gr-qc↗

arXiv2017

Analytic treatment of the excited instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes

The magnetically charged SU(2) Reissner-Nordström black-hole solutions of the coupled nonlinear Einstein-Yang-Mills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances $\{ω_n(r_+,r_-)\}_{n=0}^{n=\infty}$ (here $r_{\pm}$ are the black-hole horizon radii). Based on direct {\it numerical} computations of the black-hole instability spectra, it has recently been observed that the excited instability eigenvalues of the magnetically charged black holes exhibit a simple universal behavior. In particular, it was shown that the numerically computed instability eigenvalues of the magnetically charged black holes are characterized by the small frequency universal relation $ω_n(r_+-r_-)=λ_n$, where $\{λ_n\}$ are dimensionless constants which are independent of the black-hole parameters. In the present paper we study analytically the instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes. In particular, we provide a rigorous {\it analytical} proof for the {\it numerically}-suggested universal behavior $ω_n(r_+-r_-)=λ_n$ in the small frequency $ω_n r_+\ll (r_+-r_-)/r_+$ regime. Interestingly, it is shown that the excited black-hole resonances are characterized by the simple universal relation $ω_{n+1}/ω_n=e^{-2π/\sqrt{3}}$. Finally, we confirm our analytical results for the black-hole instability spectra with numerical computations.

hep-th↗

arXiv2017

A lower bound on the Bekenstein-Hawking temperature of black holes

We present evidence for the existence of a quantum lower bound on the Bekenstein-Hawking temperature of black holes. The suggested bound is supported by a gedanken experiment in which a charged particle is dropped into a Kerr black hole. It is proved that the temperature of the final Kerr-Newman black-hole configuration is bounded from below by the relation $T_{\text{BH}}\times r_{\text{H}}>(\hbar/r_{\text{H}})^2$, where $r_{\text{H}}$ is the horizon radius of the black hole.

gr-qc↗

arXiv2016

No-scalar-hair theorem for spherically symmetric reflecting stars

It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential $V(ψ^2)$ is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.

gr-qc↗

arXiv2016

The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror

The intriguing superradiant amplification phenomenon allows an orbiting scalar field to extract rotational energy from a spinning Kerr black hole. Interestingly, the energy extraction rate can grow exponentially in time if the black-hole-field system is placed inside a reflecting mirror which prevents the field from radiating its energy to infinity. This composed Kerr-black-hole-scalar-field-mirror system, first designed by Press and Teukolsky, has attracted the attention of physicists over the last four decades. Previous numerical studies of this spinning {\it black-hole bomb} have revealed the interesting fact that the superradiant instability shuts down if the reflecting mirror is placed too close to the black-hole horizon. In the present study we use analytical techniques to explore the superradiant instability regime of this composed Kerr-black-hole-linearized-scalar-field-mirror system. In particular, it is proved that the lower bound ${r_{\text{m}}\over{r_+}}>{1\over 2}\Big(\sqrt{1+{{8M}\over{r_-}}}-1\Big)$ provides a necessary condition for the development of the exponentially growing superradiant instabilities in this composed physical system, where $r_{\text{m}}$ is the radius of the confining mirror and $r_{\pm}$ are the horizon radii of the spinning Kerr black hole. We further show that, in the linearized regime, this {\it analytically} derived lower bound on the radius of the confining mirror agrees with direct {\it numerical} computations of the superradiant instability spectrum which characterizes the spinning black-hole-mirror bomb.

gr-qc↗

arXiv2016

Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime $Mμ\gg1$ (here $M$ and $μ$ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.

hep-th↗

arXiv2016

A mystery of black-hole gravitational resonances

More than three decades ago, Detweiler provided an analytical formula for the gravitational resonant frequencies of rapidly-rotating Kerr black holes. In the present work we shall discuss an important discrepancy between the famous {\it analytical} prediction of Detweiler and the recent {\it numerical} results of Zimmerman et. al. In addition, we shall refute the claim that recently appeared in the physics literature that the Detweiler-Teukolsky-Press resonance equation for the characteristic gravitational eigenfrequencies of rapidly-rotating Kerr black holes is not valid in the regime of damped quasinormal resonances with $\Imω/T_{\text{BH}}\gg1$ (here $ω$ and $T_{\text{BH}}$ are respectively the characteristic quasinormal resonant frequency of the Kerr black hole and its Bekenstein-Hawking temperature). The main goal of the present paper is to highlight and expose this important {\it black-hole quasinormal mystery} (that is, the intriguing discrepancy between the analytical and numerical results regarding the gravitational quasinormal resonance spectra of rapidly-rotating Kerr black holes).

hep-th↗

arXiv2016

Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field

Charged rotating Kerr-Newman black holes are known to be superradiantly unstable to perturbations of charged massive bosonic fields whose proper frequencies lie in the bounded regime $0 < ω< \text{min} \{ω_{\text{c}} \equiv m Ω_{\text{H}} + qΦ_{\text{H}},μ\}$ [here $\{Ω_{\text{H}}, Φ_{\text{H}}\}$ are respectively the angular velocity and electric potential of the Kerr-Newman black hole, and $\{m,q,μ\}$ are respectively the azimuthal harmonic index, the charge coupling constant, and the proper mass of the field]. In this paper we study analytically the complex resonance spectrum which characterizes the dynamics of linearized charged massive scalar fields in a near-extremal Kerr-Newman black-hole spacetime. Interestingly, it is shown that near the critical frequency $ω_{\text{c}}$ for superradiant amplification and in the eikonal large-mass regime, the superradiant instability growth rates of the explosive scalar fields are characterized by a non-trivial (non-monotonic) dependence on the dimensionless charge-to-mass ratio $q/μ$. In particular, for given parameters $\{M,Q, J\}$ of the central Kerr-Newman black hole, we determine analytically the optimal charge-to-mass ratio $q/μ$ of the explosive scalar field which {\it maximizes} the growth rate of the superradiant instabilities in the composed Kerr-Newman-black-hole-charged-massive-scalar-field system.

gr-qc↗

arXiv2016

Upper bound on the center-of-mass energy of the collisional Penrose process

Following the interesting work of Bañados, Silk, and West [Phys. Rev. Lett. {\bf 103}, 111102 (2009)], it is repeatedly stated in the physics literature that the center-of-mass energy, ${\cal E}_{\text{c.m}}$, of two colliding particles in a maximally rotating black-hole spacetime can grow unboundedly. For this extreme scenario to happen, the particles have to collide at the black-hole horizon. In this paper we show that Thorne's famous hoop conjecture precludes this extreme scenario from occurring in realistic black-hole spacetimes. In particular, it is shown that a new (and larger) horizon is formed {\it before} the infalling particles reach the horizon of the original black hole. As a consequence, the center-of-mass energy of the collisional Penrose process is {\it bounded} from above by the simple scaling relation ${\cal E}^{\text{max}}_{\text{c.m}}/2μ\propto(M/μ)^{1/4}$, where $M$ and $μ$ are respectively the mass of the central black hole and the proper mass of the colliding particles.

gr-qc↗