We study instabilities of the system composed of stationary scalar fields and asymptotically flat horizonless reflecting compact stars. In the probe limit, we obtain bounds on the scalar field frequency. Below this bound, stationary hairy stars are expected to suffer from nonlinear instabilities under massless field perturbations. In other words, we prove that stationary scalar hairy stars are unstable for scalar fields with small frequency.
We study the system constructed by charged scalar fields linearly coupled to asymptotically flat horizonless compact reflecting stars. We obtain bounds on the charge of the scalar field, below which the scalar hairy star is expected to suffer from nonlinear instabilities. It means that scalar hairy regular configurations are unstable for scalar fields of small charge. For the highly-charged star, there are also bounds on radii of regular compact reflecting stars. When the star radius is below the bound, the hairy star is always unstable.
We study the system of static scalar fields coupled to charged compact reflecting stars through both analytical and numerical methods. We enclose the star in a box and our solutions are related to cases without box boundaries when putting the box far away from the star. We provide bottom and upper bounds for the radius of the scalar hairy compact reflecting star. We obtain numerical scalar hairy star solutions satisfying boundary conditions and find that the radius of the hairy star in a box is continuous in a range, which is very different from cases without box boundaries where the radius is…
We study static massive scalar field condensations in the regular asymptotically flat reflecting star background. We impose Neumann reflecting surface boundary conditions for the scalar field. We show that the no hair theorem holds in the neutral reflecting star background. For charged reflecting stars, we provide bounds for radii of hairy reflecting stars. Below the lower bound, there is no regular compact reflecting star and a black hole will form. Above the upper bound, the scalar field cannot condense around the reflecting star or no hair theorems exist. And in between the bounds, we obtai…
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-mas…
We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configur…
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,…
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.
We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and AdS on the other (M-AdS wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infini…
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). …
Models with vector fields acquiring a non-vanishing vacuum expectation value along one spatial direction have been proposed to sustain a prolonged stage of anisotropic accelerated expansion. Such models have been used for realizations of early time inflation, with a possible relation to the large scale CMB anomalies, or of the late time dark energy. We show that, quite generally, the concrete realizations proposed so far are plagued by instabilities (either ghosts, or unstable growth of the linearized perturbations) which can be ultimately related to the longitudinal vector polarization presen…
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 mas…
In previous work of the author it was shown that instabilities of solutions to the wave equation develop asymptotically along the event horizon of extremal Kerr provided a certain expression H of the initial data is non-trivial on the horizon. In this note we remove this restriction by showing that instabilities develop even from initial data supported arbitrarily far away from the horizon (for which, in particular, H=0). The latter instabilities concern one order higher derivatives compared to the case where H is non-zero. The result also applies to extremal Reissner-Nordstrom. This note was …
Recent numerical simulations indicate the presence of dynamical instabilities of the f-mode in differentially rotating stars even at very low values of $T/|W|$, the ratio of kinetic to potential energy. In this Letter we argue that these may be shear instabilities which occur when the degree of differential rotation exceeds a critical value and the f-mode develops a corotation point associated with the presence of a continuous spectrum. Our explanation, which is supported by detailed studies of a simple shell model, offers a straightforward way of understanding all of the key features of these…
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 t…
Press and Teukolsky famously introduced the concept of a black hole bomb system: a scalar field scattering a Kerr black hole confined inside a mirror undergoes superradiant amplification that keeps repeating due to the reflecting boundary conditions at the mirror. A similar charged black hole bomb system exists if we have a charged scalar field propagating in a Reissner-Nordstrom black hole confined inside a box. We point out that scalar fields propagating in such a background are unstable not only to superradiance but also to a mechanism known as the near-horizon scalar condensation instabili…
It was first pointed out by Press and Teukolsky that a system composed of a spinning Kerr black hole surrounded by a reflecting mirror may develop instabilities. The physical mechanism responsible for the development of these exponentially growing instabilities is the superradiant amplification of bosonic fields confined between the black hole and the mirror. A remarkable feature of this composed black-hole-mirror-field system is the existence of a critical mirror radius, $r^{\text{stat}}_{\text{m}}$, which supports {\it stationary} (marginally-stable) field configurations. This critical (`sta…
We study collisions between pairs of bubbles nucleated in an ambient false vacuum. For the first time, we include the effects of small initial (quantum) fluctuations around the instanton profiles describing the most likely initial bubble profile. Past studies of this problem neglect these fluctuations and work under the assumption that the collisions posess an exact SO(2,1) symmetry. We use three-dimensional lattice simulations to demonstrate that for double-well potentials, small initial perturbations to this symmetry can be amplified as the system evolves. Initially the amplification is well…
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 …
Aretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner-Nordström black hole. We show that a similar instability occurs also for a massive scalar field and for coupled linearized gravitational and electromagnetic perturbations. We present numerical results for the late time behaviour of massless and massive scalar fields in the extreme RN background and show that instabilities are present for initial perturbations supported outside the horizon, e.g.\ an ingoing wavepacket. For a massless scalar we show that the numerical results for the late ti…
Binary neutron star mergers, such as the multimessenger GW170817 event, may produce hypermassive compact objects which are supported against collapse by the internal circulation of the fluid within the star. We compute their unstable modes of oscillations driven by gravitational wave radiation and shear viscosity, modeling them as triaxial Riemann ellipsoids. We work in a perturbative regime, where the gravitational radiation reaction force is taken into account at 2.5-post-Newtonian order and find unstable modes with dissipation timescales $\gtrsim 1$ ms which are relevant to the transient st…
