Static Scalar Field Research Articles

Ultra-spinning exotic compact objects supporting static massless scalar field configurations

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 a¯≡J/M2≤1 are characterized by an infinite countable set of surface radii, {rc(a¯;n)}n=1n=∞, that can support asymptotically flat static configurations made of massless scalar fields. In the present paper we study analytically the physical properties of ultra-spinning exotic compact objects with dimensionless angular momenta in the complementary regime a¯>1. It is proved that ultra-spinning reflecting compact objects with dimensionless angular momenta in the super-critical regime 1−[m/(l+2)]2≤|a¯|−1<1 are characterized by a finite discrete family of surface radii, {rc(a¯;n)}n=1n=Nr, distributed symmetrically around r=M, that can support spatially regular static configurations of massless scalar fields (here the integers {l,m} are the harmonic indices of the supported static scalar field modes). Interestingly, the largest supporting surface radius rcmax(a¯)≡maxn{rc(a¯;n)} marks the onset of superradiant instabilities in the composed ultra-spinning-exotic-compact-object-massless-scalar-field system.

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 discrete set of critical surface radii, {rc(ā; n)}n = 1n = ∞, which can support spatially regular static (marginally-stable) scalar field configurations (here ā≡J/M2 is the dimensionless angular momentum of the exotic compact object). Interestingly, the outermost critical radius rcmax≡ maxn{rc(ā; n)} marks the boundary between stable and unstable exotic compact objects: spinning objects whose reflecting surfaces are situated in the region rc > rcmax(ā) are stable, whereas spinning objects whose reflecting surfaces are situated in the region rc < rcmax(ā) 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 analytical formula for the discrete spectrum {rcmax(ā)} 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.

Asymptotically flat black holes in Horndeski theory and beyond

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.

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 $\mu$, 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 $\mu R<\sqrt{(qQ)^2-(l+1/2)^2}$ 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 $\{R_n(\mu,qQ,l)\}_{n=0}^{n=\infty}$ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.

Static scalar field solutions in symmetric gravity

We study an extension of general relativity with a second metric and an exchange symmetry between the two metrics. Such an extension might help to address some of the outstanding problems with general relativity, for example the smallness of the cosmological constant. We here derive a family of exact solutions for this theory. In this two-parameter family of solutions the gravitational field is sourced by a time-independent massless scalar field. We find that the only limit in which the scalar field entirely vanishes is flat space. The regular Schwarzschild-solution is left with a scalar field hidden in the second metric’s sector.

Circular orbits around static self-gravitating scalar field configurations

Circular orbits around static self-gravitating scalar field configurations

Horndeski scalar-tensor black hole geodesics

We examine massive particles and null geodesics for the scalar-tensor black hole in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits, corresponding to circular and elliptic orbits, are absent for the black hole solution with the static scalar field. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations.

Publisher’s Note: Biconformal symmetry and static Green functions in the higher-dimensional Reissner-Nordström spacetimes [Phys. Rev. D91, 064037 (2015)

We study a static scalar massless field created by a source located near an electrically charged higher dimensional spherically symmetric black hole. We demonstrated that there exist bi-conformal transformations relating static field solutions in the metric with different parameters of the mass M and charge Q. Using this symmetry we obtain the static scalar Green function in the higher dimensional Reissner-Nordstrom spacetimes.

Biconformal symmetry and static Green functions in the higher-dimensional Reissner-Nordström spacetimes

We study a static scalar massless field created by a source located near an electrically charged higher dimensional spherically symmetric black hole. We demonstrated that there exist bi-conformal transformations relating static field solutions in the metric with different parameters of the mass M and charge Q. Using this symmetry we obtain the static scalar Green function in the higher dimensional Reissner-Nordstrom spacetimes.

Propagation of test particles and scalar fields on a class of wormhole space-times

In this paper, we consider the problem of test particles and test scalar fields propagating on the background of a class of wormhole space-times. For test particles, we solve for arbitrary causal geodesics in terms of integrals which are solved numerically. These integrals are parametrized by the radius and shape of the wormhole throat as well as the initial conditions of the geodesic trajectory. In terms of these parameters, we compute the conditions for the geodesic to traverse the wormhole, to be reflected by the wormhole's potential or to be captured on an unstable bound orbit at the wormhole's throat. These causal geodesics are visualized by embedding plots in Euclidean space in cylindrical coordinates. For massless test scalar fields, we compute transmission coefficients and quasi-normal modes for arbitrary coupling of the field to the background geometry in the WKB approximation. We show that solutions of the scalar wave equation on this class of wormholes are stable only for certain values of the coupling constant. This analysis is interesting since recent computations of self-interactions of a static scalar field in wormhole space-times reveal some anomalous dependence on the coupling constant such as the existence of an infinite discrete set of poles. We show that this pathological behavior of the self-field is an artifact of computing the interaction for values of the coupling constant that do not lie in the domain of stability.

No-go theorem for static scalar field dark matter halos with no Noether charges

Classical scalar fields have been considered as a possible effective description of dark matter. We show that, for any metric theory of gravity, no static, spherically symmetric, regular, spatially localized, attractive, stable spacetime configuration can be sourced by the coherent excitation of a scalar field with positive definite energy density and no Noether charges. In the weak field regime, the result also applies for configurations with a repulsive gravitational potential. This extends Derrick's theorem to the case of a general (noncanonical) scalar field, including the self-gravitational effects. Some possible ways out are briefly discussed.

STATIC SPHERICALLY SYMMETRIC SCALAR FIELD SPACETIMES WITH C0 MATCHING

All the classes of static massless scalar field models currently available in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetime models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.

ONE-LOOP QUANTUM COSMOLOGICAL CORRECTION TO THE GRAVITATIONAL CONSTANT USING THE KINK SOLUTION IN DE SITTER UNIVERSE

In this paper, we show the equivalence between a classical static scalar field theory and the (closed) de Sitter cosmological model whose potential represents shape invariance property. Based on this equivalence, we calculate the one-loop quantum cosmological correction to the ground state energy of the kink-like solution in the (closed) de Sitter cosmological model in which the fluctuation potential V′′ has a shape invariance property. It is shown that this type of correction, which yields a renormalized mass in the case of scalar field theory, may be interpreted as a renormalized gravitational constant in the case of (closed) de Sitter cosmological model.

Example of a self-consistent solution for a fermion on domain wall

A self-consistent solution for a fermion coupled to static scalar field in the form of a kink (domain wall) is discussed. In particular, the case when the fermion occupies an excited nonzero frequency level in the presence of the domain-wall field is studied. The effect of the domain-wall profile distortion is calculated analytically.

Exact Solutions of Dirac Equation on (1+1)-Dimensional Spacetime Coupled to a Static Scalar Field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.

Exact solutions for the massless plane symmetric scalar field in general relativity, with cosmological constant

The Klein–Gordon equations are solved for the case of a plane-symmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that \(\Lambda \rightarrow 0\).The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.

Homogeneous scalar field and the wet dark sides of the universe

We study the possibility that a generalised real scalar field minimally coupled to gravity could explain both the galactic and the cosmological dark components of the universe. Within the framework of Einstein's Relativity we model static galactic halos by considering the most general action built from the scalar field and its first derivatives. Although the gravitational configuration is static, the scalar field may be either static, or homogeneous and linear in time. In the case of the static scalar field, the models we look at inevitably posses unphysical negative energies, and we are led to a sort of no-go result. In the case of the homogeneous scalar field, on the contrary, we find that compact objects with flat rotational curves and with the mass and the size of a typical galaxy can be successfully modeled and the Tully-Fisher relation recovered. We further show that the homogeneous scalar field deduced from the galactic halo spacetimes has an action compatible with the kinetic Unified Dark Matter models recently proposed by Scherrer. Therefore, such a homogeneous kinetic Unified Dark Matter not only may correctly mimic the galactic dynamics, but could also be used to model the present-day accelerated expansion in the universe.

ENERGY DISTRIBUTION OF THE EINSTEIN–KLEIN–GORDON SYSTEM FOR A STATIC SPHERICALLY SYMMETRIC SPACE–TIME IN (2+1) DIMENSIONS

We use Møller's energy–momentum complex in order to explicitly compute the energy and momentum density distributions for an exact solution of Einstein's field equations with a negative cosmological constant, minimally coupled to a static massless scalar field in a static, spherically symmetric background in (2+1) dimensions.

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerated horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordstrom black holes in higher dimensions.

An exact solution for static scalar fields coupled to gravity in (2+1)-dimensions

We obtain an exact solution for the Einstein’s equations with cosmological constant coupled to a scalar, static particle in static, “spherically” symmetric background in (2+1)-dimensions.