Scalar Modes Research Articles

Stationary scalar clouds around Kerr-Newman black holes

Abstract This study investigates scalar clouds around Kerr-Newman black holes within the Einstein-Maxwell-scalar model. Tachyonic instabilities are identified as the driving mechanism for scalar cloud formation. Employing the spectral method, we numerically compute wave functions and parameter space existence domains for both fundamental and excited scalar cloud modes. Our analysis demonstrates that black hole spin imposes an upper limit on the existence of scalar clouds, with excited modes requiring stronger tachyonic instabilities for their formation. These findings lay the groundwork for exploring the nonlinear dynamics and astrophysical implications of scalar clouds.

Strong cosmic censorship in de Sitter spacetimes with dark matter

After imposing the weak energy condition on dark matter, we find that even in the absence of charge, a spherically symmetric de Sitter black hole with perfect fluid dark matter may still possess a Cauchy horizon. This paper investigates the stability of the Cauchy horizon in such a black hole under perturbations from a massless scalar field. Through numerical calculations of the massless scalar field's quasinormal modes, we discover that in this spacetime, when the black hole approaches extremality, i.e., when the dark-matter parameter b approaches its maximum value bmax, the Strong Cosmic Censorship (SCC) conjecture may be violated. This is the first instance of classical SCC violation observed in a spherically symmetric, uncharged black hole. Additionally, we explore the region of SCC violation within the parameter space ΛM2−b/bmax. Our findings indicate that as the cosmological constant increases, the violation region initially expands and then contracts.

Probing massive gravitons in f(R) with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.

Mass ladder operators and quasinormal modes of the static BTZ-like black hole in the Einstein-bumblebee gravity

Abstract We investigate the mass ladder operators for the static BTZ-like black hole in the Einstein-bumblebee gravity, and probe the quasinormal frequencies of the mapped modes by the mass ladder operators for a scalar perturbation under the Dirichlet and Neumann boundary conditions. It is found that the mass ladder operators depend on the Lorentz symmetry breaking parameter, and the imaginary parts of the frequencies shifted by the mass ladder operators increase with the increase of the Lorentz symmetry breaking parameter under two boundary conditions. It should be noted that, under the Neumann boundary condition, the mapped modes caused by the mass ladder operator $D_{0,k_+}$ are unstable. Moreover, the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes, just as in the usual BTZ black hole. These results could help us to further understand the conformal symmetry and Lorentz symmetry breaking in the Einstein-bumblebee gravity.

Theory of interacting vector dark energy and fluid

In this work, we study interaction between dark energy and dark matter, where dark energy is described by a massive vector field, and dark matter is modelled as a fluid. We present a new interaction term, which affects only perturbations and can give interesting phenomenology. Then we present a general Lagrangian for the interacting vector dark energy with dark matter. For the dark energy, we choose Proca theory with G 3 term to study its phenomenological consequence. For this model, we explore both background and perturbation dynamics. We also present the no-ghost condition for tensor modes, vector modes and scalar modes. Subsequently, we also study the evolution of the overdensities of both baryon and cold dark matter in the high-k limit. We show that the effective gravitational coupling is modified for cold dark matter and baryon. We also choose a simple concrete model and numerically show a suppression of the effective gravitational coupling for cold dark matter. However, in this simple model, the suppression of the effective gravitational coupling does not result in a suppression of the matter overdensity compared to that in the ΛCDM model due to the modified background expansion.

Scalar Quasi-Normal Modes of a loop quantum black hole

We compute the Quasi-Normal Mode (QNM) frequencies for scalar perturbations for modified Schwarzschild black holes in Loop Quantum Gravity. We study the singularity-free polymerized metric characterized by two parameters encoding loop quantum effects: the minimal area gap a 0 and the polymeric deformation parameter P. We perform numerical computations using Leaver's continued fraction method and compare our results to other semi-analytical methods and existing literature. We study the effects on the QNM spectrum of variation of both deformation parameters and systematically compare to the standard Schwarzschild case. In particular we find that the scalar fundamental mode is modified from the third decimal for values of P in accordance with the most recent astrophysical constraints. We also show that qualitative differences arise for highly damped modes: on the one hand, a new crossing of the imaginary axis occurs for high values of a 0 and, on the other hand, increasing P produces a positive shift of the real part and an increase of the spacing in imaginary part between modes.

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Anomalous dimension and quasinormal modes of flavor branes

We study scalar quasinormal modes in a D3/D7 system holographically dual to a quantum field theory with chiral symmetry breaking at finite temperature. From the bottom-up approach, we consider a nontrivial dilaton profile which is responsible for the anomalous dimension of the quark condensate. It depends on a new parameter q in the model. By varying this parameter, we study the behavior of the massive and massless scalar quasinormal modes. The numerical method that we use is the spectral method, and we find that there is no pure imaginary mode for the massless case but it appears by increasing the parameter q. It is known that this mode becomes tachyonic for massive cases. Then we turn on a pseudoscalar field and using a simple ansatz study its effect on the quasinormal modes of the scalar field. By varying the parameter of the nontrivial dilaton profile in the model, we qualitatively study quasinormal modes in walking theories.

A relativistic scalar model for fractional interaction between dark matter and gravity

Abstract In a series of recent papers we put forward a “fractional gravity”&amp;#xD;framework striking an intermediate course between a modified gravity theory and an&amp;#xD;exotic dark matter (DM) scenario, which envisages the DM component in virialized&amp;#xD;halos to feel a non-local interaction mediated by gravity. The remarkable success&amp;#xD;of this model in reproducing several aspects of DM phenomenology motivates us to&amp;#xD;look for a general relativistic extension. Specifically, we propose a theory, dubbed&amp;#xD;Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stressenergy tensor couples to the scalar curvature via a non-local operator constructed with&amp;#xD;a fractional power of the d’Alembertian. We derive the field equations starting from&amp;#xD;an action principle, and then we investigate their weak field limit, demonstrating that&amp;#xD;in the Newtonian approximation the fractional gravity setup of our previous works is&amp;#xD;recovered. We compute the first-order post-Newtonian parameter γ and its relation&amp;#xD;with weak lensing, showing that although in RSFG the former deviates from its GR&amp;#xD;values of unity, the latter is unaffected. We also perform a standard scalar-vectortensor-decomposition of RSFG in the weak field limit, to highlight that gravitational&amp;#xD;waves propagate at the speed of light, though also an additional scalar mode becomes&amp;#xD;dynamical. Finally, we derive the modified conservation laws of the DM stress energy&amp;#xD;tensor in RSFG, showing that a new non-local force emerges, and hence that the DM&amp;#xD;fluid deviates from the geodesic solutions of the field equations.

CMB spectral distortions from enhanced primordial perturbations: the role of spectator axions

Primordial scalar and tensor modes can induce Cosmic Microwave Background spectral distortions during horizon re-entry. We investigate a specific mechanism proposed for this purpose, characterized by the coupling of an SU(2) gauge field to an axion undergoing a momentary stage of rapid evolution during inflation. Examining in details the perturbations produced by this model, we find that spectral distortions from the scalar modes significantly dominate those arising from the tensors. This holds true also for an earlier version of the model based on a U(1) gauge field. The scalar-induced distortions might be observed in future experiments, and the current COBE/FIRAS constraints already limit the parameter space of these models. Additionally, we find that delaying the onset of fast roll in the SU(2) scenario (to enhance the modes at the scales relevant for spectral distortions, while respecting the CMB constraints at larger scales) poses a greater challenge compared to the U(1) case. We propose a way to control the axion speed by varying the size of its coupling to the gauge fields.

Extremely small stars in scalar-tensor gravity: When stellar radius is less than Schwarzschild one

We show analytically that there exist compact stellar objects akin to neutron stars whose radius is smaller than the Schwarzschild radius defined by Arnowitt-Deser-Misner (ADM) mass. The radius of the compact object is defined by the radius where the energy density and the pressure of ordinary matter vanish, while clouds of scalar(s) can extend beyond this radius – a situation that is often encountered in modified gravity theories, like F(R) gravity and the scalar–Einstein–Gauss-Bonnet gravity. The clouds of scalar mode(s) give additional contributions to the ADM mass and as a result, the corresponding Schwarzschild radius given by the ADM mass can be larger than that of the compact object.

Constraints on quasinormal modes from black hole shadows in regular non-minimal Einstein Yang–Mills gravity

This work deals with scalar quasinormal modes using the higher-order WKB method and black hole shadow in non-minimal Einstein–Yang–Mills theory. To validate the results of quasinormal modes, time domain profiles are also investigated. We find that with an increase in the magnetic charge of the black hole, the ringdown gravitational wave increases non-linearly and the damping rate decreases non-linearly. The presence of a magnetic charge also results in a non-linear decrease in the black hole shadow. For large values of the coupling parameter, the black hole becomes a soliton solution and the corresponding ringdown gravitational wave frequency increases slowly with a decrease in the damping rate. For the soliton solutions, the shadow is also smaller. The constraints on the model parameters calculated using shadow observations of M87* and Sgr A* and an approximate analytical relation between quasinormal modes and shadows at the eikonal limit are discussed.

Adiabatic approach to the trans-Planckian problem in loop quantum cosmology

We study the scalar modes that, being observable today, were trans-Planckian before inflation, within the context of hybrid loop quantum cosmology (LQC). We analyze the dynamics of these highly ultraviolet modes by introducing modified dispersion relations to their equations of motion and discuss the impact that these relations would introduce in the power spectrum by computing the adiabaticity coefficient. More precisely, we consider two different models compatible with observations for the standard linear dispersion relation which are based on different initial conditions for the perturbations and background. One of these models avoids the issue altogether by generating less e-folds of inflation, so that the observable modes are never trans-Planckian, whereas the other suffers (arguably softly) from the trans-Planckian problem. This shows that the existence of the trans-Planckian problem in LQC is model dependent. Published by the American Physical Society 2024

Localization of scalar field on the brane-world by coupling with gravity

In this paper, we consider a coupling mechanism between the kinetic term and the gravity, in which a coupling function F (R) is introduced into the kinetic term of the five-dimensional scalar field. Based on this scenario, we investigate the localization of scalar fields in three specific braneworld models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane. The brane models considered here are regular with no singularity for scalar curvature. For the Minkowshi brane case, the zero mode can always be localized on the brane, and the massive modes can be localized or quasi-localized on the brane. For the dS4 brane case, two forms of factor F (R) is considered. The zero mode can always be localized, and the massive modes could be quasi-localized on the brane. Besides, with the second coupling factor, the scalar zero mode could be localized on the both sides of the origin of extra dimension, while the massive modes could be quasi-localized on the origin. Lastly, for the AdS4 brane case, the localization of the scalar zero mode requires the consideration of a coupling potential V (Φ, φ), while the massive modes can still be localized on the brane with an infinite number.

Charge superradiance on charged BTZ black holes

We study superradiant scattering for a charged scalar field subject to Robin (mixed) boundary conditions on a charged BTZ black hole background. Scalar field modes having a real frequency do not exhibit superradiant scattering, independent of the boundary conditions applied. For scalar field modes with a complex frequency, no superradiant scattering occurs if the black hole is static. After exploring some regions of the parameter space, we provide evidence for the existence of superradiantly scattered modes with complex frequencies for a charged and rotating BTZ black hole. Most of the superradiantly scattered modes we find satisfy Robin (mixed) boundary conditions, but there are also superradiantly scattered modes with complex frequencies satisfying Dirichlet and Neumann boundary conditions. We explore the effect of the black hole and scalar field charge on the outgoing energy flux of these superradiantly scattered modes, and also investigate their stability.

Exploring non-commutativity as a perturbation in the Schwarzschild black hole: quasinormal modes, scattering, and shadows

In this work, by a novel approach to studying the scattering of a Schwarzschild black hole, the non-commutativity is introduced as perturbation. We begin by reformulating the Klein–Gordon equation for the scalar field in a new form that takes into account the deformed non-commutative spacetime. Using this formulation, an effective potential for the scattering process is derived. To calculate the quasinormal modes, we employ the WKB method and also utilize fitting techniques to investigate the impact of non-commutativity on the scalar quasinormal modes. We thoroughly analyze the results obtained from these different methods. Moreover, the greybody factor and absorption cross section are investigated. Additionally, we explore the behavior of null geodesics in the presence of non-commutativity. Specifically, we examine the photonic, and shadow radius as well as the light trajectories for different non-commutative parameters. Therefore, by addressing these various aspects, we aim to provide a comprehensive understanding of the influence of non-commutativity on the scattering of a Schwarzschild-like black hole and its implications for the behavior of scalar fields and light trajectories.

Scalar radiation with a quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism, which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from general relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent nonlinearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well defined and under control. Moreover, our results confirm that despite being a nonlinear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behavior deep inside the Vainshtein region. Published by the American Physical Society 2024

Spatial covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Perturbation analysis* *Supported by the Natural Science Foundation of China (11975020)

We investigate a class of gravity theories respecting only spatial covariance, termed spatially covariant gravity, in the presence of an auxiliary scalar field. We examine the conditions on the Lagrangian required to eliminate scalar degrees of freedom, allowing only two tensorial degrees of freedom to propagate. Instead of strict constraint analysis, in this paper, we employ the perturbation method and focus on the necessary conditions to evade the scalar mode at the linear order in perturbations around a cosmological background. Beginning with a general action and solving the auxiliary perturbation variables in terms of a would-be dynamical scalar mode, we derive the condition to remove its kinetic term, thus ensuring that no scalar mode propagates. As an application of the general condition, we study a polynomial-type Lagrangian as a concrete example, in which all monomials are spatially covariant scalars containing two derivatives. We find that the auxiliary scalar field is essential, and new terms in the Lagrangian are allowed. Our analysis provides insights into constructing gravity theories with two degrees of freedom in the extended framework of spatially covariant gravity.

EFT corrections to scalar and vector quasinormal modes of rapidly rotating black holes

Quasinormal modes characterize the final stage of a black hole merger. In this regime, spacetime curvature is high, making these modes effective tools to probe potential corrections to general relativity. In this paper, we utilize the effective field theory framework to compute the leading-order correction to massless scalar and electromagnetic quasinormal modes. Proceeding perturbatively in the size of the effective field theory length scale, we describe a general method to compute the frequencies for Kerr black holes of any spin. In the electromagnetic case, we study both parity even and parity odd effective field theory corrections, and, surprisingly, prove that the two have the same spectrum. Furthermore, we find that, the corrected frequencies separate into two families, corresponding to the two polarizations of light. The corrections pertaining to each family are equal and opposite. Our results are validated through several consistency checks. Published by the American Physical Society 2024

Interaction of a quantum particle with gravitational wave in modified gravity theory

We present the formal solution for a quantum mechanical particle responding to gravitational wave (GW) in the framework of modified theories of gravity (MTG) where, apart from the two standard tensorial modes of polarization of GW, we have considered an additional scalar mode. The presence of this longitudinal scalar mode makes it necessary to extend the usual two-dimensional description of matter-GW interaction to a three-dimensional one. Naturally this requires non-trivial changes in the quantum mechanical treatment which we elaborate in this paper.