Odd-parity stability of black holes in Einstein-Aether gravity
Shinji Tsujikawa, Chao Zhang, Xiang Zhao, Anzhong Wang
备注：
Revtex4-1, no tables and figures. The analysis of stability against the inclined modes is added, and some typos are further corrected. Version to appear in Phys. Rev. D
In Einstein-Aether theory, we study the stability of black holes against odd-parity perturbations on a spherically symmetric and static background. For odd-parity modes, there are two dynamical degrees of freedom arising from the tensor gravitational sector and Aether vector field. We derive general conditions under which neither ghosts nor Laplacian instabilities are present for these dynamical fields. We apply these results to concrete black hole solutions known in the literature and show that some of those solutions can be excluded by the violation of stability conditions. The exact Schwarzschild solution present for $c_{13} = c_{14} = 0$, where $c_i$'s are the four coupling constants of the theory with $c_{ij}=c_i + c_j$, is prone to Laplacian instabilities along the angular direction throughout the horizon exterior. However, we find that the odd-parity instability of high radial and angular momentum modes is absent for black hole solutions with $c_{13} = c_4 = 0$ and $c_1 \geq 0$.
We develop a methodology for estimating parity-odd bispectra in the cosmic microwave background (CMB). This is achieved through the extension of the original separable modal methodology to parity-odd bispectrum domains ($\ell_1 + \ell_2 + \ell_3 = {\rm odd}$). Through numerical tests of the parity-odd modal decomposition with some theoretical bispectrum templates, we verify that the parity-odd modal methodology can successfully reproduce the CMB bispectrum, without numerical instabilities. We also present simulated non-Gaussian maps produced by modal-decomposed parity-odd bispectra, and show t…
Parity-odd non-Gaussianities create a variety of temperature bispectra in the cosmic microwave background (CMB), defined in the domain: $\ell_1 + \ell_2 + \ell_3 = {\rm odd}$. These models are yet unconstrained in the literature, that so far focused exclusively on the more common parity-even scenarios. In this work, we provide the first experimental constraints on parity-odd bispectrum signals in WMAP 9-year temperature data, using a separable modal parity-odd estimator. Comparing theoretical bispectrum templates to the observed bispectrum, we place constraints on the so-called nonlineality pa…
We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.
An analytical proof of the existence of negative modes in the odd--parity perturbation sector is given for all known non-abelian Einstein--Yang--Mills black holes. The significance of the normalizability condition in the functional stability analysis is emphasized. The role of the odd--parity negative modes in the sphaleron interpretation of the Bartnik--McKinnon solutions is discussed.
In scalar-vector-tensor theories with $U(1)$ gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity sta…
Twisted echoes of an odd quartet: Scalar-induced gravitational waves as a probe of primordial parity-violation
Università degli Studi di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Istituto Nazionale di Astrofisica (INAF), Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
Using a recently developed perturbation formalism based on curvature quantities, we investigate the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant. We show that those solutions which have no linear instabilities under odd- and even- parity spherically symmetric perturbations remain stable under odd-parity, linear, non-spherically symmetric perturbations.
We report the first operation of a rotating odd-parity Lorentz Invariance test in electrodynamics using a microwave Mach-Zehnder interferometer with permeable material in one arm. The experiment sets a direct bound to $ κ_{tr}$ of $-0.3\pm 3\times10^{-7}$. Using new power recycled waveguide interferometer techniques (with the highest spectral resolution ever achieved of $2\times10^{-11} rad/\sqrt{Hz}$) we show an improvement of several orders of magnitude is attainable in the future.
We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd- parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solu…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincaré gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian piece…
We discuss the problem of regularizing correlators in conformal field theories. The only way to do it in coordinate space is to interpret them as distributions. Unfortunately except for the simplest cases we do not have tabulated mathematical results. The way out we pursue here is to go to momentum space and use Feynman diagram techniques and their regularization methods. We focus on the energy-momentum tensor correlators and, to gain insight, we compute and regularize 2-point functions in 2d with various techniques both in coordinate space and in momentum space, obtaining the same results. Th…
We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian instability. In order for the black hole solutions to be stable, we study their generalized "Regge-Wheeler potential". It turns out that the problem is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon to prove the stability. We found that these conditions are similar to the no-ghost and Lapla…
We present the first experimental test of Lorentz invariance using the frequency difference between counter-propagating modes in an asymmetric odd-parity optical resonator. This type of test is $\sim10^{4}$ more sensitive to odd-parity and isotropic (scalar) violations of Lorentz invariance than equivalent conventional even-parity experiments due to the asymmetry of the optical resonator. The disadvantages of odd parity resonators have been negated by the use of counter-propagating modes, delivering a high level of immunity to environmental fluctuations. With a non-rotating experiment our resu…
It has been suggested that a naked singularity may be a good candidate for a strong gravitational wave burster. The naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study odd-parity mode of gravitational waves from a naked singularity of the Lema\^ıtre-Tolman-Bondi space-time. The wave equation for gravitational waves are solved by numerical integration using the single null coordinate. The result is that the naked singularity is not a strong source of the odd-parity gravitational radiation although the metric perturbation grows in the central region. Therefor…
We investigate the point-parity and mirror-parity handedness of the large angle anisotropy in the cosmic microwave background (CMB). In particular we consider whether the observed low CMB quadrupole could more generally signal odd point-parity, i.e. suppression of even multipoles. Even though this feature is ``visually'' present in most renditions of the WMAP dataset we find that it never supports parity preference beyond the meagre 95% confidence level. This is fortunate as point parity handedness implies almost certainly a high level of galactic contamination. Mirror reflection parity, on th…
The galaxy bispectrum contains a wealth of information about the early universe, gravity, as well as astrophysics such as galaxy bias. In this paper, we study the parity-odd part of the galaxy bispectrum which is hitherto unexplored. In the standard cosmological model, the odd-parity bispectrum is generated by galaxy velocities through redshift-space distortions. While small in the case of General Relativity coupled with smooth dark energy, the signal could be larger in modified gravity scenarios. Thus, apart from being a very useful consistency test of measurements of galaxy clustering, the o…
We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for the treatment in the ``close limit approximation'' of the collision of counterrotating black holes.
We derive a set of no-go theorems and yes-go examples for the parity-odd primordial trispectrum of curvature perturbations. We work at tree-level in the decoupling limit of the Effective Field Theory of Inflation and assume scale invariance and a Bunch-Davies vacuum. We show that the parity-odd scalar trispectrum vanishes in the presence of any number of scalar fields with arbitrary mass and any parity-odd scalar correlator vanishes in the presence of any number of spinning fields with massless de Sitter mode functions, in agreement with the findings of Liu, Tong, Wang and Xianyu [1]. The same…
The odd parity gravitational Quasi-Normal Mode spectrum of black holes with non-trivial scalar hair in Horndeski gravity is investigated. We study `almost' Schwarzschild black holes such that any modifications to the spacetime geometry (including the scalar field profile) are treated as small quantities. A modified Regge-Wheeler style equation for the odd parity gravitational degree of freedom is presented to quadratic order in the scalar hair and spacetime modifications, and a parameterisation of the modified Quasi-Normal Mode spectrum is calculated. In addition, statistical error estimates f…
We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.
We study Kerr black holes with synchronised non-trivial parity-odd massive scalar hair in four dimensional asymptotically flat space-time. These axially symmetric stationary spinning solutions of the minimally coupled Einstein-Klein-Gordon theory provide yet another example of bound states in synchronous rotation with the event horizon. We discuss the properties of these parity-odd hairy black holes and boson stars and exhibit their domain of existence. Considering the ergo-regions of these hairy black holes, we show that apart from the previously discussed ergo-sphere and ergo-Saturn, they su…
We undertake the construction of quadratic parity-violating terms involving the curvature in the four-dimensional metric-affine gravity. We demonstrate that there are only 12 linearly independent scalars, plus an additional one that can be removed by using the Pontryagin invariant. Several convenient bases for this sector are provided in both components and differential form notation. We also particularize our general findings to some constrained geometries like Weyl-Cartan and metric-compatible connections.
We consider the behaviour of odd-parity perturbations of those self-similar Lemaître-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretat…
The motion of a spherical dust cloud is described by the Lemaitre-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counter example to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the `nakedness' of this singularity against o…
Supported by the use of a regular scalar field we find a black hole solution in the Einstein-Gauss-Bonnet model. From the obtained solution we can recover the Schwarzschild black hole as in other works. Later, by implementing the odd parity perturbations method we study the stability of the linearized equations of motion of the model, we find the explicit form of the Regge-Wheeler potential and we explore the condition of vanishing perturbations at the horizon of the black hole. We test the stability of the obtained solution by checking the positivity condition of the Regge-Wheeler potential. …
The gravitational radiation generated by a particle in a close unbounded orbit around a neutron star is computed as a means to study the importance of the $w$ modes of the neutron star. For simplicity, attention is restricted to odd parity (``axial'') modes which do not couple to the neutron star's fluid modes. We find that for realistic neutron star models, particles in unbounded orbits only weakly excite the $w$ modes; we conjecture that this is also the case for astrophysically interesting sources of neutron star perturbations. We also find that for cases in which there is significant excit…
Recent theoretical work has shown that spin $1/2$ particles moving through unpolarized matter which sources torsion fields experience a new type of parity-even and time-reversal-odd optical potential if the matter is spinning in the lab frame. This new type of optical potential can be sought experimentally using the helicity dependence of the total cross sections for longitudinally polarized neutrons moving through a rotating cylindrical target. In combination with recent experimental constraints on short-range P--odd, T--even torsion interactions derived from polarized neutron spin rotation i…
