Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single complex kink condensates, multiple complex kinks condensates, and twisted kink crystal condensates in which both the amplitude and the phase of the order parameter modulate in space. Analyzing the gauge-invariant phase difference in the single complex kink condensates, we find the nonmonotonic behavior with respect to the current. We confirm that the multiple complex kinks condensates and the twisted kink crystal condensates are well described by the analytic solutions obtained from the Gross-Neveu model or the Nambu-Jona-Lasinio model. We also analyze the thermodynamic stability of the complex kink(s) condensates by computing the free energy. Our results imply that holographic superconductor model provides the boundary physics which is effectively represented by the Ginzburg-Landau theory with higher corrections.

We study non-Einstein Bach-flat gravitational instanton solutions that can be regarded as the generalization of the Taub-NUT/bolt and Eguchi-Hanson solutions of Einstein gravity to conformal gravity. These solutions include non-Einstein spaces which are either asymptotically locally flat spacetimes or asymptotically locally anti–de Sitter (AlAdS). Nevertheless, solutions with different asymptotic conditions exist: we find geometries that present a weakened AlAdS asymptotia, exhibiting the typical low decaying mode of conformal gravity. This permits us to identify the simple Neumann boundary condition that, as it happens in the asymptotically AdS sector, selects the Einstein solution out of the solutions of conformal gravity. All the geometries present nonvanishing Hirzebruch signature and Euler characteristic, being single-centered instantons. We compute the topological charges as well as the Noether charges of the Taub-NUT/bolt and Eguchi-Hanson spacetimes, which happen to be finite. This enables us to study the thermodynamic properties of these geometries.

We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in the directions tangential to the constant radial surfaces in the Bondi coordinates. The analysis is performed for general dimensions, and the difference between the four-dimensional cases and the higher-dimensional cases is stressed. In four dimensions, some assumptions are required to guarantee the null geodesics to reach future null infinity, in addition to the conditions of asymptotic flatness. Without these assumptions, gravitational waves may prevent photons from reaching null infinity. In higher dimensions, by contrast, such assumptions are not necessary, and gravitational waves do not affect the asymptotic behavior of null geodesics.

The detection of gravitational waves from extreme-mass-ratio inspirals with upcoming space-borne detectors will allow for unprecedented tests of general relativity in the strong-field regime. Aside from assessing whether black holes are unequivocally described by the Kerr metric, such detections may place constraints on the degree of spacetime symmetry. In particular, depending on exactly how a hypothetical departure from the Kerr metric manifests, the Carter symmetry, which implies the integrability of the geodesic equations, may be broken. Here, we examine the gravitational waveforms associated with nonintegrable extreme-mass-ratio inspirals involving a small-mass companion and a supermassive compact object of general relativity, namely the Manko-Novikov spacetime. We show that the waveforms display sudden frequency jumps when the companion transverses resonant islands. These findings demonstrate that such abrupt manifestations in the gravitational-wave frequencies are generic, have a genuine astrophysical origin, and function as a distinctive signature of chaotic phenomena in extreme-mass-ratio binaries.

We investigate gravitational lensing by a primary photon sphere which is a sphere filled with unstable circular light orbits, and by a secondary photon sphere on a wormhole throat in a black-bounce spacetime, which is suggested in [F. S. N. Lobo et al., Phys. Rev. D 103, 084052 (2021)] in strong deflection limits. There is an antiphoton sphere between the primary photon sphere and the secondary photon sphere. If a light source and an observer are on the same side of the wormhole throat, in addition to an infinite number of images slightly outside of both the primary and secondary photon spheres, an infinite number of images formed by light rays reflected by the potential barrier near the antiphoton sphere, slightly inside the primary photon sphere, might be observed.

We study correlation analysis for monopole components of stochastic gravitational wave backgrounds, including the maximally allowed polarization degrees. We show that, for typical detector networks, the correlation analysis can probe virtually five spectra: three for the intensities of the tensor, vector, and scalar modes and two for the chiral asymmetries of the tensor and vector modes. The chiral asymmetric signal for the vector modes has been left untouched so far. In this paper, we derive the overlap reduction function for this signal and thus complete the basic ingredients required for widely dealing with polarization degrees. We comprehensively analyze the geometrical properties of all the five overlap reduction functions. In particular, we point out the importance of reflection transformations for configuring preferable networks in the future.

We provide a reanalysis of the $5D$ Kaluza-Klein theory by implementing the polymer representation of the dynamics, both on a classical and a quantum level, in order to introduce in the model information about the existence of a cut off scale. We start by showing that, in the framework of semiclassical quantum mechanics, the $5D$ Bianchi I model admits a solution in which three space directions expand isotropically, while the remaining one is static, offering in this way a very valuable scenario to implement a Kaluza-Klein paradigm, identifying in such a static dimension the compactified one. We then analyze the behavior of geodesic motion in the context of the polymer representation, as referred to a $5D$ space-time with a static dimension. We demonstrate that such a revised formulation allows overcoming one of the puzzling questions of the standard Kaluza-Klein model corresponding to the limit of the charge to mass ratio for a particle, inapplicable to any fundamental one. Indeed, here, such a ratio can be naturally attributed to particles predicted by the Standard Model and no internal contradiction of the theory arises on this level. Finally, we study the morphology of the field equation associated with a charged scalar particle, i.e., we analyze a Klein-Gordon equation, whose fifth coordinate is viewed in the polymer representation. Here we obtain the surprising result that, although the Kaluza-Klein tower has a deformed structure characterized by irregular steps, the value predicted for the particle mass can be, in principle, set within the Standard Model mass distribution. Hence, the problem of the Planckian value of such mass, typical of the standard formulation, is now overcome. However, a problem with the charge to mass ratio still survives in this quantum field formulation.

We provide a prescription to compute the gravitational multipole moments of compact objects for asymptotically de Sitter spacetimes. Our prescription builds upon a recent definition of the gravitational multipole moments in terms of Noether charges associated to specific vector fields, within the residual harmonic gauge, dubbed multipole symmetries. We first derive the multipole symmetries for spacetimes which are asymptotically de Sitter; we also show that these symmetry vector fields eliminate the nonpropagating degrees of freedom from the linearized gravitational wave equation in a suitable gauge. We then apply our prescription to the Kerr-de Sitter black hole and compute its multipole structure. Our result recovers the Geroch-Hansen moments of the Kerr black hole in the limit of the vanishing cosmological constant.

In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical, and cosmological consequences. In particular, over a pseudo-Riemannian space-time base manifold, we define a fiber structure with two scalar fields. The resulting space is a 6-dimensional vector bundle endowed with a nonlinear connection. We provide the form of the geodesics and the Raychaudhuri and general field equations, both in the Palatini and metrical methods. When applied at a cosmological framework, this novel geometrical structure induces extra terms in the modified Friedmann equations, leading to the appearance of an effective dark energy sector, as well as of an interaction of the dark mater sector with the metric. We show that we can obtain the standard thermal history of the universe, with the sequence of matter and dark-energy epochs, and furthermore the effective dark-energy equation-of-state parameter can lie in the quintessence or phantom regimes, or exhibit the phantom-divide crossing.

We consider $f(R)$ gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential. When the scalar field backreacts to the metric we find (at large distances) scalarized Schwarzschild-AdS and Schwarzschild-AdS-like black hole solutions. At small distances, due to strong curvature effects and the scalar dynamics, we find a rich structure of scalarized black hole solutions. When the scalar field is nonminimally coupled to gravity we also find scalarized black hole solutions at small distances.

We consider the properties of a static axially symmetric wormhole described by an exact solution of Einstein’s field equations and investigate how we can distinguish such a hypothetical object from a black hole. To this aim, we explore the motion of test particles and photons in the equatorial plane of the wormhole’s space-time and compare it with the particle dynamics in the well-known space-times of Schwarzschild and Kerr black holes. We show that precise simultaneous measurement of test particle motion and photon motion may provide the means to distinguish the wormhole geometry from that of a black hole.

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll 1$ with rotation parameter $a$, the GB term is given by a term for Schwarzschild black hole, whereas the CS term takes a linear term of $a$. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. We use the ($2+1$)-dimensional hyperboloidal foliation method to show the tachyonic instability for slowly rotating black holes by considering the time evolution of a spherically symmetric scalar mode. A threshold (existence) curve is obtained from the constant scalar modes under time evolution, which means the boundary between stable and unstable black holes. It is found that the slowly rotating black holes turn out to be unstable against a spherically symmetric scalar-mode propagation for positive coupling $\alpha$. However, we could not find tachyonic instability and any $a$-bound for scalarization for negative coupling $\alpha$.

We reconsider the widely held view that the Mannheim–Kazanas (MK) vacuum solution for a static, spherically symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter. This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically symmetric representation of the galactic mass distribution. Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation performed in the conformally equivalent Schwarzschild–de-Sitter (SdS) metric, where the latter does not predict flat rotation curves. This difference arises since the mass of particles in CG must instead be generated dynamically through interaction with a scalar field. The energy-momentum of this required scalar field means that, in a general conformal frame from the equivalence class of CG solutions outside a static, spherically symmetric matter distribution, the spacetime is not given by the MK vacuum solution. A unique frame does exist, however, for which the metric retains the MK form, since the scalar field energy-momentum vanishes despite the field being nonzero and radially dependent. Nonetheless, we show that in both this MK frame and the Einstein frame, in which the scalar field is constant, massive particles follow timelike geodesics of the SdS metric, thereby resolving the apparent frame dependence of physical predictions and unambiguously yielding rotation curves with no flat region. Moreover, we show that attempts to model rising rotation curves by fitting the coefficient of the quadratic term in the SdS metric individually for each galaxy are also precluded, since the scalar field equation of motion introduces an additional constraint relative to the vacuum case, such that the coefficient of the quadratic term in the SdS metric is most naturally interpreted as proportional to a global cosmological constant. We also comment briefly on how our analysis resolves the long-standing uncertainty regarding gravitational lensing in the MK metric.

Rapid localization of gravitational-wave events is important for the success of the multimessenger observations. The forthcoming improvements and constructions of gravitational-wave detectors will enable detecting and localizing compact-binary coalescence events even before mergers, which is called early warning. The performance of early warning can be improved by considering modulation of gravitational wave signal amplitude due to the Earth’s rotation and the precession of a binary orbital plane caused by the misaligned spins of compact objects. In this paper, for the first time we estimate localization precision in the early warning quantitatively, taking into account an orbital precession. We find that a neutron star—black hole binary at $z=0.1$ can typically be localized to $100{\mathrm{deg}}^2$ and $10{\mathrm{deg}}^2$ at the time of 12–15 minutes and 50–300 seconds before merger, respectively, which cannot be achieved without the precession effect.

The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more efficient calculation of the multipole moments, applying methods introduced by Bäckdahl and Herberthson. For the nonvacuum electromagnetic case, our results for the octupole and higher moments differ from the results already published in the literature. The reason for this difference is that we correct an earlier unnoticed mistake in the power series solution of the Ernst equations. We also apply the presented method to directly calculate the multipole moments of a five-parameter charged magnetized generalization of the Kerr and Tomimatsu-Sato exact solutions.

We present a consistent way of coupling three-dimensional Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell-Chern-Simons gravity generically containing two massless spin-2 fields coupled with a massless Majorana fermion of spin $\frac{5}{2}$ whose novel underlying superalgebra is explicitly constructed. We then present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the Inönü-Wigner contraction procedure of precise combinations of the $\mathfrak{o}\mathfrak{s}\mathfrak{p}(1|4)$ and the $\mathfrak{s}\mathfrak{p}(4)$ algebras. This allows us to construct distinct types of hyper-Maxwell-Chern-Simons theories that extend to include generically interacting nonpropagating spin-4 fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.

We propose a novel probe of fundamental physics that involves the exploration of temporal correlations between the multi-frequency electromagnetic (EM) signal and the subthreshold GW signal or stochastic gravitational wave background (SGWB) originating from coalescing binaries. This method will be useful for the detection of EM counterparts associated with the subthreshold/SGWB signal. Exploiting the time delay between concomitant emission of the gravitational wave and EM signals enables inference of the redshifts of the contributing sources by studying the time delay dilation due to cosmological expansion, provided that the time-lag between the emission of gravitational wave signal and the EM signal acts like a standard clock. Measurement of the inevitable time-domain correlations between different frequencies of gravitational and EM waves, most notably in gamma-rays, will test several aspects of fundamental physics and gravitation theory, and enable a new pathway for current and future gravitational wave telescopes to study the universal nature of binary compact objects to high redshifts.

A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum ${\mathrm{\Delta }}_{\zeta }^2(k_{\mathrm{peak}})\sim \mathcal{O}({10}^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $\mathcal{O}({10}^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies $|f_{\mathrm{NL}}(k_{\mathrm{peak}},k_{\mathrm{peak}},k_{\mathrm{peak}})|\gtrsim {\mathrm{\Delta }}_{\zeta }^2(k_{\mathrm{peak}})/(23{\delta }_c^3)\sim \mathcal{O}({10}^{-2})$. Whether the PBH abundance is suppressed or enhanced depends on the $f_{\mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter $f_{\mathrm{NL}}(k_{\mathrm{peak}},k_{\mathrm{peak}},k_{\mathrm{peak}})\sim \mathcal{O}(1)$ takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array.

We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $\delta \tau$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic Sunyaev Zel’dvich effect can not. We measure this new observable using a Planck $y$-map as well as a map of optical-depth fluctuations that we reconstruct from Planck CMB temperature data. We use our measurements to derive a first CMB only upper limit on the temperature inside ionized bubbles, $T_{\mathrm{b}}\lesssim 7.0\times {10}^5\mathrm{K}$ ($2\sigma$). We also present future forecasts, assuming a fiducial model with characteristic reionization bubble size $R_{\mathrm{b}}=5\mathrm{Mpc}$ and $T_{\mathrm{b}}=5\times {10}^4\mathrm{K}$. The signal-to-noise ratio of the fiducial cross-correlation using a signal dominated $y$-map from the Probe of Inflation and Cosmic Origins (PICO) becomes $\simeq 7$ with CMB-S4 $\delta \tau$ and $\simeq 13$ with CMB-HD $\delta \tau$. For the fiducial model, we predict that the CMB-HD—PICO cross-correlation should achieve an accurate measurement of the reionization parameters; $T_{\mathrm{b}}\simeq {49800}_{-5100}^{+4500}\mathrm{K}$ and $R_{\mathrm{b}}\simeq {5.09}_{-0.79}^{+0.66}\mathrm{Mpc}$. Since the power spectrum of the electron density fluctuations is constrained by the $\delta \tau$ autospectrum, the temperature constraints should be only weakly model dependent on the details of the electron distributions and should be statistically representative of the temperature in ionized bubbles during reionization. This cross-correlation could, therefore, become an important observable for future CMB experiments.

Primordial gravitational waves (GWs) carry the imprints of the dynamics of the universe during its earliest stages. With a variety of GW detectors being proposed to operate over a wide range of frequencies, there is great expectation that observations of primordial GWs can provide us with an unprecedented window to the physics operating during inflation and reheating. In this work, we closely examine the effects of the regime of reheating on the spectrum of primordial GWs observed today. We consider a scenario wherein the phase of reheating is described by an averaged equation of state (EoS) parameter with an abrupt transition to radiation domination as well as a scenario wherein there is a gradual change in the effective EoS parameter to that of radiation due to the perturbative decay of the inflaton. We show that the perturbative decay of the inflaton leads to oscillations in the spectrum of GWs, which, if observed, can possibly help us decipher finer aspects of the reheating mechanism. We also examine the effects of a secondary phase of reheating arising due to a brief epoch driven possibly by an exotic, noncanonical, scalar field. Interestingly, we find that, for suitable values of the EoS parameter governing the secondary phase of reheating, the GWs can be of the strength as suggested by the recent NANOGrav observations. We conclude with a discussion of the wider implications of our analysis.