The integration over the Möbius variables leading to the Cachazo-He-Yuan double-color $n$-point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants ${\sigma }_r,{\sigma }_s,{\sigma }_t$, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the $n-3$ integrations is explained, each exposing one of the $n-3$ propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing Möbius constants at 0, 1, and $\infty$.

Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of the universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression has the advantages of being of quasilocal nature and independent of specific spacetime symmetries in order to be well defined. Therefore, we propose it as a definition for general quasilocal universal horizons. Using the new formalism, we show that there is no universal analog of cosmological horizons for Friedmann-Lemaître-Robertson-Walker models for any scale factor function, and we also state that quasilocal universal horizons are restricted to trapped regions of the spacetime. Using the evolution equation, we analyze the formation of universal horizons under a truncated Hořava-Lifshitz theory, in spherical symmetry, showing the existence of regions in parameter space where the universal horizon formation cannot be smooth from the center, under some physically reasonable assumptions. We conclude with our view on the next steps for the understanding of black holes in nonrelativistic gravity theories.

We present the separation of the Teukolsky master equation for the test field of arbitrary spin on the background of the rotating $C$-metric. We also summarize and simplify some known results about Debye potentials of these fields on type D background. The equation for the Debye potential is also separated. Solving for the Debye potential of the electromagnetic field we show that on the extremely rotating $C$-metric no magnetic field can penetrate through the outer black hole horizon—we thus recover the Meissner effect for the $C$-metric.

The gravitational coupling of a long-wavelength tidal field with small-scale density fluctuations leads to anisotropic distortions of the locally measured small-scale matter correlation function. Since the local correlation function is known to be statistically isotropic in the absence of such tidal interactions, the tidal distortions can be used to reconstruct the long-wavelength tidal field and large-scale density field in analogy with the cosmic microwave background lensing reconstruction. In this paper we present the theoretical framework of cosmic tidal reconstruction and test the reconstruction in numerical simulations. We find that the density field on large scales can be reconstructed with good accuracy and the cross-correlation coefficient between the reconstructed density field and the original density field is greater than 0.9 on large scales ($k\lesssim 0.1h/\mathrm{Mpc}$), with the filter scale $\sim 1.25\mathrm{Mpc}/h$. This is useful in the 21 cm intensity mapping survey, where the long-wavelength radial modes are lost due to a foreground subtraction process.

Dark energy equation of state $w(z)$ parametrizations with two parameters and given monotonicity are generically either convex or concave functions. This makes them suitable for fitting either freezing or thawing quintessence models but not both simultaneously. Fitting a data set based on a freezing model with an unsuitable (concave when increasing) $w(z)$ parametrization [like Chevallier-Polarski-Linder (CPL)] can lead to significant misleading features like crossing of the phantom divide line, incorrect $w(z=0)$, incorrect slope, etc., that are not present in the underlying cosmological model. To demonstrate this fact we generate scattered cosmological data at both the level of $w(z)$ and the luminosity distance $D_L(z)$ based on either thawing or freezing quintessence models and fit them using parametrizations of convex and of concave type. We then compare statistically significant features of the best fit $w(z)$ with actual features of the underlying model. We thus verify that the use of unsuitable parametrizations can lead to misleading conclusions. In order to avoid these problems it is important to either use both convex and concave parametrizations and select the one with the best ${\chi }^2$ or use principal component analysis thus splitting the redshift range into independent bins. In the latter case, however, significant information about the slope of $w(z)$ at high redshifts is lost. Finally, we propose a new family of parametrizations $w(z)=w_0+w_a(\frac{z}{1+z}{)}^n$ which generalizes the CPL and interpolates between thawing and freezing parametrizations as the parameter $n$ increases to values larger than 1.

The Schrödinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrödinger-Newton equation, and we show that it can be realized with existing technology.

We derive the photon propagator in light-shell gauge (LSG) $v_{\mu }{A}^{\mu }=0$, where $v^{\mu }={(1,\widehat{r})}^{\mu }$. This gauge is an important ingredient of the light-shell effective theory—an effective theory for describing high energy jet processes on a 2-dimensional spherical shell expanding at the speed of light around the point of the initial collision producing the jets. Since LSG is a noncovariant gauge, we cannot calculate the LSG propagator by using the standard procedure for covariant gauges. We therefore employ a new technique for computing the propagator, which we hope may be of relevance in other gauges as well.

In this paper we present a model of subcritical hybrid inflation with a Pati-Salam (PS) symmetry group. Both the inflaton and waterfall fields contribute to the necessary $e$-foldings of inflation, while only the waterfall field spontaneously breaks PS hence monopoles produced during inflation are diluted during the inflationary epoch. The model is able to produce a tensor-to-scalar ratio, $r<0.09$ consistent with the latest BICEP2/Keck and Planck data, as well as scalar density perturbations and spectral index, $n_s$, consistent with Planck data. For particular values of the parameters, we find $r=0.084$ and $n_s=0.0963$. The energy density during inflation is directly related to the PS breaking scale, $v_{\mathrm{PS}}$. The model also incorporates a ${\mathbb{Z}}_4^R$ symmetry which can resolve the $\mu$ problem and suppress dimension 5 operators for proton decay, leaving over an exact $R$ parity. Finally the model allows for a complete three-family extension with a $D_4$ family symmetry which reproduces low energy precision electroweak and LHC data.

Gauge mediation predicts 10 TeV or heavier squarks because such a heavy stop is required to explain the observed 125 GeV Higgs boson mass without a large trilinear soft mass term in the minimal supersymmetric standard model. Although such a high scale cannot be searched by the LHC directly, gauge mediation also predicts a hierarchy ${\mu }^2\ll B_{\mu }$ by a simple and naive solution of the $\mu$ problem. We point out that this simple and naive way of generating the $\mu$ ($B_{\mu }$) term works in the case of 10 TeV or heavier squarks with a slight breaking of a grand unified theory relation among messenger $B$-terms. Furthermore, the upper bound on the Higgsino mass is obtained from the observed Higgs boson mass, perturbativity of a relevant coupling, and a condition avoiding tachyonic sneutrinos and stop. It turns out that the light Higgsino of $\mathcal{O}(100)\mathrm{GeV}$ is a promising signal of gauge mediation.

Violations of $CPT$ invariance can induce neutrino-to-antineutrino transitions. We study this effect for solar neutrinos and use the upper bound on the solar neutrino-to-antineutrino transition probability from the KamLAND experiment to constrain $CPT$-symmetry-violating coefficients of the general Standard-Model Extension. The long propagation distance from the Sun to the Earth allows us to improve existing limits by factors ranging from about a thousand to ${10}^{11}$.

Recently, it was established in Einstein-Maxwell-Dilaton gravity that the Kovtun-Son-Starinets viscosity/entropy ratio associated with anti-de Sitter planar black holes can be viewed as the boundary dual to the generalized Smarr relation of the black holes in the bulk. In this paper, we establish this relation in Einstein gravity with general minimally coupled matter and also in theories with an additional nonminimally coupled scalar field. We consider two examples for explicit demonstrations.

Compton scattering of polarized radiation in a strong magnetic field is considered. The recipe for calculation of the scattering matrix elements, the differential and total cross sections based on quantum electrodynamic second-order perturbation theory is presented for the case of arbitrary initial and final Landau level, electron momentum along the field and photon momentum. Photon polarization and electron spin state are taken into account. The correct dependence of natural Landau level width on the electron spin state is taken into account in a general case of arbitrary initial photon momentum for the first time. A number of steps in the calculations were simplified analytically making the presented recipe easy to use. The redistribution functions over the photon energy, momentum and polarization states are presented and discussed. The paper generalizes already known results and offers a basis for the accurate calculation of radiation transfer in a strong $B$ field, for example, in strongly magnetized neutron stars.

We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.

We study charged scalar perturbations in the background of a regular magnetic black hole. In this case, the charged scalar perturbation does not result in superradiance. By using a careful time-domain analysis, we show that the charge of the scalar field can change the real part of the quasinormal frequency, but has little impact on the imaginary part of the quasinormal frequency and the behavior of the late-time tail. Therefore, the regular magnetic black hole may be stable under the perturbations of a charged scalar field at the linear level.

We study the holographic superconductor-normal metal-superconductor (SNS) Josephson junction in de Rham-Gabadadze-Tolley massive gravity. If the boundary theory is independent of spatial directions, i.e., if the chemical potential is homogeneous in spatial directions, we find that the graviton mass parameter will make it more difficult for the normal metal-superconductor phase transition to take place. In the holographic model of the Josephson junction, it is found that the maximal tunneling current will decrease according to the graviton mass parameter. Besides, the coherence length of the junction decreases as well with respect to the graviton mass parameter. If one interprets the graviton mass parameter as the effect of momentum dissipation in the boundary field theory, this indicates that the stronger the momentum dissipation is, the smaller the coherence length is.

Is cosmic censorship special to general relativity, or can it survive a violation of local Lorentz invariance? Recent studies have shown that singularities in Lorentz -violating Einstein-Aether (or Horava-Lifshitz) theories can lie behind a universal horizon in simple black hole spacetimes. Even infinitely fast signals cannot escape these universal horizons. We extend this result, for an incompressible aether, to $3+1\mathrm{d}$ dynamical or spinning spacetimes which possess inner Killing horizons, and show that a universal horizon always forms in between the outer and (would-be) inner horizons. This finding suggests a notion of cosmic censorship, given that geometry in these theories never evolves beyond the universal horizon (avoiding potentially singular inner Killing horizons). A surprising result is that there are 3 distinct possible stationary universal horizons for a spinning black hole, only one of which matches the dynamical spherical solution. This motivates dynamical studies of collapse in Einstein-Aether theories beyond spherical symmetry, which may reveal instabilities around the spherical solution.

For observers in curved spacetimes, elements of the dual space of the set of linearized Poincaré transformations from an observer’s tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an operational procedure by which observers can measure such quantities using only information about the spacetime curvature at their location. When applied by observers near spacelike or null infinity in stationary, vacuum, asymptotically flat spacetimes, there is a sense in which the procedure yields the well-defined linear and angular momenta of the spacetime. We also describe a general method by which observers can transport local linear and angular momenta from one point to another, which improves previous prescriptions. This transport is not path independent in general, but becomes path independent for the measured momenta in the same limiting regime. The transport prescription is defined in terms of differential equations, but it can also be interpreted as parallel transport in a particular direct-sum vector bundle. Using the curvature of the connection on this bundle, we compute and discuss the holonomy of the transport law. We anticipate that these measurement and transport definitions may ultimately prove useful for clarifying the physical interpretation of the Bondi-Metzner-Sachs charges of asymptotically flat spacetimes.

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of nonspinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr–de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for “static observers,” a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon’s equations are clarified.

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension $D=9$, which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet, and third-order Lovelock theories. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

We study the shadows cast by the different types of rotating regular black holes viz. Ayón-Beato-García (ABG), Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$). Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically, and the distortion parameter increases when the values of these parameters increase. A comparison with the standard Kerr case is also investigated. We have also studied the influence of the plasma environment around regular black holes to discuss its shadow. The presence of the plasma affects the apparent size of the regular black hole’s shadow to be increased due to two effects: (i) gravitational redshift of the photons and (ii) radial dependence of plasma density.