Although finding numerically the quasinormal modes of a nonrotating black hole is a well-studied question, the physics of the problem is often hidden behind complicated numerical procedures aimed at avoiding the direct solution of the spectral system in this case. In this article, we use the exact analytical solutions of the Regge-Wheeler equation and the Teukolsky radial equation, written in terms of confluent Heun functions. In both cases, we obtain the quasinormal modes numerically from spectral condition written in terms of the Heun functions. The frequencies are compared with ones already published by Andersson and other authors. A new method of studying the branch cuts in the solutions is presented—the epsilon method. In particular, we prove that the mode $n=8$ is not algebraically special and find its value with more than 6 firm figures of precision for the first time. The stability of that mode is explored using the $ϵ$ method, and the results show that this new method provides a natural way of studying the behavior of the modes around the branch cut points.

We study a seesaw-type extension of the standard model in which the symmetry group is enlarged by a global $U(1)$. We introduce adequate scalar and fermion representations which naturally explain the smallness of neutrino masses. With the addition of a viable scalar dark matter candidate, an original scenario of leptogenesis emerges. We solve the relevant set of Boltzmann equations and show how leptogenesis can be successfully implemented at the TeV scale. The constraints on the scalar mass spectrum are derived and the dark matter phenomenology is discussed.

We link the recently discovered black hole-qubit correspondence to the structure of extra dimensions. In particular we show that for toroidal compactifications of type IIB string theory simple qubit systems arise naturally from the geometrical data of the tori parametrized by the moduli. We also generalize the recently suggested idea of the attractor mechanism as a distillation procedure of GHZ-like entangled states on the event horizon, to moduli stabilization for flux attractors in F-theory compactifications on elliptically fibered Calabi-Yau four-folds. Finally using a simple example we show that the natural arena for qubits to show up is an embedded one within the realm of fermionic entanglement of quantum systems with indistinguishable constituents.

Photons may convert into axion-like particles and back in the magnetic field of various astrophysical objects, including active galaxies, clusters of galaxies, intergalactic space and the Milky Way. This is a potential explanation for the candidate neutral ultra-high energy ($E>{10}^{18}\mathrm{eV}$) particles from distant BL Lac type objects which probably have been observed by the High Resolution Fly’s Eye experiment. Axions of the same mass and coupling may explain also TeV photons detected from distant blazars.

In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the equations of motion. The first-order equations strongly simplify the study of linear stability, which is implemented on general grounds. They also lead to a direct investigation of twinlike theories, which is used to introduce a family of models that support the same defect structure, with the very same energy density and linear stability.

We construct Lifshitz field theories in $4+1$ dimensions which retain $3+1$-d Lorentz invariance and therefore ensure a unique limiting speed in the $3+1$-d world. Such a construction is potentially useful in developing field-theoretic ultraviolet completions of extra-dimensional field theories. The extra dimension $y$ is treated asymmetrically from the usual three spatial dimensions by introducing derivatives of order $2n$ with respect to $y$ in the action. We show that $\lambda {\varphi }^4$ theory becomes progressively less nonrenormalizable by power counting as $n$ is increased. This suggests that the nonlocal theory obtained in the $n\to \infty$ limit may be complete in the ultraviolet.

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-$\frac{1}{2}$ particle system characterized by a generic Hamiltonian is worked out in detail. It is shown that there exists, within the structure of quaternionic quantum mechanics, a canonical reduction to three spatial dimensions upon which standard quantum theory is retrieved. In this dimensional reduction, three of the five dynamical variables are shown to oscillate around a cylinder, thus behaving in a quasi-one-dimensional manner at large distances. An analogous mechanism is shown to exist in the case of octavic Hamiltonians, where the ambient physical space has nine dimensions. Possible experimental tests in search for the signature of extra dimensions at low energies are briefly discussed.

Chern-Simons (CS) modified gravity is an extension to general relativity (GR) in which the metric is coupled to a scalar field, resulting in modified Einstein field equations. In the dynamical theory, the scalar field is itself sourced by the Pontryagin density of the space-time. In this paper, the coupled system of equations for the metric and the scalar field is solved numerically for slowly rotating neutron stars described with realistic equations of state and for slowly rotating black holes. An analytic solution for a constant-density nonrelativistic object is also presented. It is shown that the black hole solution cannot be used to describe the exterior space-time of a star as was previously assumed. In addition, whereas previous analysis were limited to the small-coupling regime, this paper considers arbitrarily large coupling strengths. It is found that the CS modification leads to two effects on the gravitomagnetic sector of the metric: (i) Near the surface of a star or the horizon of a black hole, the magnitude of the gravitomagnetic potential is decreased and frame-dragging effects are reduced in comparison to GR. (ii) In the case of a star, the angular momentum $J$, as measured by distant observers, is enhanced in CS gravity as compared to standard GR. For a large coupling strength, the near-zone frame-dragging effects become significantly screened, whereas the far-zone enhancements saturate at a maximum value $\Delta J_{\max }\sim (M/R)J_{\mathrm{GR}}$. Using measurements of frame-dragging effects around the Earth by Gravity Probe B and the LAGEOS satellites, a weak but robust constraint is set to the characteristic CS length scale, ${\xi }^{1/4}\lesssim {10}^8\mathrm{km}$.

An inspiraling object of mass $\mu$ around a Kerr black hole of mass $M(\gg \mu )$ experiences a continuous transition near the innermost stable circular orbit from adiabatic inspiral to plunge into the horizon as gravitational radiation extracts its energy and angular momentum. We investigate the collision of such an object with a generic counterpart around a Kerr black hole. We find that the angular momentum of the object is fine-tuned through gravitational radiation and that the high-velocity collision of the object with a generic counterpart naturally occurs around a nearly maximally rotating black hole. We also find that the center-of-mass energy can be far beyond the Planck energy for dark matter particles colliding around a stellar mass black hole and as high as ${10}^{58}\mathrm{erg}$ for stellar mass compact objects colliding around a supermassive black hole, where the present transition formalism is well justified. Therefore, rapidly rotating black holes can accelerate objects inspiraling around them to energy high enough to be of great physical interest.

Primordial black holes (PBHs) that form from the collapse of density perturbations are more clustered than the underlying density field. In a previous paper, we showed the constraints that this has on the prospects of PBH dark matter. In this paper we examine another consequence of this clustering: the formation of bound systems of PBHs in the early universe. These would hypothetically be the earliest gravitationally collapsed structures, forming when the universe is still radiation dominated. Depending upon the size and occupation of the clusters, PBH merging occurs before they would have otherwise evaporated due to Hawking evaporation.

Einstein-matter theories in which hairy black-hole configurations have been found are studied. We prove that the nontrivial behavior of the hair must extend beyond the null circular orbit (the photonsphere) of the corresponding spacetime. We further conjecture that the region above the photonsphere contains at least 50% of the total hair’s mass. We support this conjecture with analytical and numerical results.

We study the cosmology of a generalized Galileon field $\varphi$ with five covariant Lagrangians in which $\varphi$ is replaced by general scalar functions $f_i(\varphi )$ ($i=1,\dots ,5$). For these theories, the equations of motion remain at second order in time derivatives. We constrain the forms of the functions $f_i(\varphi )$ from the requirement to possess de Sitter solutions responsible for dark energy. There are two possible choices for power-law functions $f_i(\varphi )$, depending on whether the coupling $F(\varphi )$ with the Ricci scalar $R$ is independent of $\varphi$ or depends on $\varphi$. The former corresponds to the covariant Galileon theory that respects the Galilean symmetry in the Minkowski space-time. For generalized Galileon theories we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar and tensor perturbations as well as the condition for the stability of de Sitter solutions. We also carry out a detailed analytic and numerical study for the cosmological dynamics in those theories.

A surprising exact result for the Einstein field equations is that if pressure-free matter is moving in a shear-free way, then it must be either expansion-free or rotation-free. It has been suggested this result is also true for any barotropic perfect fluid, but a proof has remained elusive. We consider the case of barotropic perfect-fluid solutions linearized about a Robertson-Walker geometry, and prove that the result remains true except for the case of a specific highly nonlinear equation of state. We argue that this equation of state is nonphysical, and hence the result is true in the linearized case for all physically realistic barotropic perfect fluids. This result, which is not true in Newtonian cosmology, demonstrates that the linearized solutions, believed to result in standard local Newtonian theory, do not always give the usual behavior of Newtonian solutions.

Recently it was shown that if the matter congruence of a general relativistic perfect fluid flow in an almost FLRW universe is shear-free, then it must be either expansion or rotation-free. Here we generalize this result for a general $f(R)$ theory of gravity and show there exist scenarios where this result can be avoided. This suggests that there are situations where linearized fourth-order gravity shares properties with Newtonian theory not valid in General Relativity.

Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and outcomes of particular experiments, according to a single probability formula. This provides complete unification of the eternally inflating multiverse and many worlds in quantum mechanics. In this paper, we elucidate how cosmological parameters can be calculated in this framework, and study the probability distribution for the value of the cosmological constant. We consider both positive and negative values, and find that the observed value is consistent with the calculated distribution at an order of magnitude level. In particular, in contrast to the case of earlier measure proposals, our framework prefers a positive cosmological constant over a negative one. These results depend only moderately on how we model galaxy formation and life evolution therein.

We study the possibility of late forming dark matter, where a scalar field, previously trapped in a metastable state by thermal or finite density effects, goes through a phase transition near the era matter-radiation equality and begins to oscillate about its true minimum. Such a theory is motivated generally if the dark energy is of a similar form, but has not yet made the transition to dark matter, and, in particular, arises automatically in recently considered theories of neutrino dark energy. If such a field comprises the present dark matter, the matter power spectrum typically shows a sharp break at small, presently nonlinear scales, below which power is highly suppressed and previously contained acoustic oscillations. If, instead, such a field forms a subdominant component of the total dark matter, such acoustic oscillations may imprint themselves in the linear regime.

It is shown that the extremal Reissner-Nordström black hole, the nonextremal one with multiple scattering particles, and the Schwarzschild black hole with radial head-on particles are stable under the collision of the particles near the horizon, if the backreaction effect and the effect generated by gravity of particles are involved. Moreover, the collision near Reissner-Nordström black holes with astrophysically typical mass can not generate the Planck-scale center-of-mass energy. However, the head-on collision near the typical primordial black hole could just occur at the Planck-energy scale.

We analyze the effects of the $s$-channel Higgs bosons exchange on the charginos-pair and neutralinos-pair production in proton-proton collision at the CERN Large Hadron Collider (LHC) in the following channels: $pp\to {\tilde{\chi }}^{+}{\tilde{\chi }}^{-}/{\tilde{\chi }}^0{\tilde{\chi }}^0+X$, within the minimal supersymmetric standard model (MSSM). Assuming the usual GUT relation between $M_1$ and $M_2$ at the weak scale, we found that substantial enhancement can be obtained through $s$-channel Higgs bosons exchange in the mixed regime where $M_2\sim |\mu |$ with moderate to large $\tan \beta$ at the resonance of the heavy Higgs bosons. By combining the phenomenological constraints on neutralinos and charginos, we may still find regions of parameter space where charginos-pair and neutralinos-pair production at the LHC from $b\overline{b}$ initial state can be large and observable at LHC. We also compute the full complete set of electroweak (EW) contributions to $pp\to gg\to {\tilde{\chi }}^{+}{\tilde{\chi }}^{-}/{\tilde{\chi }}^0{\tilde{\chi }}^0+X$ at the one-loop level in the general MSSM. The analytical computation of the complete tree-level amplitude for $b\overline{b}\to {\tilde{\chi }}^{+}{\tilde{\chi }}^{-}/{\tilde{\chi }}^0{\tilde{\chi }}^0+X$, including $s$-channel Higgs exchange, is given.

The recent excess observed by CDF in $B_s^0\to {\mu }^{+}{\mu }^{-}$ is interpreted in terms of a possible supersymmetric origin. An analysis is given of the parameter space of mSUGRA and nonuniversal SUGRA under the combined constraints from LHC-7 with $1.04{\mathrm{fb}}^{-1}$ of integrated luminosity, under the new XENON-100 limits on the neutralino-proton spin-independent cross section and under the CDF $B_s^0\to {\mu }^{+}{\mu }^{-}$ 90% C.L. limit reported to arise from an excess number of dimuon events. It is found that the predicted value of the branching ratio $B_s^0\to {\mu }^{+}{\mu }^{-}$ for mSUGRA parameter points consistent with all constraints contains the following set of next to lightest particles beyond the standard model: chargino, stau, stop or $CP$ odd (even) Higgs. The lower bounds of sparticles, including those from the LHC, XENON and CDF $B_s^0\to {\mu }^{+}{\mu }^{-}$ constraint, are exhibited and the shift in the allowed range of sparticle masses arising solely due to the extra constraint from the CDF result is given. It is pointed out that the two-sided CDF 90% C.L. limit puts upper bounds on sparticle masses. An analysis of possible signatures for early discovery at the LHC is carried out corresponding to the signal region in $B_s^0\to {\mu }^{+}{\mu }^{-}$. Implications of GUT-scale nonuniversalities in the gaugino and Higgs sectors are discussed.

We report a direct lattice calculation of the $K$ to $\pi \pi$ decay matrix elements for both the $\Delta I=1/2$ and $3/2$ amplitudes $A_0$ and $A_2$ on $2+1$ flavor, domain wall fermion, ${16}^3\times 32\times 16$ lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical $K\to \pi \pi$ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve $\mathrm{Re}(A_0)$ from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude $A_0$, a calculation central to understanding the $\Delta =1/2$ rule and testing the standard model of $CP$ violation in the kaon system.