Taking the WKB approximation to solve the Dirac field equation in a Schwarzschild black hole spacetime, we can get the classical momenta. Employing the classical momenta and state density equation corrected by a modified dispersion relation, we will obtain the number of quantum states with energy less than $\omega$. Then, it is used to calculate the statistical-mechanical entropy of the Dirac field. Solving the integral for $r$ exactly, we obtain the leading term of entropy that is proportional to the event horizon area, and correction terms take the form of $A^{-1}$, but the logarithmic correction term by this approach is not given.

A classical thought-experiment to destroy black holes was envisaged by Wald in 1974: it consists of throwing particles with large angular momentum into an extremal black hole, checking whether their capture can overspin the black hole past the extremal limit and create a naked singularity. Wald showed that in the test-particle limit, particles that would be otherwise capable of producing naked singularities are simply scattered. Recently, Jacobson and Sotiriou showed that if one considers instead a black hole that is almost, but not exactly extremal, then in the absence of backreaction effects particle capture could indeed overspin the spacetime above the Kerr limit. Here we analyze backreaction effects and show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.

A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an event in spacetime can be fully described by emission coordinates: the proper emission time of each pulse measured at the event. The proper emission time of each pulse from four different pulsars—interpolated as necessary—provides the four spacetime coordinates of the reception event in the emission coordinate system. If more than four pulsars are available, the redundancy can improve the accuracy of the determination and/or resolve degeneracies resulting from special geometrical arrangements of the sources and the event. We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. Our approach uses a continuous solution of the eikonal equation describing the backward null cone from the event. The pulsar proper time at the instant the null cone intersects the pulsar world line is one of the four required coordinates. The process is complete (modulo degeneracies) when four pulsar world lines have been crossed by the light cone. The numerical method is applied in two different examples: measuring emission coordinates of an event in Minkowski spacetime, using pulses from four pulsars stationary in the spacetime; and measuring emission coordinates of an event in Schwarzschild spacetime, using pulses from four pulsars freely falling toward a static black hole. These numerical simulations are merely exploratory, but with improved resolution and computational resources the method can be applied to more pertinent problems. For instance one could measure the emission coordinates, and therefore the trajectory, of the Earth.

We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of $N$ scalar fields and the metric, for arbitrary bulk and boundary scalar potentials. In particular the effect of the energy-momentum tensor of the scalar fields on the geometry is fully taken into account, together with all the perturbations of the system. The equations are explicitly written as an eigenvalue problem, which can be readily solved to determine the stability of the system and obtain the properties of the fluctuations, such as masses and couplings. As an example, we study a dynamical soft-wall model with two bulk scalar fields used to model the hadron spectrum of QCD and the Higgs sector of electroweak physics. It is shown that there are no tachyonic modes, and that there is a (radion) mode whose mass is suppressed by a large logarithm compared to that of the other Kaluza-Klein modes.

We derive some basic equations related to the redshift drift, and we show how some dark energy (DE) properties can be retrieved from it. We consider, in particular, three kinds of DE models which exhibit a characteristic signature in their redshift drift while no such signature would be present in their luminosity-distances: a sudden change of the equation of state parameter $w_{\mathrm{DE}}$ at low redshifts, oscillating DE, and finally an equation of state with spikes at low redshifts. Accurate redshift-drift measurements would provide interesting complementary probes for some of these models and for models with varying gravitational coupling. While the redshift drift would efficiently constrain models with a spike at $z\sim 1$, the signature of the redshift drift for models with large variations at very low redshifts $z<0.1$ would be unobservable, allowing a large arbitrariness in the present expansion of the Universe.

To seek a deeper understanding of wave propagation on the Schwarzschild spacetime, we investigate the relationship between (i) the light cone of an event and its caustics (self-intersections), (ii) the large-$l$ asymptotics of quasinormal modes (QNMs), and (iii) the singular structure of the retarded Green function (GF) for the scalar field. First, we recall that the GF has a (partial) representation as a sum over QNMs. Next, we extend a recently developed expansion method to obtain asymptotic expressions for QNM wave functions and their residues. We employ these asymptotics to show (approximately) that the QNM sum is singular on the light cone, and to obtain approximations for the GF which are valid close to the light cone. These approximations confirm a little-known prediction: the singular part of the GF undergoes a transition each time the light cone passes through a caustic, following a repeating fourfold sequence. We conclude with a discussion of implications and extensions of this work.

We investigate here the particle acceleration and high energy collision in the Kerr geometry containing a naked singularity. We show that the center of mass energy of collision between two particles, dropped in from a finite but arbitrarily large distance along the axis of symmetry is arbitrarily large, provided the deviation of the angular momentum parameter from the mass is very small for the Kerr naked singularity. The collisions considered here are between particles, one of them ingoing and the other one being initially ingoing but which later emerges as an outgoing particle, after it suffers a reflection from a spatial region, which has a repulsive gravity in the vicinity of the naked singularity. High energy collisions take place around a region which marks a transition between the attractive and repulsive regimes of gravity. We make a critical comparison between our results and the BSW acceleration mechanism [M. Banados, J. Silk, and S. M. West, Phys. Rev. Lett. 103, 111102 (2009).] for extremal Kerr black holes, and argue that the scenario we give here has certain distinct advantages. If compact objects exist in nature with exterior Kerr superspinning geometry, then such high energy collisions would have a significant impact on the physical processes occurring in its surrounding and could possibly lead to their own observational signatures. As an aside, we also suggest a curious Gedanken collider physics experiment which could in principle be constructed in this geometry.

We consider supersymmetric shifted hybrid inflation models with a red-tilted scalar spectral index $n_s$ in agreement with the WMAP 7-yr central value. If nonminimal supergravity corrections are included, these models can also support a tensor-to-scalar ratio as large as $r\simeq 0.02$, which may be observable by the Planck Satellite. In contrast to the standard supersymmetric hybrid inflation scenario, topological defects produced via gauge symmetry breaking are inflated away in the shifted version of the theory.

We study the $k$-inflation models where the inflaton field has a noncanonical kinetic term. In particular, we consider the Dirac-Born-Infeld (DBI) form for the kinetic energy of the inflaton field. We consider quadratic and quartic potentials as well as the potential for the natural inflation. We use a modified version of MODECODE [M. J. Mortonson, H. V. Peiris, and R. Easther, Phys. Rev. D 83, 043505 (2011).] to calculate the power spectrum of the primordial perturbations generated by the inflaton field and subsequently use the WMAP7 results to constrain the models. Interestingly, with the DBI type kinetic term, less gravity waves are produced as one approaches scale invariance. This is true for all the potentials considered. Unlike the canonical case, this feature, in particular, helps the quartic ($\lambda {\varphi }^4$) potential with the DBI type kinetic term to be consistent with the WMAP data.

We show that, in constructions with additional intersecting D-branes, brane-antibrane inflation may naturally occur in a warm regime, such that strong dissipative effects damp the inflaton’s motion, greatly alleviating the associated $\eta$-problem. We illustrate this for D3-$\overline{\mathrm{D}3}$ inflation in flat space with additional flavor D7 branes, where for a Coulomb-like or quadratic hybrid potential a sufficient number of e-folds may be obtained for perturbative couplings and $\mathcal{O}(10–{10}^4)$ branes. This is in clear contrast with the corresponding cold scenarios, thus setting the stage for more realistic constructions within fully stabilized compactifications. Such models generically predict a negligible amount of tensor perturbations and non-Gaussianity $f_{NL}\sim \mathcal{O}(10)$.

We study asymptotically safe gravity with Einstein-Hilbert truncation taking into account the renormalization group running of both gravitational and cosmological constants. We show that the classical behavior of the theory is equivalent to a specific class of Jordan-Brans-Dicke theories with a vanishing Brans-Dicke parameter, and a potential determined by the renormalization group equation. The theory may be reformulated as an $f(R)$ theory. In the simplest cosmological scenario, we find large-field inflationary solutions near the Planck scale where the effective field theory description breaks down. Finally, we discuss the implications of a running gravitational constant to background dynamics via cosmological perturbation theory. We show that compatibility with general relativity requires that contributions from the running gravitational constant to the stress energy tensor are taken into account in the perturbation analysis.

We explore the possibility that the dark matter is a condensate of a very light vector boson. Such a condensate could be produced during inflation, provided the vector mass arises via the Stueckelberg mechanism. We derive bounds on the kinetic mixing of the dark matter boson with the photon, and point out several potential signatures of this model.

A fundamental limit to the sensitivity of optical interferometers is imposed by Brownian thermal fluctuations of the mirrors’ surfaces. This thermal noise can be reduced by using larger beams which “average out” the random fluctuations of the surfaces. It has been proposed previously that wider, higher-order Laguerre-Gaussian modes can be used to exploit this effect. In this paper, we show that susceptibility to spatial imperfections of the mirrors’ surfaces limits the effectiveness of this approach in interferometers used for gravitational-wave detection. Possible methods of reducing this susceptibility are also discussed.

The analytical expressions and the numerical values of the renormalization constants of dimension 3 static-light currents are given at one-loop order of perturbation theory in the framework of heavy quark effective theory and with an improved gauge action: the static quark is described by the HYP-smeared action and the light quark is of Wilson kind. This completes a work started a few years ago and is actually an intermediate step in the measurement of the decay constants $f_B$ and $f_{B_s}$ by the European Twisted Mass Collaboration (arXiv:1107.1441).

We study the potential of processes $pp\to p\gamma \gamma p\to pt\overline{t}p$ in scenarios of the Arkani-Hamed–Dimopoulos–Dvali and the Randall-Sundrum model at the LHC. We obtain 95% C.L. bounds on the model parameters. We show top quark spin asymmetry can be detected and discerned from the standard model with these extra dimensional models.

We present a detailed investigation to establish that lepton-number ($L$) violating supersymmetry (SUSY) can be effectively probed at the LHC in the practically background-free same-sign trilepton ($\mathrm{SS}3\ell$) and same-sign four-lepton ($\mathrm{SS}4\ell$) channels. With this in view, we extend our earlier analysis of $\mathrm{SS}3\ell$ and $\mathrm{SS}4\ell$ signals by considering situations based on minimal supergravity as well as a phenomenological SUSY model. We find that the $R$-parity violating scenario predicts large event rates, for both the 7 and 14 TeV runs. Furthermore, we show that it is extremely unlikely to ever achieve similar rates in $R$-parity conserving SUSY. In addition, we show how $\mathrm{SS}3\ell$ and $\mathrm{SS}4\ell$, in conjunction with the mixed-sign trilepton and four-lepton channels, can be used to extract dynamical information about the underlying SUSY theory, namely, the Majorana character of the decaying lightest neutralino and the nature of $L$-violating couplings. We define suitable variables and relationships between them which can be verified experimentally and which are largely independent of the SUSY production cross sections and the cascade decay branching fractions. These theoretical predictions are validated by Monte Carlo simulations including detector and background effects.

We calculate the Boer–Mulders effect contribution to the $\cos 2\varphi$ azimuthal asymmetry of unpolarized dilepton production near the $Z$-pole. Based on the tree-level expression in the transverse momentum dependent factorization framework, we show that the corresponding asymmetry near the $Z$-pole is negative, which is opposite to the asymmetry in the low $Q^2$ region, dominated by the production via a virtual photon. We calculate the asymmetry generated by the Boer–Mulders effect near the $Z$-pole at the Relativistic Heavy Ion Collider (RHIC), with $\sqrt{s}=500\mathrm{GeV}$. We find that the magnitude of the asymmetry is several percent, and therefore it is measurable. The experimental confirmation of this sign change of the asymmetry from the low $Q^2$ region to the $Z$-pole provides direct evidence of the chiral-odd structure of quarks inside an unpolarized nucleon.

We assess the importance of final state interactions in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$, stressing the consistency between two- and three-body interactions. The basic building block in the calculation is a $K\pi$ amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the $\kappa$ and the $K^{*}(1430)$, and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a resummation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector-weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.

Branching fractions of the decays $H_b\to H_c{\pi }^{-}{\pi }^{+}{\pi }^{-}$ relative to $H_b\to H_c{\pi }^{-}$ are presented, where $H_b$ ($H_c$) represents ${\overline{B}}^0$ ($D^{+}$), $B^{-}$ ($D^0$), ${\overline{B}}_s^0$ ($D_s^{+}$), and ${\Lambda }_b^0$ (${\Lambda }_c^{+}$). The measurements are performed with the LHCb detector using $35{\mathrm{pb}}^{-1}$ of data collected at $\sqrt{s}=7\mathrm{TeV}$. The ratios of branching fractions are measured to be $[\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})]/[\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-})]=2.38\pm 0.11\pm 0.21$, $[\mathcal{B}(B^{-}\to D^0{\pi }^{-}{\pi }^{+}{\pi }^{-})]/[\mathcal{B}(B^{-}\to D^0{\pi }^{-})]=1.27\pm 0.06\pm 0.11$, $[\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})]/[\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{\pi }^{-})]=2.01\pm 0.37\pm 0.20$, $[\mathcal{B}({\Lambda }_b^0\to {\Lambda }_c^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})]/[\mathcal{B}({\Lambda }_b^0\to {\Lambda }_c^{+}{\pi }^{-})]=1.43\pm 0.16\pm 0.13$ We also report measurements of partial decay rates of these decays to excited charm hadrons. These results are of comparable or higher precision than existing measurements.

A five-dimensional pure Yang-Mills theory, with the fifth coordinate compactified on the orbifold $S^1/Z_2$ of radius $R$, leads to a four-dimensional theory which is governed by two types of infinitesimal gauge transformations, namely, the well-known standard gauge transformations (SGT) dictated by the ${\mathrm{SU}}_4(N)$ group under which the zero Fourier modes $A_{\mu }^{(0)a}$ transform as gauge fields, and a set of nonstandard gauge transformations (NSGT) determining the gauge nature of the Kaluza-Klein (KK) excitations $A_{\mu }^{(m)a}$. By using a SGT-covariant gauge-fixing procedure for removing the degeneration associated with the NSGT, we integrate out the KK excitations and obtain a low-energy effective Lagrangian expansion involving all of the independent canonical-dimension-six operators that are invariant under the SGT of the ${\mathrm{SU}}_4(N)$ group and that are constituted by light gauge fields, $A_{\mu }^{(0)a}$, exclusively. It is shown that this effective Lagrangian is invariant under the SGT, but it depends on the gauge-fixing of the gauge KK excitations. Our result shows explicitly that the one-loop contributions of the KK excitations to light (standard) Green’s functions are renormalizable.