In this paper, a minimal surface in q-deformed AdS5 × S5 with a cusp boundary is studied in detail. This minimal surface is dual to a cusped Wilson loop in dual field theory. We find that the area of the minimal surface has both logarithmic squared divergence and logarithmic divergence. The logarithmic squared divergence cannot be removed by either Legendre transformation or the usual geometric subtraction. We further make an analytic continuation to the Minkowski signature, taking the limit such that the two edges of the cusp become light-like, and extract the anomalous dimension from the coefficient of the logarithmic divergence. This anomalous dimension goes back smoothly to the results in the undeformed case when we take the limit that the deformation parameter goes to zero
Photon motion in a Michelson interferometer is re-analyzed in terms of both geometrical optics and wave optics. The classical paths of the photons in the background of a gravitational wave are derived from the Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of a gravitational wave are presented in a fiat-space approximation. Both methods show that even the envelope of the response of an interferometer depends on the frequency of a gravitational wave, but it is almost independent of the frequency of the mirror＇s vibrations.
In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bodendorfer et al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.
Recently, the LIGO Scientific Collaboration and Virgo Collaboration published the second observation of a gravitational wave, GW151226 [Phys. Rev. Lett. 116, 241103（2016）], from a binary black hole coalescence with initial masses about 14 M and 8 M. They claimed that the peak gravitational strain was reached at about 450 Hz, the inverse of which is longer than the average time a photon stays in the Fabry-Perot cavities in the two arms.In this case, the phase-difference of a photon in the two arms due to the propagation of a gravitational wave does not always increase as the photon stays in the cavities. It might even be cancelled to zero in extreme cases. When the propagation effect is taken into account, we find that the claimed signal GW151226 almost disappears.
The contraction method in different limits to obtain 22 different realizations of kinematical algebras isapplied to study the supersymmetric extension of AdS algebra and its contractions. It is shown that p2 h p＇, c2 and g＇ algebras, in addition to d_, p, n_, g and c algebras, have supersymmetric extension, while n-2, g2 and g＇2 algebras have no supersymmetric extension. The connections among the superalgebras are established.
Recently, the observations on the earth tide at Shiquanhe and Wushi were used to show that gravity propagates at the speed of light. Based on the brief review of general relativity and the Newtonian gravitational theory, we re-analyze the experiments and cannot reach the same conclusion from the observations.
