The electro-optic modulators (EOM) are devices designed to modulate a laser beam. Depending on the configuration adopted by the EOM, they can be used to change the polarization state, to modulate the phase or the amplitude of the laser [1]. It is also possible to simultaneously modulate the amplitude and phase of the beam [2]. The EOM have multiple applications, for example frequency modulation spectroscopy [3, 4], modulation transfer spectroscopy [5, 6], two tone frequency modulation spectroscopy [7, 8], laser frequency stabilization and cavity length locking [9, 10]. Specifically, the EOM are used in the Laser Interferometer Gravitational-Wave Observatory (LIGO) where they play an important role. These observatories, which have recently achieved the first direct observation of gravitational waves emitted by black hole coalescence, are capable of detecting perturbations of the space time on the order of 10 m. For these outstanding observations LIGO has recently received the 2017 Nobel Prize in Physics. To achieve these sensitivity levels it is necessary to accurately control the length of the two Fabry-Perot cavities, (each cavity 4 Km in length) so that they are always in optical resonance. The length control system is done via a variation of the Pound-Drever-Hall technique to generate sidebands in the laser beams that go to the cavities. The sidebands are generated by EOM that produce a phase modulation in the laser beam [11]. To achieve phase modulation, the index of refraction of the crystal used in the EOM is modulated by periodic, slowly varying external electric field. This external field is perpendicular to the direction of the laser wave and both are aligned with the principal axis of the crystal. However, besides the required phase modulation, the experimental setup of the EOM also produced an unwanted modulation in the amplitude of the transmitted wave. This residual amplitude modulation (RAM) can be regarded as noise added to the laser beam. Depending on the spurious change in intensity, there is evidence that this could affect the calibration of the Fabry-Perot cavities [12]. This is important for future observations of Advanced LIGO when searching for much weaker sources of gravitational radiation like coalescence of neutrons stars. The RAM was attributed to deficiencies in the phase modulation process. According to several authors, there are many sources that could contribute to RAM:

The residual amplitude modulation (RAM) is a spurious effect of the phase modulation in the laser beam power. In this work we show that the optical modulators that are used to generate the sidebands on the laser beam generate a RAM that should be regarded as a fundamental level of noise in the optical setup.

The residual amplitude modulation ($\mathrm{RAM}$) is the undesired, non-zero amplitude modulation that usually occurs when a phase modulation based on the electro-optic effect is imprinted on a laser beam. In this work, we show that electro-optic modulators (EOMs) that are used to generate the sidebands on the laser beam also generate a $\mathrm{RAM}$ in the optical setup. This result contradicts standard textbooks, which assume the amplitude remains unchanged in the process and should be considered as a fundamental $\mathrm{RAM}$ ($\mathrm{RAM_{F}}$) for these devices. We present a classical model for the propagation of an infrared laser with frequency $\omega_{0}$ in a wedge-shaped crystal and an EOM with an RF modulating signal of frequency $\Omega$. Since ${\Omega}\ll \omega_{0}$, we solve Maxwell's equations in a time-varying media via a WKB approximation and we write the electromagnetic fields in terms of quasi-plane waves. From the emerging fields of the setup, we compute the associated $\mathrm{RAM_{F}}$ and show that it depends on the phase-modulation depth $m$ and the quotient $\left(\frac{\Omega}{\omega_{0}}\right)$. The $\mathrm{RAM_{F}}$ values obtained for the EOMs used in gravitational wave detectors are presented. Finally, the cancellation of $\mathrm{RAM_{F}}$ is analyzed.

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditions on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as, the Gauss-Bonnet versions of the BonnorVaidya(de Sitter/anti-de Sitter) solution, a global monopole and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditions on the energymomentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.

Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the inclusion of the 1/R curvature terms in the gravitational action and the use of the Palatini formalism offer an alternative explanation for cosmological acceleration. In this work we show not only that this model of Vollick does not have a good Newtonian limit, but also that any f(R) theory with a pole of order n in R=0 and its second derivative respect to R evaluated at Ro is not zero, where Ro is the scalar curvature of background, does not have a good Newtonian limit.

Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.

We study the collision of two slowly rotating, initially nonboosted, black holes in the close limit. A "punctures" modification of the Bowen-York method is used to construct conformally flat initial data appropriate to the problem. We keep only the lowest nontrivial orders capable of giving rise to radiation of both gravitational energy and angular momentum. We show that even with these simplifications, an extension to higher orders of the linear Regge-Wheeler-Zerilli black hole perturbation theory is required to deal with the evolution equations of the leading contributing multipoles. This extension is derived, together with appropriate extensions of the Regge-Wheeler and Zerilli equations. The data are numerically evolved using these equations to obtain the asymptotic gravitational waveforms and amplitudes. Expressions for the radiated gravitational energy and angular momentum are derived and used together with the results of the numerical evolution to provide quantitative expressions for the relative contribution of different terms, and their significance is analyzed.

We reconsider here the model where large quantum gravity effects were first found, but now in its Null Surface Formulation (NSF). We find that although the set of coherent states for $Z$, the basic variable of NSF, is as restricted as it is the one for the metric, while some type of small deviations from these states may cause huge fluctuations on the metric, the corresponding fluctuations on $Z$ remain small.

Using the continuity of the scalar $Ψ_2$ (the mass aspect) at null infinity through $i_o$ we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of $Ψ_2$ at $i_o$ plays the role of the base space. We also show that the restriction of the available symplectic form to each ``fiber'' is degenerate. By finding the orbit manifold of this degenerate direction we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a Hilbert space can be constructed on each ``fiber'' if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the Hilbert spaces of different foliations they define superselection sectors on the space of asymptotic quantum states.

Using the continuity of the scalar (the mass aspect) at null infinity through , we show that the space of radiative solutions of general relativity can be foliated by identifying each leaf with the value of at . We then show that each non-trivial leaf has a natural intrinsic symplectic form which, given the available geometric structure, does not admit a unique extension to the full solution space. A Hilbert space structure is then constructed for every point on each leaf. Since there is no natural correspondence between the Hilbert spaces of different leaves, they define superselection sectors on the space of asymptotic quantum states.