General Relativity And Quantum Cosmology

The influence of the medium on the gravitational deflection of light rays is widely discussed in literature for the simplest non-trivial case: cold non-magnetized plasma. In this article, we generalize these studies to the case of an arbitrary transparent dispersive medium with a given refractive index. We calculate the deflection angle of light ray moving in a general spherically symmetric metric in the presence of medium with the spherically symmetric refractive index. The equation for the radius of circular light orbits is also derived. We discuss in detail the properties of these results and various special cases. In particular, we show that multiplying the refractive index by a constant does not affect the deflection angle and radius of circular orbits. At the same time, the presence of dispersion makes the trajectories different from the case of vacuum even in spatially homogeneous medium. As one of the applications of our results, we calculate the correction to the angle of vacuum gravitational deflection for the case when a massive object is surrounded by homogeneous but dispersive medium. As another application, we present the calculation of the shadow of a black hole surrounded by medium with arbitrary refractive index. Our results can serve as a basis for studies of various plasma models beyond the cold plasma case.

Aims. We estimate the number of pulsars, detectable as continuous gravitational wave sources with the current and future gravitational-wave detectors, assuming a simple phenomenological model of evolving non-axisymmetry of the rotating neutron star. Methods. We employ a numerical model of the Galactic neutron star population, with the properties established by comparison with radio observations of isolated Galactic pulsars. We generate an arbitrarily large synthetic population of neutron stars and evolve their period, magnetic field, and position in space. We use a gravitational wave emission model based on exponentially decaying ellipticity - a non-axisymmetry of the star, with no assumption of the origin of a given ellipticity. We calculate the expected signal in a given detector for a 1 year observations and assume a detection criterion of the signal-to-noise ratio of 11.4 - comparable to a targeted continous wave search. We analyze the population detectable separately in each detector: Advanced LIGO, Advanced Virgo, and the planned Einstein Telescope. In the calculation of the expected signal we neglect signals frequency change due to the source spindown and the Earth motion with respect to the Solar barycentre. Results. With conservative values for the neutron stars evolution: supernova rate once per 100 years, initial ellipticity ϵ 0 = 1e-5 with no decay of the ellipticity η = t hub = 1e4 Myr, the expected number of detected neutron stars is below one: 0.15 (based on a simulation of 10 M stars) for the Advanced LIGO detector. A broader study of the parameter space ( ϵ 0 , η ) is presented. With the planned sensitivity for the Einstein Telescope, and assuming the same ellipiticity model, the expected detection number is: 26.4 pulsars during a 1-year long observing run.

We examine a quantised massive scalar field in (1+1) -dimensional spatially compact cosmological spacetimes in which the early time and late time expansion laws provide distinguished definitions of Fock "in" and "out" vacua, with the possible exception of the spatially constant sector, which may become effectively massless at early or late times. We show, generalising the work of Ford and Pathinayake, that when such a massive zero mode occurs, the freedom in the respective "in" and "out" states is a family with two real parameters. As an application, we consider massive untwisted and twisted scalar fields in the (1+1) -dimensional spatially compact Milne spacetime, where the untwisted field has a massive "in" zero mode. We demonstrate, by a combination of analytic and numerical methods, that the choice of the massive "in" zero mode state has a significant effect on the response of an inertial Unruh-DeWitt detector, especially in the excitation part of the spectrum. The detector's peculiar velocity with respect to comoving cosmological observers has the strongest effect in the "in" vacuum of the untwisted field, where it shifts the excitation and de-excitation resonances towards higher values of the detector's energy gap.

An interesting proposal for detecting gravitational waves involves quantum metrology of Bose-Einstein condensates (BECs). We consider a forced modulation of the BEC trap, whose frequency matches that of an incoming continuous gravitational wave. The trap modulation induces parametric resonance in the BEC, which in turn enhances sensitivity of the BEC to gravitational waves. We find that such a BEC detector could potentially be used to detect gravitational waves across several orders of magnitude in frequency, with the sensitivity depending on the speed of sound, size of the condensate, and frequency of the phonons. We outline a possible BEC experiment and discuss the current technological limitations. We also comment on the potential noise sources as well as what is necessary for such a detector to become feasible.

General Relativity predicts only two tensor polarization modes for gravitational waves while at most six possible polarization modes of gravitational waves are allowed in the general metric theory of gravity. The number of polarization modes is totally determined by the specific modified theory of gravity. Therefore, the determination of polarization modes can be used to test gravitational theory. We introduce a concrete data analysis pipeline for a single space-based detector such as LISA to detect the polarization modes of gravitational waves. Apart from being able to detect mixtures of tensor and extra polarization modes, this method also has the added advantage that no waveform model is needed and monochromatic gravitational waves emitted from any compact binary system with known sky position and frequency can be used. We apply the data analysis pipeline to the reference source J0806.3+1527 of TianQin with 90-days' simulation data, and we show that α viewed as an indicative of the intrinsic strength of the extra polarization component relative to the tensor modes can be limited below 0.5 for LISA and below 0.2 for Taiji. We investigate the possibility to detect the nontensorial polarization modes with the combined network of LISA, TianQin and Taiji and find that α can be limited below 0.2.

We continue our study of the optical properties of the solar gravitational lens (SGL). Taking the next step beyond representing it as an idealized monopole, we now characterize the gravitational field of the Sun using an infinite series of multipole moments. We consider the propagation of electromagnetic (EM) waves in this gravitational field within the first post-Newtonian approximation of the general theory of relativity. The problem is formulated within the Mie diffraction theory. We solve Maxwell's equations for the EM wave propagating in the background of a static gravitational field of an extended gravitating body, while accounting for multipole contributions. Using a wave-theoretical approach and the eikonal approximation, we find an exact closed form solution for the Debye potentials and determine the EM field at an image plane in the strong interference region of the lens. The resulting EM field is characterized by a new diffraction integral. We study this solution and show how the presence of multipoles affects the optical properties of the lens, resulting in distinct diffraction patterns. We identify the gravitational deflection angle with the individual contributions due to each of the multipoles. Treating the Sun as an extended, axisymmetric, rotating body, we show that each zonal harmonics causes light to diffract into an area whose boundary is a caustic of a particular shape. The appearance of the caustics modifies the point-spread function (PSF) of the lens, thus affecting its optical properties. The new wave-theoretical solution allows the study gravitational lensing by a realistic lens that possesses an arbitrary number of gravitational multipoles. This {\em angular eikonal method} represents an improved treatment of realistic gravitational lensing. It may be used for a wave-optical description of many astrophysical lenses.

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a group of isometries of dimension r acting on s-dimensional orbits are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic and they offer an IDEAL labeling that improves previously known invariant studies.

The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the conformal version, namely the wrong continuity equation, indefiniteness of the quantum mass, and wrong description of massless particles in the singularity resolution argument, by using appropriate disformal transformations.

We have computed the properties of compact objects like neutron stars based on equation of state (EOS) deduced from a core-envelope model of superdense stars. Such superdense stars have been studied by solving the Einstein's equation based on pseudo-spheroidal and spherically symmetric space-time geometry. The computed star properties are compared with those obtained based on nuclear matter equations of state. From the mass-radius ( M?�R ) relationship obtained here, we are able to classify compact stars in three categories: (i) highly compact self -bound stars that represents exotic matter compositions with radius lying below 9 km (ii) normal neutron stars with radius between 9 to 12 km and (iii) soft matter neutron stars having radius lying between 12 to 20 km. Other properties such as Keplerian frequency, surface gravity and surface gravitational redshift are also computed for all the three types. The present work would be useful for the study of highly compact neutron like stars having exotic matter compositions.

We study the thermodynamics and dynamics of high-dimensional Einstein-power-Yang-Mills black holes in conformal gravity. Specifically, we investigate a class of conformally related black holes whose metrics differ by a scale factor. We show that a suitable scale factor cures the geodesic incompleteness and the divergence of Kretschmann scalars at the center of black holes. In the aspect of thermodynamics, we analyse the Hawking temperature, the entropy, and the specific heat, and verify the existence of second-order phase transitions. We find that the thermodynamics of this class of conformally related black holes is independent of scale factors. In the aspect of dynamics, we find that the quasinormal modes of minimally coupled scalar field perturbations are dependent on scale factors. Quite interesting is that the behavior of quasinormal mode frequencies also supports the independence of scale factors for the second-order phase transitions. Our results show that the scale factors produce distinct thermodynamic and dynamic effects in the conformally related Einstein-power-Yang-Mills black holes, which provides an interesting connection between thermodynamics and dynamics of black holes in conformal gravity.