General Relativity And Quantum Cosmology

We test the Grumiller's quantum motivated modified gravity model, which at large distances modifies the Newtonian potential and describes the galactic rotation curves of disk galaxies in terms of a Rindler acceleration term without the need of any dark matter, against the baryonic Tully-Fisher feature that relates the total baryonic mass of a galaxy with flat rotation velocity of the galaxy. We estimate the Rindler acceleration parameter from observed baryonic mass versus rotation velocity data of a sample of sixty galaxies. Grumiller's model is found to describe the observed data reasonably well.

The observation of gravitational waves from LIGO and Virgo detectors inferred the mergers rates to be 23.9 +14.9 ??.6 Gpc ?? yr ?? for binary black holes and 320 +490 ??40 Gpc ?? yr ?? for binary neutron stars. These rates suggest that there is a significant chance that two or more of these signals will overlap with each other during their lifetime in the sensitivity-band of future gravitational-wave detectors such as the Cosmic Explorer and Einstein Telescope. The detection pipelines provide the coalescence time of each signal with an accuracy O(10ms) . We show that using the information of the coalescence time, it is possible to correctly infer the properties of these "overlapping signals" with the current data-analysis infrastructure. Studying different configurations of the signals, we conclude that the inference is robust provided that the two signals are not coalescing within less than ????s . Signals whose coalescence epochs lie within ??.5s of each other suffer from significant biases in parameter inference, and new strategies and algorithms are required to overcome such biases.

We investigate the quantum cosmologies of the Bianchi IX and VIII models when a cosmological constant, aligned electromagnetic field and free scalar field are present. The conserved quantity p ? associated with our free scalar field results in ? classically being a quantity which monotonically increases with respect to time, thus allowing it to fulfill the role of an 'emergent' internal clock for our constrained quantum systems. We embark on this investigation to better understand how matter sources can affect general anisotropic quantum cosmologies. To aid us we use the Euclidean-signature semi classical method to obtain our wave functions and analyze them. In addition we study briefly the quantum Taub models when an e ? potential and aligned electromagnetic field are present. One of the interesting things we found was that our aligned electromagnetic field, depending on how strong it is, can create or destroy geometric states in our 'excited' state wave functions that quantum Bianchi IX universes can tunnel in and out of. This creation of a state is somewhat similar to how non-commutativity in the minisuperspace variables can cause new quantum states to emerge in the quantum Kantowski-Sachs and Bianchi I models. Our results further show the utility of the Euclidean-signature semi classical method towards tackling Lorentzian signature problems without having to invoke a Wick rotation. This feature of not needing to apply a Wick rotation makes this method potentially very useful for tackling a variety of problems in bosonic relativistic field theory and quantum gravity.

In the past few years, the detection of gravitational waves from compact binary coalescences with the Advanced LIGO and Advanced Virgo detectors has become routine. Future observatories will detect even larger numbers of gravitational-wave signals, which will also spend a longer time in the detectors' sensitive band. This will eventually lead to overlapping signals, especially in the case of Einstein Telescope (ET) and Cosmic Explorer (CE). Using realistic distributions for the merger rate as a function of redshift as well as for component masses in binary neutron star and binary black hole coalescences, we map out how often signal overlaps of various types will occur in an ET-CE network over the course of a year. We find that a binary neutron star signal will typically have tens of overlapping binary black hole and binary neutron star signals. Moreover, it will happen up to tens of thousands of times per year that two signals will have their end times within seconds of each other. In order to understand to what extent this would lead to measurement biases with current parameter estimation methodology, we perform injection studies with overlapping signals from binary black hole and/or binary neutron star coalescences. Varying the signal-to-noise ratios, the durations of overlap, and the kinds of overlapping signals, we find that in most scenarios the intrinsic parameters can be recovered with negligible bias. However, biases do occur for a short binary black hole or a quieter binary neutron star signal overlapping with a long and louder binary neutron star event when the merger times are sufficiently close. Hence our studies show where improvements are required to ensure reliable estimation of source parameters for all detected compact binary signals as we go from second-generation to third-generation detectors.

Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einsteins Field equations for vacuum, yields the Schwarzschild Metric as the unique solution, which essentially is the statement of the well known Birkhoffs Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian space-times provide more isometries than expected from the original metric holonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis to analyze the Einsteins Vacuum Field Equations so as to obtain the Symmetry Generators of the corresponding Differential Equation. Additionally, applying the Noether Point Symmetry method we have obtained the conserved quantities corresponding to the generators of the Schwarzschild Lagrangian and paving way to reformulate the Birkhoffs Theorem from a different approach.

Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, casting them in a unified notation. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theory's foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and post-adiabatic evolution and waveform-generation schemes. Our presentation includes some new results but is intended primarily as a reference for practitioners.

We investigate the gravitational perturbations of the Schwarzschild black hole in the nonlocal gravity model recently proposed by Deser and Woodard (DW-II). The analysis is performed in the localized version in which the nonlocal corrections are represented by some auxiliary scalar fields. We find that the nonlocal corrections do not affect the axial gravitational perturbations, and hence the axial modes are completely identical to those in General Relativity (GR). However, the polar modes get different from their GR counterparts when the scalar fields are excited at the background level. In such a case the polar modes are sourced by an additional massless scalar mode and, as a result, the isospectrality between the axial and the polar modes breaks down. We also perform a similar analysis for the predecessor of this model (DW-I) and arrive at the same conclusion for it.

We study the black hole's shadow for Schwarzschild - de Sitter and Kerr - de Sitter metrics with the contribution of the cosmological constant \Lambda. Based on the reported parameters of the M87* black hole shadow we obtain constraints for the ? and show the agreement with the cosmological data. It is shown that, the coupling of the \Lambda-term with the spin parameter reveals peculiarities for the photon spheres and hence for the shadows. Within the parametrized post-Newtonian formalism the constraint for the corresponding \Lambda-determined parameter is obtained.

As the interaction between the black holes and highly energetic infalling charged matter receives quantum corrections, the basic laws of black hole mechanics have to be carefully rederived. Using the covariant phase space formalism, we generalize the first law of black hole mechanics, both "equilibrium state" and "physical process" versions, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, F ab F ab and F ab ?�F ab . Derivation of this law demands a specific treatment of the Lagrangian parameters, similar to embedding of the cosmological constant into thermodynamic context. Furthermore, we discuss the validity of energy conditions, several complementing proofs of the zeroth law of black hole electrodynamics and some aspects of the recently generalized Smarr formula, its (non-)linearity and relation to the first law.

We consider f(R) gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential in (2+1) -dimensions. Without specifying the form of the f(R) function, we first obtain an exact black hole solution dressed with scalar hair with the scalar charge to appear in the f(R) function and we discuss its thermodynamics. This solution at large distances gives a hairy BTZ black hole, and it reduces to the BTZ black hole when the scalar field decouples. In a pure f(R) gravity supported by the scalar field, we find an exact hairy black hole similar to the BTZ black hole with phantom hair and an analytic f(R) form and discuss its thermodynamics.