General Relativity and Quantum Cosmology (gr-qc)

Abstract: In this paper we present the general spherically symmetric solution to the vacuum equations of Cotton gravity. The obtained metric solution reveals the presence of singularities at the photosphere of a spherical source, which obstruct the formation of Schwarzschild-like black holes. The solution is characterized by two integration constants that can be associated with the Hubble horizon and utilized to model the dark matter and dark energy. We examine the diverse features of the solution, including the introduction of long-range modifications to Newton's force through the incorporation of the velocity-squared repulsive term.

Abstract: We analyze the evolution of the mass density contrast in spherical perturbations of flat Friedman-Lemaitre-Robertson-Walker cosmologies. Both dark matter and dark energy are included. In the absence of dark energy the evolution equation coincides with that obtained by Bonnor within the ``Newtonian cosmology''.

Abstract: Recent developments in the field of gravitational physics, including the emergence of gravitational wave astronomy, black hole images, and more accurate telescopes, have allowed us to probe the strong-field character of gravity in a novel and revolutionary manner. This accessibility related to strong gravity brings into the foreground discussions about potential modifications to General Relativity (GR) that are particularly relevant in high curvature regimes. The most straightforward way to generalise GR is to consider an additional degree of freedom, in the form of a scalar field. In this thesis, we study generalised scalar tensor theories that predict interesting strong-gravity phenomenology. First, we review scalar no-hair theorems and the conditions under which they can be evaded. Next, we study solutions of black holes with scalar hair and the way in which higher derivative terms alter their properties. We then move our discussion to the spontaneously scalarized solutions, which only deviate from GR in the strong-field regime. We propose a model consistent with compact object scalarization, that allows for a GR attractor at late times, without fine-tuning (EsRGB model). Then, we proceed to study properties of black holes and neutron stars in this theory, revealing the interesting phenomenology of the solutions. We also study the radial stability of black holes in EsRGB and perform a preliminary analysis of the hyperbolicity of the problem. Finally, we take a look at the shadows of black holes and wormholes in theories with scalar fields, in light of recent observations of black hole shadows.

Abstract: We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. By using the Minimal Geometric Deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that describing the background geometry and scalar field source, respectively. Regarding the Schwarzschild-AdS metric as a background geometry, we derive analytical approximate solutions of scalar field and deformation metric functions with Homotopy Analysis Method (HAM), providing their analytical approximations to fourth order. Moreover, we discuss the accuracy of the analytical approximations, showing they are sufficiently accurate throughout the exterior spacetime.

Abstract: In this paper, we present a metric ansatz represents rotating traversable wormhole named topologically charged rotating Schwarzschild-Klinkahmer wormhole space-time. We discuss geodesics motion of test particles and photon ray around this topologically charged rotating wormhole background.

Abstract: We study the model of spherically symmetric and spatially homogeneous gravitational collapse of a minimally coupled scalar field. Our study focuses on obtaining the scalar field potential that leads to a final equilibrium state in the gravitational collapse. We demonstrate the existence of a class of scalar field solutions that can indeed result in such an end equilibrium state.

Abstract: The Gauss-Bonnet topological scalar is presented in metric-teleparallel formalism as well as in the symmetric and general teleparallel formulations. In all of the aforementioned frameworks, the full expressions are provided explicitly in terms of torsion, non-metricity and Levi-Civita covariant derivative. The number of invariant terms of this form is counted and compared with the number which can appear in the corresponding effective field theory. Although the difference in this number is not very large, it is found that the Gauss-Bonnet invariant excludes some of the effective field theory terms. This result sheds new light on how General Relativity symmetries can be maintained at higher order in teleparallel theories: this fact appears to be highly nontrivial in the teleparallel formulation. The importance of the so-called ``pseudo-invariant'' theories like $f(T)$- and $f(T,T_\mathcal{G})$-gravity is further discussed in the context of teleparallel Gauss-Bonnet gravity.

Abstract: We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision.

Abstract: Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is to show (in several ways) that such surfaces also satisfy a diameter bound.

Abstract: Quasinormal modes characterize the final stage of a black hole merger. In this regime, spacetime curvature is high, these modes can be used to probe potential corrections to general relativity. In this paper, we utilize the effective field theory framework to compute the leading order correction to massless scalar and electromagnetic quasinormal modes. Proceeding perturbatively in the size of the effective field theory length scale, we describe a general method to compute the frequencies for Kerr black holes of any spin. In the electromagnetic case, we study both parity even and parity odd effective field theory corrections, and, surprisingly, prove that the two have the same spectrum. Furthermore, we find that, the corrected frequencies separate into two families, corresponding to the two polarizations of light. The corrections pertaining to each family are equal and opposite. Our results are validated through several consistency checks.

Abstract: Over the next decade, third-generation interferometers and the space-based LISA mission will observe binaries in galactic centers involving supermassive black holes with millions of solar masses. More precise measurements of more extreme events that probe stronger gravitational fields can have a tremendous impact on fundamental physics, astrophysics, and cosmology. However, at the galactic scale, accretion disks, dark matter halos, and dense populations of compact objects can interact gravitationally with coalescing bodies. The role these astrophysical structures play in the evolution and gravitational-wave signature of binary systems remains largely unexplored and previous studies have often relied on ad-hoc Newtonian approximations. In this thesis, we aim to improve this picture. We study how tidal deformations of matter surrounding black holes can mask off deviations from General Relativity. We also explore the deep connection between light rings -- closed orbits of massless particles -- and the proper oscillation modes of compact objects. We show that independently of the presence of an environment, the light ring controls the late-time appearance of infalling matter to distant observers and how the final black hole formed in a collision relaxes to stationarity. Finally, we develop the first fully-relativistic framework capable of studying gravitational wave emission in non-vacuum environments. We apply it to galactic black-hole binaries surrounded by a dark matter halo and observe the conversion between matter and gravitational waves. This coupling results in significant changes in the energy flux emitted, which could help constrain the properties of galactic matter distributions.

Abstract: There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The standard quantum mechanical framework requires a notion of time evolution and a proper definition of an invariant inner product having a probability interpretation, both of which are seemingly problematic in quantum gravity. We show that these two issues can actually be solved by introducing the embedding coordinates as dynamical variables \`a la Isham and Kuchar. The extended theory is identical to general relativity but has a larger group of gauge symmetries. The Wheeler-DeWitt equations describe the change of the wave-function from one arbitrary spacelike slice to another, however the constraint algebra makes this evolution purely kinematical and furthermore enforces the wave-function to be constrained in the subspace of zero-energy states. An inner product can also be introduced having all the necessary requirements. In this formalism big-bang appears as a finite field space boundary on which certain boundary conditions must be imposed for mathematical consistency. We explicitly illustrate this point both in the full theory and in the minisuperspace approximation.

Abstract: We report on critical phenomena in the gravitational collapse of the electromagnetic field in axisymmetry using cylindrical coordinates. We perform detailed numerical simulations of four families of dipole and quadrupole initial data fine-tuned to the onset of black hole formation. It has been previously observed that families which bifurcate into two on-axis critical solutions exhibit distinct growth characteristics from those which collapse at the centre of symmetry. In contrast, our results indicate similar growth characteristics and periodicity across all families of initial data, including those examined in earlier works. More precisely, for all families investigated, we observe power-law scaling for the maximum of the electromagnetic field invariant ($\mathrm{max}|F_{\mu\nu}F^{\mu\nu}| \sim |p-p^{\star}|^{-2\gamma}$) with $\gamma \approx 0.149(9)$. We find evidence of approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $\Delta \approx 0.62(8)$ across all families of initial data. Our methodology, while reproducing the results of prior studies up to a point, provides new insights into the later stages of critical searches and we propose a mechanism to explain the observed differences between our work and the previous calculations.

Abstract: In this paper, we study circular orbits, effective potential, and thin-accretion disk of a black hole in symmergent gravity within the Novikov-Thorne model in a way including the energy flux and temperature distribution. We determine bounds on symmergent gravity parameters and conclude that the accretion disk could be used as an astrophysical tool to probe symmergent gravity.