General Relativity and Quantum Cosmology (gr-qc)

Abstract: We derived four novel classes of spherically symmetric but non-asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect via the Generalized Uncertainty Principle (GUP). Here, we considered the effect of this quantum correction, described by the parameter $\gamma$, on a toy model galaxy with dark matter and the three well-known dark matter distributions: the Cold Dark Matter (CDM), Scalar Field Dark Matter (SFDM), and the Universal Rotation Curve (URC). We aimed to find constraints to $\gamma$ by applying these solutions to the known supermassive black holes: Sgr. A* and M87*, in conjunction with the available Event Horizon telescope. We then examined the effect of $\gamma$ on the event horizon, photonsphere, and shadow radii, where we observed unique deviations from the Schwarzschild case. As for the shadow radii, we obtained bounds for the values of $\gamma$ on each black hole solution at $1\sigma$ confidence level. Our results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of $\gamma$, which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively.

Abstract: Singularities in any physical theory are either remarkable indicators of the unknown underlying fundamental theory, or indicate a change in the description of the physical reality. In General Relativity there are three fundamental kinds of singularities that might occur, firstly the black hole spacelike crushing singularities, e.g. in the Schwarzschild case and two cosmological spacelike singularities appearing in finite-time, namely, the Big Bang singularity and the Big Rip singularity. In the case of black hole and Big Bang singularity, the singularity indicates that the physics is no longer described by the classical gravity theory but some quantum version of gravity is probably needed. The Big Rip is a future singularity which appears in the context of General Relativity due to a phantom scalar field needed to describe the dark energy era. Apart from the Big Rip singularity, a variety of finite-time future singularities, such as, sudden singularity, Big Freeze singularity, generalized sudden singularity, $w$-singularity and so on, are allowed in various class of cosmological models irrespective of their origin. The occurrence of these finite-time singularities has been intensively investigated in the context of a variety of dark energy, modified gravity, and other alternative cosmological theories. These singularities suggest that the current cosmological scenario is probably an approximate version of a fundamental theory yet to be discovered. In this review we provide a concrete overview of the cosmological theories constructed in the context of Einstein's General Relativity and modified gravity theories that may lead to finite-time cosmological singularities. We also discuss various approaches suggested in the literature that could potentially prevent or mitigate finite-time singularities within the cosmological scenarios.

Abstract: In a generic theory of gravity coupled to matter fields, the Smarr formula and the first law of thermodynamics of black holes do not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory; and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that changes the role of the couplings from the constants in a theory to the free parameters in solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

Abstract: Ultralight boson is one of the potential candidates for dark matter. If exists, it can be generated by a rapidly rotating black hole via superradiance, extracting the energy and angular momentum of the black hole and forming a boson cloud. The boson cloud can be affected by the presence of a companion star, generating fruitful dynamical effects and producing characteristic gravitational wave signals. We study the dynamics of the boson cloud in a binary black hole system, in particular, we develop a framework to study the mass transfer between two black holes. It is found that bosons occupying the growing modes of the central black hole can jump to the decaying modes of the companion black hole, resulting in cloud depletion. This mechanism of cloud depletion is different from that induced by the resonant perturbation from the companion.

Abstract: We consider a dark energy model consisting of a scalar field simultaneously coupled to the Gauss-Bonnet invariant and dark matter such that the observational gravitational wave speed constraint on the Gauss-Bonnet term is respected. In the early era, the Gauss-Bonnet term caused the scalar field to remain at a stable point. In this period, dark energy density was negligible. Next, due to the dark matter redshift and the conformal coupling, the initial $Z_2$ symmetry was broken, and the activated field climbed up its potential and provided conditions for late-time acceleration. In this scenario, the Gauss-Bonnet term is not directly involved in the late-time evolution but alleviates the coincidence problem.

Abstract: Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry. However, if clock degrees of freedom (self-)interact non-trivially, they in general have turning points where their momenta vanish. At and beyond a turning point, the evolution of other degrees of freedom is no longer described directly by changes of the clock parameter because it stops and then turns back, while time is moving forward. Previous attempts to describe quantum evolution relative to a clock with turning points have failed and led to frozen evolution in which degrees of freedom remain constant while the clock parameter, interpreted directly as a substitute for monotonic time, is being pushed beyond its turning point. Here, a new method previously used in oscillator systems is applied to a tractable cosmological model, given by an isotropic universe with spatial curvature and scalar matter. The re-collapsing scale factor presents an example of a clock with a single turning point. The method succeeds in defining unitary and freeze-free evolution by unwinding the turning point of the clock, introducing an effective monotonic time parameter that is related to but not identical with the non-monotonic clock degree of freedom. Characteristic new quantum features are found around the turning point, based on analytical and numerical calculations.