General Relativity and Quantum Cosmology (gr-qc)

Abstract: We present and discuss new families of hairy charged black hole solutions in asymptotically anti-de Sitter space in three dimensions. The coupled Einstein-Maxwell-scalar gravity system, that carries the coupling $f(\phi)$ between the scalar and Maxwell fields is solved, and exact hairy black hole solutions are obtained analytically. The hairy solutions are obtained for three different profiles of the coupling function: (i) $f(\phi)=1$, corresponding to no direct coupling between the scalar and Maxwell fields, (ii) $f(\phi)=e^{-\phi}$, and (iii) $f(\phi)=e^{-\phi^2/2}$; corresponding to non-minimal coupling between them. For all these couplings the scalar field and curvature scalars are regular everywhere outside the horizon. We analyze the thermodynamics of the hairy black hole and find drastic changes in its thermodynamic structure due to the scalar field. For $f(\phi)=1$, there exists a critical value of the hairy parameter above which the charged hairy black hole exhibits the Hawking/Page phase transition, whereas no such phase transition occurs below this critical value. Similarly, for $f(\phi)=e^{-\phi}$ and $f(\phi)=e^{-\phi^2/2}$, the hairy solution exhibits a small/large black hole phase transition for above critical values of the hairy parameter. Interestingly, for these couplings, the thermodynamic phase diagram of three-dimensional hairy charged black holes resembles that of a higher-dimensional RN-AdS black hole, albeit with two second-order critical points.

Abstract: The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile has been recently constructed in the context of scalar-tensor theories. Unlike General Relativity, the regular Hayward metric is realized as an exact background metric in the Effective Field Theory with timelike scalar profile without resorting to special matter field, such as nonlinear electrodynamics. The fundamental quasinormal mode for axial graviational perturbations of this black hole has been considered recently with the help of various methods. Here we make a further step in this direction and find that, unlike the fundamental mode, a few first overtones deviate from their Schwarzschild limit at a much higher rate. This outburst of overtones occurs because the overtones are extremely sensitive to the least change of the near-horizon geometry. The analytical formula for quasinormal modes is obtained in the eikonal regime. In addition, we calculated grey-body factors and showed that regular Hayward black hole with a scalar hair has smaller grey-body factor than the Schwarzschild one. Integration of the wave-like equation in time-domain shows that the power-law tails following the ring-down phase at late times are indistinguishable from the Schwarzschild ones.

Abstract: A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric $g_{ab}(x)$ etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form $\mathscr{G}_{ab \ldots i'j' \ldots}(x,x')$. A deeper look then reveals a subtle interplay interplay between non-locality and the limit $G\hbar/c^3 \to 0$. In particular, the so called emergent gravity paradigm -- in which gravitational dynamics/action/spacetime are emergent and characterised by an *entropy functional* -- arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This essay describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

Abstract: We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Using the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger, this Loop Quantum Gravity-induced lower bound is shown to be entirely consistent with the data.

Abstract: We reconsider the problem of a slowly rotating homogeneous star, or Schwarzschild star, when its compactness goes beyond the Buchdahl bound and approaches the gravastar limit $R\to 2M$. We compute surface and integral properties of such configuration by integrating the Hartle-Thorne structure equations for slowly rotating relativistic masses, at second order in angular velocity. In the gravastar limit, we show that the metric of a slowly rotating Schwarzschild star agrees with the Kerr metric, thus, within this approximation, it is not possible to tell a gravastar from a Kerr black hole by any observations from the spacetime exterior to the horizon.

Abstract: In this work we investigate observational signatures of a primordial power spectrum with exponential infrared suppression, motivated by the choice of a non-oscillatory vacuum in a bouncing and inflationary geometry within Loop Quantum Cosmology (LQC). We leave the parameter that defines the scale at which suppression occurs free and perform a Bayesian analysis, comparing with CMB data. The data shows a preference for some of the suppression to be within the observable window. Guided by this analysis, we choose concrete illustrative values for this parameter. We show that the model affects only slightly the parity anomaly, but it is capable of alleviating the lensing and power suppression anomalies.

Abstract: Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy degree of freedom interacts with a ghost. These theories have Hamiltonians unbounded from above and from below, are integrable, and contain free functions. We show analytically that their classical motion is bounded for all initial data. Moreover, we derive conditions allowing for Lyapunov stable equilibrium points. A subclass of these stable systems has simple polynomial potentials with stable equilibrium points entirely due to interactions with the ghost. All these findings are fully supported by numerical computations which we also use to gather evidence for stability in various nonintegrable systems.

Abstract: This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a Hilbert space at each lattice site along with the corresponding representation of the conventional commutation relations, and which manifestly realizes the positive--definiteness of the spatial metric even in the quantum theory. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We also emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.