Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$. The holonomy correction in ${\bf H}_\Delta$ is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$ (which often chosen as the minimal area gap in Loop Quantum Gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\sim 1/{\Delta}^2$. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii $\sim \sqrt{\Delta}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.

Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the self-dual black hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the loop quantum gravity. From our results, we can check that the self-dual black hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes $$\xi =0$$ ξ = 0 and $$\xi =1/6$$ ξ = 1 / 6 , i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.

Dying AdS Schwarzschild black hole

The criteria for thermal stability of a most general quantum black hole derived by us appeared in the form of a series of inequalities connecting second-order derivatives of black hole mass with respect to its parameters, which determine the mass of the black hole. These nullify the concept of positivity of specific heat as the sole criteria for thermal stability. Using this most general stability criterion, we prove here that AdS Schwarzschild black holes are no longer stable anywhere in their parameter space if cosmological constant is allowed to vary. We also calculate the fluctuations of both horizon area and cosmological constant of this black hole. We calculate specific heat of it and compare this with Hawking’s prediction.

Electromagnetic albedo of Quantum Black Holes

We compute the albedo (or reflectivity) of electromagnetic waves off the electron-positron Hawking plasma that surrounds the horizon of a Quantum Black Hole. We adopt the “modified firewall conjecture” for fuzzballs [1, 2], where we consider significant electromagnetic interaction around the horizon. While prior work has treated this problem as an electron-photon scattering process, we find that the incoming quanta interact collectively with the fermionic excitations of the Hawking plasma at low energies. We derive this via two different methods: one using relativistic plasma dispersion relation, and another using the one-loop correction to photon propagator. Both methods find that the reflectivity of long wavelength photons off the Hawking plasma is significant, contrary to previous claims. This leads to the enhancement of the electromagnetic albedo for frequencies comparable to the Hawking temperature of black hole horizons in vacuum. We comment on possible observable consequences of this effect.

Loop Quantum Black Hole Extensions Within the Improved Dynamics

We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains semi-classical states that approximate general relativity coupled to an effective anisotropic fluid. The singularity is eliminated and the space-time can be continued into a white hole space-time. This is similar to previously considered scenarios based on a loop quantum gravity quantization.

Quantum BTZ black hole

We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS4, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article.

Phase transition in decaying black holes

We had earlier derived the most general criteria for thermal stability of a quantum black hole, with arbitrary number of parameters, in any dimensional spacetime. These conditions appeared in form of a series of inequalities connecting second order derivatives of black hole mass with respect to its parameters. Some black holes like asymptotically flat rotating charged black holes do not satisfy all the stability criteria simultaneously, but do satisfy some of them in certain region of parameter space. They are known as “Quasi Stable” black holes. In this paper, we will show that quasi stable black holes although ultimately decay under Hawking radiation undergo phase transitions. These phase transitions are different from phase transition in ADS Schwarzschild black hole. These are marked by sign changes in certain physical quantities apart from specific heat of the black hole. We will also discuss the changes in the nature of fluctuations of the parameters of these quasi stable black holes with different phases.