Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

BLACK-HOLE HAVING ELECTRIC HAIRS FOR POSITIVE COSMOLOGICAL CONSTANT Λ>0 ON A COSMIC HORIZON SCALE ~1/√Λ

This paper is a technical review for a more deliberate paper (Bhattacharya & Lahiri, 2007) where it has been shown that on a positive cosmological scale with Λ>0 having a cosmic horizon scale ~1/√Λ, there exists the soft electric hairs for the solution having the T_00 components of the stress-energy tensor T_μν i.e., ρ=0 on black hole horizon B_H having the maximum density at black hole singularity B_S where cosmic horizon C_H and black hole horizon B_H has only been considered. KEYWORDS: Black Hole – Cosmic Horizon – TOV Limit – Stress-Energy Tensor – Positive Cosmological Constant

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.

Correlation functions in finite temperature CFT and black hole singularities

We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

Non-singular black holes with a zero-shear S-brane

We propose a construction with which to resolve the black hole singularity and enable an anisotropic cosmology to emerge from the inside of the hole. The model relies on the addition of an S-brane to the effective action which describes the geometry of space-time. This space-like defect is located inside of the horizon on a surface where the Weyl curvature reaches a limiting value. We study how metric fluctuations evolve from the outside of the black hole to the beginning of the cosmological phase to the future of the S-brane. Our setup addresses i) the black hole singularity problem, ii) the cosmological singularity problem and iii) the information loss paradox since the outgoing Hawking radiation is entangled with the state inside the black hole which becomes the new universe.

Hawking evaporation of Einstein–Gauss–Bonnet AdS black holes in $$D\geqslant 4$$ dimensions

Einstein–Gauss–Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein–Gauss–Bonnet gravity in various spacetime dimensions with both positive and negative coupling constant $$\alpha $$ α . By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $$\alpha >0$$ α > 0 , in $$D\geqslant 6$$ D ⩾ 6 cases, the black holes will be completely evaporated in a finite time, which resembles the Schwarzschild-AdS case in Einstein gravity. While in $$D=4,5$$ D = 4 , 5 cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $$\alpha >0, D=4,5$$ α > 0 , D = 4 , 5 will solve the terminal temperature divergent problem of the Schwarzschild-AdS case. For $$\alpha <0$$ α < 0 , in all dimensions, the black hole will always spend a finite time to a minimal mass corresponding to the smallest horizon radius $$r_{min}=\sqrt{2|\alpha |}$$ r min = 2 | α | which coincide with an additional singularity. This implies that there may exist constraint conditions to the choice of coupling constant.

Rescuing a black hole in the large-q coupled SYK model

In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-q theory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2 vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-q and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

Proper time to the black hole singularity from thermal one-point functions

We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.

Towards Black-Hole Singularity-Resolution in the Lorentzian Gravitational Path Integral

Quantum gravity is expected to resolve the singularities of classical general relativity. Based on destructive interference of singular spacetime-configurations in the path integral, we find that higher-order curvature terms may allow to resolve black-hole singularities both in the spherically symmetric and axisymmetric case. In contrast, the Einstein action does not provide a dynamical mechanism for singularity-resolution through destructive interference of these configurations.