In bosonic closed string field theory the "tachyon potential" is a potential for the tachyon, the dilaton, and an infinite set of massive fields. Earlier computations of the potential did not include the dilaton and the critical point formed by the quadratic and cubic interactions was destroyed by the quartic tachyon term. We include the dilaton contributions to the potential and find that a critical point survives and appears to become more shallow. We are led to consider the existence of a closed string tachyon vacuum, a critical point with zero action that represents a state where space-time ceases to be dynamical. Some evidence for this interpretation is found from the study of the coupled metric-dilaton-tachyon effective field equations, which exhibit rolling solutions in which the dilaton runs to strong coupling and the Einstein metric undergoes collapse.

We study the low-energy effective field equations that couple gravity, the dilaton, and the bulk closed string tachyon of bosonic closed string theory. We establish that whenever the tachyon induces the rolling process, the string metric remains fixed while the dilaton rolls to strong coupling. For negative definite potentials we show that this results in an Einstein metric that crunches the universe in finite time. This behavior is shown to be rather generic even if the potentials are not negative definite. The solutions are reminiscent of those in the collapse stage of a cyclic universe cosmology where scalar field potentials with negative energies play a central role.

Abstract. The standard Hawking formula predicts the complete evaporation of black holes.In this paper, we introduce effects of quantum gravity into fermions' tunneling from ReissnerNordstrom and Kerr black holes. The quantum gravity effects slow down the increase of Hawking temperatures. This property naturally leads to a residue mass in black hole evaporation. The corrected temperatures are affected by the quantum numbers of emitted fermions. Meanwhile, the temperature of the Kerr black hole is a function of θ due to the rotation.arXiv:1307.0172v2 [gr-qc]

Inspired by the recent "Complexity = Action" conjecture, we use the approach proposed by Lehner et al. to calculate the rate of the action of the WheelerDeWitt patch at late times for static uncharged and charged black holes in f (R) gravity. Our results have the same expressions in terms of the mass, charge, and electrical potentials at the horizons of black holes as in Einstein's gravity. In the context of f (R) gravity, the Lloyd bound is saturated for uncharged black holes but violated for charged black holes near extremality. For charged black holes far away from the ground states, the Lloyd bound is violated in four dimensions but satisfied in higher dimensions.

In this review, we discuss effects of quantum gravity on black hole physics. After a brief review of the origin of the minimal observable length from various quantum gravity theories, we present the tunneling method. To incorporate quantum gravity effects, we modify the Klein-Gordon equation and Dirac equation by the modified fundamental commutation relations. Then we use the modified equations to discuss the tunneling radiation of scalar particles and fermions. The corrected Hawking temperatures are related to the quantum numbers of the emitted particles. Quantum gravity corrections slow down the increase of the temperatures. The remnants are observed as M Res. The mass is quantized by the modified Wheeler-DeWitt equation and is proportional to n in quantum gravity regime. The thermodynamical property of the black hole is studied by the influence of quantum gravity effects.