Near horizon dynamics of three dimensional black holes

We perform the Hamiltonian reduction of three dimensional Einstein gravity with negative cosmological constant under constraints imposed by near horizon boundary conditions. The theory reduces to a Floreanini–Jackiw type scalar field theory on the horizon, where the scalar zero modes capture the global black hole charges. The near horizon Hamiltonian is a total derivative term, which explains the softness of all oscillator modes of the scalar field. We find also a (Korteweg–de Vries) hierarchy of modified boundary conditions that we use to lift the degeneracy of the soft hair excitations on the horizon.

Spherically Symmetric Geometries inf(T)andf(R)Gravitational Theories

Using the well know relation between Ricci scalar,R, and torsion scalar,T, that is,R=-T-2∇αTα, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is,T=TμναSαμν=0or (ii) total derivative term, that is,∇αTαwithTαis the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution forf(T)andf(R)gravitational theories.

MINBU Distribution of Two-Dimensional Quantum Gravity: Simulation Result and Semiclassical Analysis

We analyze the MINBU distribution of two-dimensional quantum gravity. New data of R2-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. In the distribution, the cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing (or roughening) force of R2-term. The dependence on the central charge cm and on the R2-coupling are explained for R2-gravity, which includes the ordinary 2d quantum gravity. The R2-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles. The surface topology is that of a sphere.

THERMODYNAMIC PROPERTIES, PHASES AND CLASSICAL VACUA OF TWO-DIMENSIONAL R2 GRAVITY

Two-dimensional quantum R2 gravity is studied in the semiclassical way. The thermodynamic properties, such as the equation of state, the temperature and the entropy, are examined. The classical solutions (vacua) of the R2 Liouville equation are obtained by making use of the well-known solution of the ordinary Liouville equation. They are constant curvature solutions. The positive constant curvature solution and the negative one are, after proper infrared regularization, “dual” each other. Each solution has two branches (±). We characterize all phases appearing in all solutions and branches. The topology constraint and the area constraint are properly taken into account. A total derivative term and an infrared regularization play important roles. The topology of a sphere is mainly considered.