Classical and quantum properties of two-dimensional black holes

Various dynamical aspects of a non-trivial theory of gravitation in (1+1) dimensions are investigated. It is shown that many features of Einstein's general relativity for (3+1) dimensions are qualitatively and to some extent quantitatively duplicated in this theory, including gravitational collapse, cosmological solutions and gravitational waves. Contact with Newton's theory is made and post-Newtonian expansions of the theory give relativistic corrections, similar to those of general relativity. Therefore this theory is presented as viable for both pedagogical purposes as well as a laboratory for the testing of new theoretical ideas.

http://iopscience.iop.org/article/10.1088/0264-9381/8/1/022/pdf

Gravitation and cosmology in (1 + 1) dimensions

A survey of black hole physics in two spacetime dimensions is presented. Basic properties, specific solutions and quantum aspects are considered in turn. The relationship between string theoretic black holes and those arising in other (1+l)-dimensional theories of gravity is discussed.

Lower dimensional black holes

We present a comprehensive analysis of the spacetime structure and thermodynamics of (1 + 1)−dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length √ � cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant �, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.

/pdf/aspects-of-noncommutative-1-1-dimensional-black-holes-30z1m86781.pdf

Aspects of noncommutative (1+1)-dimensional black holes

The authors investigate the causal structure of (1+1)-dimensional spacetimes. For two sets of field equations they show that at least locally any spacetime is a solution for an appropriate choice of the matter fields. For the theories under consideration they investigate how smoothness of their black hole solutions affects time orientation. The authors show that if an analogue to Hawking's area theorem holds in two spacetime dimensions, it must actually state that the size of a black hole never increases, contrary to what happens in four dimensions. Finally, they discuss the applicability of the Penrose and Hawking singularity theorems to two spacetime dimensions.

/pdf/the-causal-structure-of-two-dimensional-spacetimes-16dxlu6iea.pdf

The Causal Structure of Two-Dimensional Spacetimes

A variety of two-dimensional theories of gravitation with and without torsion are considered. We discuss the invariance properties and geometrical structure of each. One such theory considered predicts nontrivial dynamics for the evolution of the two-dimensional spacetime. We obtain some exact solutions for this theory.

Theories of Gravitation in Two-Dimensions

It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.

Reinterpretation of the Non-Linear Sigma Model with Torsion

The Weyl anomaly is computed for a class of two-dimensional algebraically extended bosonic {sigma} models. Although these models are classically equivalent to the standard bosonic {sigma} models with torsion, it is shown that they differ radically at the quantum level. In particular, a reasonable choice for the one-loop partition function for the algebraically extended models contains a nonlocal anomalous contribution which cannot be canceled in any dimension. This curious feature appears to be a generic property of a particular type of gauge-invariant vector-scalar coupling in two-dimensional gravity theories.

D. Vincent

Papers

Theories of Gravitation in Two-Dimensions

Reinterpretation of the Non-Linear Sigma Model with Torsion

Quantum properties of algebraically extended bosonic sigma models.