Generalized Dilaton Theories Research Articles

Islands in Generalized Dilaton Theories

This work systematically studies the island formula in the general asymptotically flat eternal black holes in generalized dilaton gravity theories or higher-dimensional spherical black holes. Under some reasonable and mild assumptions, we prove that (the boundary of) the island always appears barely outside the horizon in the late time of Hawking radiation, so the information paradox is resolved. In particular, we find a proper island in the Liouville black hole that solves the previous the puzzle.

The universality of islands outside the horizon

We systematically calculate the quantum extremal surface (QES) associated with Hawking radiation for general D-dimensional (D ≥ 2) asymptotically flat (or AdS) eternal black holes using the island formula. We collect the Hawking radiation particles by a non-gravitational bath and find that a QES exists in the near-horizon region outside the black hole when c · G(D) is smaller enough where c is the central charge of the conformal matter and G(D) the D-dimensional Newton constant. The locations of the QES in these backgrounds are obtained and the late-time radiation entropy saturates the two times of black hole entropy. Finally, we numerically check that the no island configuration exists once c · G(D) exceeds a certain upper bound in two-dimensional generalized dilaton theories (GDT). When c · G(D) close to the upper bound, the backreaction of the matter field on the background can not be neglected. We also consider the conditions of existence of the island configuration with the backreaction and prove that the upper bound also exist for the Witten black hole and Weyl-related Witten black hole.

Noether charge and black hole entropy in modified theories of gravity

The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole is one-quarter of the horizon area in $f(R)$ theories coupled to conformally invariant matter. If matter is present that is not conformally invariant, the entropy is still proportional to the area of the black hole, but the coefficient is generally not one-quarter. The entropy of black holes in generalized dilaton theories and in theories with Lagrangians that depend on an arbitrary function of the Ricci tensor are also examined.

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models, among them spherically reduced theories and the string inspired dilaton black hole (CGHS model). We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way asymptotic states, tree-level vertices and tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the CGHS model all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.

Virtual black holes in generic 2D dilaton theories

Recent years have seen remarkable progress in the quantum treatment of two dimensional models of gravity, so called Generalized Dilaton Theories (GDTs), which include, most prominently, the Schwarzschild Black Hole (BH) and the string inspired dilaton BH. In this note some of the latest results for GDTs with matter are summarized.

Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

Hawking radiation in d = 4 is regarded as a well understood quantum theoretical feature of Black Holes or of other geometric backgrounds with an event horizon. On the other hand, the dilaton theory, emerging after spherical reduction, and generalized dilaton theories only during the last years became the subject of numerous studies which unveiled a surprisingly difficult situation. Recently we have found some solution to the problem of Hawking flux in spherically reduced gravity which has the merit of using a minimal input. It leads to exact cancellation of negative contributions to this radiative flux, encountered in other approaches at infinity, so that our result asymptotically coincides with the one of minimally coupled scalars. The use of an integrated action is avoided — although we have been able to present also that quantity in a closed expression. This short review also summarizes and critically discusses recent activities in this field, including the problem of “conformal frames” for the background and questions which seem to be open in our own approach as well as in others.

Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

AbstractHawking radiation in d = 4 is regarded as a well understood quantum theoretical feature of Black Holes or of other geometric backgrounds with an event horizon. On the other hand, the dilaton theory, emerging after spherical reduction, and generalized dilaton theories only during the last years became the subject of numerous studies which unveiled a surprisingly difficult situation. Recently we have found some solution to the problem of Hawking flux in spherically reduced gravity which has the merit of using a minimal input. It leads to exact cancellation of negative contributions to this radiative flux, encountered in other approaches at infinity, so that our result asymptotically coincides with the one of minimally coupled scalars. The use of an integrated action is avoided — although we have been able to present also that quantity in a closed expression. This short review also summarizes and critically discusses recent activities in this field, including the problem of “conformal frames” for the background and questions which seem to be open in our own approach as well as in others.

Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity

Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes of mass and energy. The gravity models for which our arguments are valid include theories with dynamical torsion and so-called generalized dilaton theories (GDTs). Our analysis of the canonical action principle (i) provides a rigorous correspondence between the most general first-order two-dimensional Einstein–Cartan model (ECM) and GDT and (ii) allows us to extract in a virtually simultaneous manner the “true degrees of freedom” for both ECMs and GDTs. For all such models, the existence of an absolutely conserved (in vacuo) quantityCis a generic feature, with (minus)Ccorresponding to the black-hole mass parameter in the important special cases of spherically symmetric four-dimensional general relativity and standard two-dimensional dilaton gravity. The massCalso includes (minimally coupled) matter into a “universal mass function.” We place particular emphasis on the (quite general) class of models within GDT possessing a Minkowski-like groundstate solution (allowing comparison betweenC and the Arnowitt–Deser–Misner mass for such models).

Hawking radiation and masses in generalized dilaton theories

A generalized dilaton action is considered of which the standard dilaton black hole and spherically reduced gravity are particular cases. The Arnowitt - Deser - Misner (ADM) and the Bondi - Sachs (BS) mass are calculated. Special attention is paid to both the asymptotic conditions for the metric as well as for the reference spacetime. For the latter one we suggest a modified expression thereby obtaining a new definition of energy. Depending on the parameters of the model the Hawking radiation behaves like a positive or negative power of the mass.

On the completeness of the black hole singularity in 2D dilaton theories

The black hole of the widely used ordinary 2D-dilaton model (DBH) deviates from the Schwarzschild black hole (SBH) of General Relativity in one important feature: Whereas non-null extremals or geodesics show the expected incompleteness this turns out not to be the case for the null extremals. After a simple analysis in Kruskal coordinates for singularities with power behavior of this - apparently up to now overlooked - property we discuss the global structure of a large family of generalized dilaton theories which does not only contain the DBH and SBH but also other proposed dilaton theories as special cases. For large ranges of the parameters such theories are found to be free from this defect and exhibit global SBH behavior.

Classical and quantum gravity in dimensions: I. A unifying approach

We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang - Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution becomes accessible within a few lines of calculation only. In this first of a series of papers we set the stage for a thorough global investigation of classical and quantum aspects of more or less all available 2D gravity - Yang - Mills models.