Trace Anomaly Induced Effective Action and Hawking Radiation for 2d Dilatonic Supergravity

We construct the theory of 2d dilatonic supergravity(SG) with matter and dilaton supermultiplets coupled to dilaton functions. Trace anomaly and induced effective action for matter supermultiplet are calculated (what gives also large-N effective action for dilatonic SG). Study of black holes and Hawking radiation which turns out to be zero in supersymmetric CGHS model with dilaton coupled matter is presented. In the same way one can study spherically symmetric collapse for other 4d SG using simplified 2d approach.Comment: LaTeX file, 9 pag

Modified gravity with ln⁡R\ln R terms and cosmic acceleration

The modified gravity with $\ln R$ or $R^{-n} (\ln R)^m$ terms which grow at small curvature is discussed. It is shown that such a model which has well-defined newtonian limit may eliminate the need for dark energy and may provide the current cosmic acceleration. It is demonstrated that $R^2$ terms are important not only for early time inflation but also to avoid the instabilities and the linear growth of the gravitational force. It is very interesting that the condition of no linear growth for gravitational force coincides with the one for scalar mass in the equivalent scalar-tensor theory to be very large. Thus, modified gravity with $R^2$ term seems to be viable classical theory.Comment: LaTeX file, 16 pages, discussion and references are adde

Instabilities and Anti-Evaporation of Reissner-Nordstr\"om Black Holes in modified F(R)F(R) gravity

We study the instabilities and related anti-evaporation of the extremal Reissner-Nordstr\"om (RN) black hole in $F(R)$ gravity. It is remarkable that the effective electric charge can be generated for some solutions of $F(R)$ gravity without electromagnetic field. The anti-evaporation effect occurs but it emerges only in the strong coupling limit of the effective gravitational coupling. The instabilities of RN black hole are also investigated when the electromagnetic sector is added to the action of $F(R)$ gravity. We show the anti-evaporation occurs in the Maxwell-$F(R)$ gravity with the arbitrary gravitational coupling constant although it does not occur in the Maxwell-Einstein gravity. Furthermore, general spherically-symmetric solution of $F(R)$ gravity in the Einstein frame is obtained.Comment: LaTeX 11 pages, no figure, publication data: Physics Letters B 735, 376-382 (2014

On the instability of effective potential for non-abelian toroidal D-brane

We calculate the one-loop effective potential for the toroidal non-abelian D-brane in the constant magnetic SU(2) gauge field. The study of its properties shows that the potential is unbounded below. This fact indicates the instability of the non-abelian D-brane in the background under consideration like the instability of chromomagnetic vacuum in SU(2) gauge theory.Comment: to be published in Phys.Lett.B, 11 pages with 1 figure (ps file), LaTeX fil

Effective Lagrangian and static black holes in 2D dilatonic gravity inspired by quantum effects

We study the effective action in 2D dilaton-Maxwell quantum gravity. Working with the one-loop renormalizable subset of such theories, we construct the improved effective Lagrangian which contains curvature under logarithm. This effective Lagrangian leads to new classical dilatonic gravity inspired by quantum effects. The static black holes (BH) solutions which may play the role of a remnant after the Hawking radiation for such theory are carefully investigated. The effective Lagrangian for Gross-Neveu-dilaton gravity is also constructed (in 1/N expansion).Comment: Latex file, 13 pages, published in Mod.Phys.Lett. A12 (1997) 925 (revised version

Quantum escape of sudden future singularity

We consider finite-time, future (sudden or Big Rip type) singularities which may occur even when strong energy condition is not violated but equation of state parameter is time-dependent. Recently, example of such singularity has been presented by Barrow, we found another example of it. Taking into account back reaction of conformal quantum fields near singularity, it is shown explicitly that quantum effects may delay (or make milder) the singularity. It is argued that if the evolution to singularity is realistic, due to quantum effects the universe may end up in deSitter phase before scale factor blows up. This picture is generalized for braneworld where sudden singularity may occur on the brane with qualitatively similar conclusions.Comment: LaTeX file, 13 pages, minor corrections, version to appear in PL

Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe

We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic FRW cosmology. We formulate several versions of modified gravity compatible with Solar System tests where the following sequence of cosmological epochs occurs: a. matter dominated phase (with or without usual matter), transition from decceleration to acceleration, accelerating epoch consistent with recent WMAP data b. $\Lambda$CDM cosmology without cosmological constant. As a rule, such modified gravities are expressed implicitly (in terms of special functions) with late-time asymptotics of known type (for instance, the model with negative and positive powers of curvature). In the alternative approach, it is demonstrated that even simple versions of modified gravity may lead to the unification of matter dominated and accelerated phases at the price of the introduction of compensating dark energy.Comment: LaTeX file, 12 pages, discussion is extended, version to appear Physical review