An Einstein-like theory of gravity with a non-newtonian weak-field limit

We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as \ln r . The Newtonian term GM/r appears only as subleading. Our model can be used to give a phenomenological explanation of the rotation curves of the galaxies without postulating the presence of dark matter. This can be achieved only by giving up at galactic scales Einstein equivalence principle.Comment: Final version, accepted for publication on General Relativity and Gravitatio

Acoustic analogs of two-dimensional black holes

We present a general method for constructing acoustic analogs of the black hole solutions of two-dimensional (2D) dilaton gravity. Because by dimensional reduction every spherically symmetric, four-dimensional (4D) black hole admits a 2D description, the method can be also used to construct analogue models of 4D black holes. We also show that after fixing the gauge degrees of freedom the 2D gravitational dynamics is equivalent to an one-dimensional fluid dynamics. This enables us to find a natural definition of mass $M$, temperature $T$ and entropy $S$ of the acoustic black hole. In particular the first principle of thermodynamics $dM=TdS$ becomes a consequence of the fluid dynamics equations. We also discuss the general solutions of the fluid dynamics and two particular cases, the 2D Anti-de sitter black hole and the 4D Schwarzschild black hole.Comment: some references adde

The dualities of 3D dilaton gravity

We investigate Brans-Dicke dilaton gravity theories in 2+1 dimensions. We show that the reduced field equations for solutions with diagonal metric and depending only on one spacetime coordinate have a continuous O(2) symmetry. Using this symmetry we derive general static and cosmological solutions of the theory. The action of the discrete group O(2,Z) on the space of the solutions is discussed. Three-dimensional string effective theory and three-dimensional general relativity are discussed in detail. In particular, we find that the previously discovered black string solution is dual to a spacetime with a conical singularity.Comment: 15 pages, LaTex file, no figure

Induced gravity and entanglement entropy of 2D black holes

Using the fact that 2D Newton constant is wholly induced by a conformal field theory, we derive a formula for the entanglement entropy of the anti-de Sitter black hole in two spacetime dimensions. The leading term in the large black hole mass expansion of our formula reproduces exactly the Bekenstein-Hawking entropy S_{BH}, whereas the subleading term behaves as ln S_{BH}. This subleading term has the universal form typical for the entanglement entropy of physical systems described by effective conformal fields theories (e.g. one-dimensional statistical models at the critical point).Comment: 6 page

Asymptotically flat black holes sourced by a massless scalar field

We derive exact, asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a non trivial scalar field with $1/r$ asymptotic behaviour. They are determined using an ansatz for the scalar field profile and working out, together with the metric functions, the corresponding form of the scalar self-interaction potential. Near to the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution. We also work out a consistent thermodynamical description of our black hole solutions. For large mass our hairy black holes have the same thermodynamical behaviour of the Schwarzschild black hole, whereas for small masses they differ substantially from the latter.Comment: 12 pages, no figures. Refs. [27-33] added. Some remarks about previous derivation and stability of solution (5.4) adde

How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?

Motivated by the new theoretical paradigm that views spacetime geometry as emerging from the entanglement of a pre-geometric theory, we investigate the issue of the signature of the presence of horizons and localized matter on the entanglement entropy (EE) S_E for the case of three-dimensional AdS (AdS_3) gravity. We use the holographically dual two-dimensional CFT on the torus and the related modular symmetry in order to treat bulk black holes and conical singularities (sourced by pointlike masses not shielded by horizons) on the same footing. In the regime where boundary tori can be approximated by cylinders we are able to give universal expressions for the EE of black holes and conical singularities. We argue that the presence of horizons/localized matter in the bulk is encoded in the EE in terms of (i) enhancement/reduction of the entanglement of the AdS_3 vacuum, (ii) scaling as area/volume of the leading term of the perturbative expansion of S_E, (iii) exponential/periodic behaviour of S_E, (iv) presence of unaccessible regions in the noncompact/compact dimension of the boundary cylinder. In particular, we show that the reduction effect of matter on the entanglement of the vacuum found by Verlinde for the de Sitter vacuum extends to the AdS_3 vacuumComment: 16 pages, no figure

Holography of charged dilatonic black branes at finite temperature

We investigate bulk and holographic features of finite-temperature black brane solutions of 4D anti-de Sitter Einstein-Maxwell-dilaton-gravity (EMDG). We construct, numerically, black branes endowed with non trivial scalar hairs for broad classes of EMDG. We consider both exponential and power-law forms for the coupling functions, as well as several charge configurations: purely electric, purely magnetic and dyonic solutions. At finite temperature the field theory holographically dual to these black brane solutions has a rich and interesting phenomenology reminiscent of electron motion in metals: phase transitions triggered by nonvanishing VEV of scalar operators, non-monotonic behavior of the electric conductivities as function of the frequency and of the temperature, Hall effect and sharp synchrotron resonances of the conductivity in presence of a magnetic field. Conversely, in the zero temperature limit the conductivities for these models show a universal behavior. The optical conductivity has a power-law behavior as a function of the frequency, whereas the DC conductivity is suppressed at small temperatures.Comment: 29 pages 14 figures, typos corrected, reference adde

Dark Energy from holographic theories with hyperscaling violation

We show that analytical continuation maps scalar solitonic solutions of Einstein-scalar gravity, interpolating between an hyperscaling violating and an Anti de Sitter (AdS) region, in flat FLRW cosmological solutions sourced by a scalar field. We generate in this way exact FLRW solutions that can be used to model cosmological evolution driven by dark energy (a quintessence field) and usual matter. In absence of matter, the flow from the hyperscaling violating regime to the conformal AdS fixed point in holographic models corresponds to cosmological evolution from power-law expansion at early cosmic times to a de Sitter (dS) stable fixed point at late times. In presence of matter, we have a scaling regime at early times, followed by an intermediate regime in which dark energy tracks matter. At late times the solution exits the scaling regime with a sharp transition to a dS spacetime. The phase transition between hyperscaling violation and conformal fixed point observed in holographic gravity has a cosmological counterpart in the transition between a scaling era and a dS era dominated by the energy of the vacuum.Comment: 18 pages, 4 figures. V2:Some typo errors and Eq. (3.12) corrected, three references adde