Minimal Log Gravity

Minimal Massive Gravity (MMG) is an extension of three-dimensional Topologically Massive Gravity that, when formulated about Anti-de Sitter space, accomplishes to solve the tension between bulk and boundary unitarity that other models in three dimensions suffer from. We study this theory at the chiral point, i.e. at the point of the parameter space where one of the central charges of the dual conformal field theory vanishes. We investigate the non-linear regime of the theory, meaning that we study exact solutions to the MMG field equations that are not Einstein manifolds. We exhibit a large class of solutions of this type, which behave asymptotically in different manners. In particular, we find analytic solutions that represent two-parameter deformations of extremal Banados-Teitelboim-Zanelli (BTZ) black holes. These geometries behave asymptotically as solutions of the so-called Log Gravity, and, despite the weakened falling-off close to the boundary, they have finite mass and finite angular momentum, which we compute. We also find time-dependent deformations of BTZ that obey Brown-Henneaux asymptotic boundary conditions. The existence of such solutions show that Birkhoff theorem does not hold in MMG at the chiral point. Other peculiar features of the theory at the chiral point, such as the degeneracy it exhibits in the decoupling limit of the Cotton tensor, are discussed.Comment: 13 pages. v2 minor typos corrected. Accepted for publication in Phys. Rev.

AdS and Lifshitz black hole solutions in conformal gravity sourced with a scalar field

In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass and zero entropy, although they have non-zero temperature. A similar behavior has been observed in previous works, where the integration constant is not associated with a conserved charge, and it can be interpreted as a kind of gravitational hair. On the other hand, the Lifshitz black holes with dynamical exponent $z=4$ have non-zero conserved charges, and the first law of black hole thermodynamics holds. Also, we analyze the horizon thermodynamics for the Lifshitz black holes with $z=4$, and we show that the first law of black hole thermodynamics arises from the field equations evaluated on the horizon. Furthermore, we study the propagation of a conformally coupled scalar field on these backgrounds and we find the quasinormal modes analytically in several cases. We find that for anti-de Sitter black holes and Lifshitz black holes with $z=4$, there is a continuous spectrum of frequencies for Dirichlet boundary condition; however, we show that discrete sets of well defined quasinormal frequencies can be obtained by considering Neumann boundary conditions

About the coordinate time for photons in Lifshitz Space-times

In this paper we studied the behavior of radial photons from the point of view of the coordinate time in (asymptotically) Lifshitz space-times, and we found a generalization to the result reported in previous works by Cruz et. al. [Eur. Phys. J. C {\bf 73}, 7 (2013)], Olivares et. al. [Astrophys. Space Sci. {\bf 347}, 83-89 (2013)], and Olivares et. al. [arXiv: 1306.5285]. We demonstrate that all asymptotically Lifshitz space-times characterized by a lapse funcion $f(r)$ which tends to one when $r\rightarrow \infty$, present the same behavior, in the sense that an external observer will see that photons arrive at spatial infinity in a finite coordinate time. Also, we show that radial photons in the proper system cannot determine the presence of the black hole in the region $r_+<r<\infty$, because the proper time results to be independent of the lapse function $f(r)$.Comment: 5 pages, 4 figures, accepted for publication on EPJ

Fermionic greybody factors of two and five-dimensional dilatonic black holes

We study fermionic perturbations in the background of a two and five-dimensional dilatonic black holes. Then, we compute the reflection and transmission coefficients and the absorption cross section for fermionic fields, and we show numerically that the absorption cross section vanishes in the low and high frequency limit. Also we find that beyond a certain value of the horizon radius $r_0$ the absorption cross section for five-dimensional dilatonic black hole is constant. Besides, we have find that the absorption cross section decreases for higher angular momentum, and it decreases when the mass of the fermionic field increases.Comment: Accepted in EPJ

Particle collisions near a three-dimensional warped AdS black hole

In this paper we consider the warped AdS$_{3}$ black hole solution of topologically massive gravity with a negative cosmological constant, and we investigate the possibility that it acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon, which is known as the Ba\~nados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum $(L_c)$ of the particle decreases when the parameter that controls the stretching deformation ($\nu$) increases. Also, we show that despite the particle with $L_c$ can exist for certain values of the conserved energy outside the horizon, it will never reach the event horizon; therefore, the black hole can not act as a particle accelerator with arbitrarily high CM energy on the event horizon. However, such particle could also exist inside the outer horizon being the BSW process possible on the inner horizon. On the other hand, for the extremal warped AdS$_{3}$ black hole, the particle with $L_c$ and energy $E$ could exist outside the event horizon and the CM energy blows up on the event horizon if its conserved energy fulfill the condition $E^{2}>\frac{(\nu^{2}+3)l^{2}}{3(\nu^{2}-1)}$, being the BSW process possible.Comment: 11 pages, 6 figure