On the Scalar-Vector-Tensor Gravity: Black Hole, Thermodynamics and Geometrothermodynamics

Recently, a new class of modified gravity theories formulated via an additional scalar and vector field on top of the standard tensor field has been proposed. The direct implications of these theories are expected to be relevant for cosmology and astrophysics. In the present work, we revisit the modified framework of the scalar-vector-tensor theories of gravity. Surprisingly, we discover novel metric function for the black hole solutions. We also investigate the semi-classical thermodynamics of the black holes and study the thermodynamic properties of the obtained solutions. Moreover, we quantify the entropy and the temperature of the new black hole and also calculate the heat capacity. Finally, we also apply the formalism of the geometrothermodynamics to examine thermodynamic properties of the new black hole. This formalism yields results consistent with those obtained from the usual thermodynamic implementation.Comment: v2: 8 pages, 4 figures, texts modified and references added, version accepted by Physics Letters

Real Classical Geometry with arbitrary deficit parameter(s) α(I)\alpha(_{I}) in Deformed Jackiw-Teitelboim Gravity

An interesting deformation of the Jackiw-Teitelboim (JT) gravity has been proposed by Witten by adding a potential term $U(\phi)$ as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from integration over $\phi$ as $R(x)+2=2\alpha \delta(\vec{x}-\vec{x}')$. The resulting Euclidean metric suffered from a conical singularity at $\vec{x}=\vec{x}'$. A possible geometry modeled locally in polar coordinates $(r,\varphi)$ by $ds^2=dr^2+r^2d\varphi^2,\varphi \cong \varphi+2\pi-\alpha$. In this letter we showed that there exists another family of "exact" geometries for arbitrary values of the $\alpha$. A pair of exact solutions are found for the case of $\alpha=0$. One represents the static patch of the AdS and the other one is the non static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with $\alpha\neq 0$. We address a type of the phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at $x=x'$. We extended the study to the exact space of metrics satisfying the constraint $R(x)+2=2\sum_{i=1}^{k}\alpha_i\delta^{(2)}(x-x'_i)$ as a modulo diffeomorphisms for an arbitrary set of the deficit parameters $(\alpha_1,\alpha_2,..,\alpha_k)$. The space is the moduli space of Riemann surfaces of genus $g$ with $k$ conical singularities located at $x'_k$ denoted by $\mathcal{M}_{g,k}$.Comment: 21 pages, v3, New sections about BH solutions, time dependent geometry added, Title modified . References adde