Scalar curvature

About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.

Black holes in vector-tensor theories

Abstract: We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordstrom (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.

Three-dimensional space-times

Abstract: A real version of the Newman-Penrose formalism is developed for (2+1)-dimensional space-times. The complete algebraic classification of the (Ricci) curvature is given. The field equations of Deser, Jackiw, and Templeton, expressing balance between the Einstein and Bach tensors, are reformulated in triad terms. Two exact solutions are obtained, one characterized by a null geodesic eigencongruence of the Ricci tensor, and a second for which all the polynomial curvature invariants are constant.

A note on constant curvature solutions in cylindrically symmetric metric $f(R)$ Gravity

Abstract: In the previous work we introduced a new static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity\cite{1}. Now we obtain a 2-parameter family of exact solutions which contains cosmological constant and a new parameter as $\beta$. This solution corresponds to a constant Ricci scalar. We proved that in $f(R)$ gravity, the constant curvature solution in cylindrically symmetric cases is only one member of the most generalized Tian family in GR. We show that our constant curvature exact solution is applicable to the exterior of a string. Sensibility of stability under initial conditions is discussed.

On the non-minimal gravitational coupling to matter

Abstract: The connection between f(R) theories of gravity and scalar–tensor models with a 'physical' metric coupled to the scalar field is well known. In this work, we pursue the equivalence between a suitable scalar theory and a model that generalizes the f(R) scenario, encompassing both a non-minimal scalar curvature term and a non-minimum coupling of the scalar curvature and matter. This equivalence allows for the calculation of the PPN parameters β and γ and, eventually, a solution to the debate concerning the weak-field limit of f(R) theories.