Determining the Topology and Deflection Angle of Ringholes via Gauss-Bonnet Theorem

In this letter, we use a recent wormhole solution known as a ringhole [Gonzalez-Diaz, Phys.\ Rev.\ D {\bf 54}, 6122, 1996] to determine the surface topology and the deflection angle of light in the weak limit approximation using the Gauss-Bonnet theorem (GBT). We apply the GBT and show that the surface topology at the wormhole throat is indeed a torus by computing the Euler characteristic number. As a special case of the ringhole solution, one can find the Ellis wormhole which has the surface topology of a 2-sphere at the wormhole throat. The most interesting results of this paper concerns the problem of gravitational deflection of light in the spacetime of a ringhole geometry by applying the GBT to the optical ringhole geometry. It is shown that, the deflection angle of light depends entirely on the geometric structure of the ringhole geometry encoded by the parameters $b_0$ and $a$, being the ringhole throat radius and the radius of the circumference generated by the circular axis of the torus, respectively. As special cases of our general result, the deflection angle by Ellis wormhole is obtained. Finally, we work out the problem of deflection of relativistic massive particles and show that the deflection angle remains unaltered by the speed of the particles.Comment: 7 pages, two-column, 1 figur

Light Deflection with Torsion Effects Caused by a Spinning Cosmic String

Using a new geometrical method introduced by Werner, we find the deflection angle in the weak limit approximation by a spinning cosmic string in the context of the Einstein-Cartan (EC) theory of gravity. We begin by adopting the String-Randers optical metric, then we apply the Gauss-Bonnet theorem to the optical geometry and derive the leading terms of the deflection angle in the equatorial plane. Calculations shows that light deflection is affected by the intrinsic spin of the cosmic string and torsion.Comment: 7 pages, accepted for publication in European Physical Journal

Quantum Tunneling of Spin-1 Particles from a 5D Einstein-Yang-Mills-Gauss-Bonnet Black Hole Beyond Semiclassical Approximation

In the present paper we study the Hawking radiation as a quantum tunneling effect of spin-$1$ particles from a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (5D EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results in a set of five differential equations, and reproduces in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the entropy of the 5D EYMGB black hole and show that the quantum corrected specific heat indicates the possible existence of a remnant.Comment: 7 pages, accepted by EPL (Europhysics Letters