Static wormholes on the brane inspired by Kaluza-Klein gravity

TL;DR

This paper derives static, spherically symmetric solutions from 5D Kaluza-Klein gravity that include black holes, wormholes, and naked singularities, revealing new features like multiple extremal surfaces and non-horizon throats in brane-world scenarios.

Contribution

It introduces novel static brane-world solutions with multiple extremal surfaces and non-horizon wormholes, extending previous models and exploring their physical properties.

Findings

Solutions include black holes, wormholes, and naked singularities.

Existence of multiple extremal surfaces with different properties.

Wormhole throats can be smaller than Schwarzschild radius, lacking horizons.

Abstract

We use static solutions of 5-dimensional Kaluza-Klein gravity to generate several classes of static, spherically symmetric spacetimes which are analytic solutions to the equation $^{(4)}R = 0$, where $^{(4)}R$ is the four-dimensional Ricci scalar. In the Randall $&$ Sundrum scenario they can be interpreted as vacuum solutions on the brane. The solutions contain the Schwarzschild black hole, and generate new families of traversable Lorenzian wormholes as well as nakedly singular spacetimes. They generalize a number of previously known solutions in the literature, e.g., the temporal and spatial Schwarzschild solutions of braneworld theory as well as the class of self-dual Lorenzian wormholes. A major departure of our solutions from Lorenzian wormholes {\it a la} Morris and Thorne is that, for certain values of the parameters of the solutions, they contain three spherical surfaces (instead of one) which are extremal and have finite area. Two of them have the same size, meet the "flare-out" requirements, and show the typical violation of the energy conditions that characterizes a wormhole throat. The other extremal sphere is "flaring-in" in the sense that its sectional area is a local maximum and the weak, null and dominant energy conditions are satisfied in its neighborhood. After bouncing back at this second surface a traveler crosses into another space which is the double of the one she/he started in. Another interesting feature is that the size of the throat can be less than the Schwarzschild radius $2 M$, which no longer defines the horizon, i.e., to a distant observer a particle or light falling down crosses the Schwarzschild radius in a finite time.