Metric theory of gravity with torsion in an extra dimension

We consider a theory of gravity with a hidden extra dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra dimension and the extra dimension stays hidden at the level of four-dimensional geodesic motion. At the kinematic level, the theory maps onto general relativity, but the dynamical field equations that follow from the action principle deviate markedly from the standard Einstein equations. We study static spherically symmetric vacuum solutions and homogeneous-isotropic cosmological solutions that emerge from the field equations. In both cases, we find solutions of significant physical interest. Most notably, we find positive mass solutions with naked singularity that match the well-known Schwarzschild solution at large distances but lack an event horizon. In the cosmological context, we find an oscillatory scenario, in contrast to the inevitable singular big bang of the standard cosmology.

Figure 1

Schematic representation of the 5D geometry.

Figure 2

Solutions for $a(t)$ for different values of the deceleration parameter for $k=0$ and $k=+1$.

Figure 3

$\beta$ is plotted as a function of $c$.

Figure 4

Numerical solution to $F(r)$ with $\lambda =-1$.

Figure 5

Schematic behavior of $A(r)$ and $B(r)$.