Existence of Wormhole solutions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1922" altimg="si6.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.16667em" /><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity under non-commutative geometries

Wormhole geometries in modified teleparallel gravity and theenergy conditions

Self-consistent Wormhole Solutions of Semiclassical Gravity

We present the first results of a self-consistent solution of the semiclassical Einstein field equations corresponding to a Lorentzian wormhole coupled to a quantum scalar field. The specific solution presented here represents a wormhole connecting two asymptotically spatially flat regions. In general, the diameter of the wormhole throat, in units of the Planck length, can be arbitrarily large,...

Gravity in Non-Commutative Geometry

We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gr...

Evolving wormhole geometries

In the last two decades, there has been a revival on the study of classical wormhole solutions either in General Relativity (GR) or in alternative theories of gravitation. A cornerstone in this revival has been the paper of Morris and Thorne [1] in which, they derived the properties that a space-time must have in order to hold up such a geometry. Let us recall that the most salient feature of t...

Non-commutative Zariski geometries and their classical limit

We undertake a case study of two series of nonclassical Zariski geometries. We show that these geometries can be realised as representations of certain noncommutative C∗-algebras and introduce a natural limit construction which for each of the two series produces a classical U(1)-gauge field over a 2-dimensional Riemann surface.