Compact scalar field solutions in EiBI gravity

We discuss exact scalar field solutions describing gravitating compact objects in the Eddington-inspired Born–Infeld (EiBI) gravity, a member of the class of (metric-affine formulated) Ricci-based gravity (RBG) theories. We include a detailed account of the RBGs/GR correspondence exploited to analytically solve the field equations. The single parameter [Formula: see text] of the EiBI model defines two branches for the solution. The [Formula: see text] branch may be described as a “shell with no interior”, and constitutes an ill-defined, geodesically incomplete spacetime. The more interesting [Formula: see text] branch admits the interpretation of a “wormhole membrane”, an exotic horizonless compact object with the ability to transfer particles and light from any point on its surface (located slightly below the would-be Schwarzschild radius) to its antipodal point, in a vanishing fraction of proper time. This is a single example illustrating how the structural modifications introduced by the metric-affine formulation may lead to significant departures from General relativity (GR) even at astrophysically relevant scales, giving rise to physically plausible objects radically different from those we are used to think of in the metric approach, and that could act as a black hole mimickers whose shadows might present distinguishable signals.

Spherical Venn Diagrams with Involutory Isometries

In this paper we give a construction, for any $n$, of an $n$-Venn diagram on the sphere that has antipodal symmetry; that is, the diagram is fixed by the map that takes a point on the sphere to the corresponding antipodal point. Thus, along with certain diagrams due to Anthony Edwards which can be drawn with rotational and reflective symmetry, for any isometry of the sphere that is an involution, there exists an $n$-Venn diagram on the sphere invariant under that involution. Our construction uses a recursively defined chain decomposition of the Boolean lattice.

Ray paths and caustics on a slightly oblate ellipsoid

We investigate the ray paths from a point-source S on a slightly oblate ellipsoidal shell. The caustics are found to form a 4-star, i.e. a regular, 4-cusped hypocycloid, centred on the point antipodal to S. The length-scale of the 4-star varies as ϵ cos 2 λ , where ϵ is the eccentricity and λ is the latitude of the antipodal point.