M. Karam Ouharou

Forty years ago it was proposed that gas phase organic chemistry in the interstellar medium can be initiated by the methyl cation CH 3 +  ( 1–3 ), but hitherto it has not been observed outside the Solar System ( 4, 5 ). Alternative routes involving processes on grain surfaces have been invoked ( 6, 7 ). Here we report JWST observations of CH+3CH3+ in a protoplanetary disk in the Orion star forming region. We find that gas-phase organic chemistry is activated by UV irradiation. Introduction : In the realm of cosmic evolution, protoplanetary disks serve as the cradles of new star systems and planetary bodies. These disks, composed of gas and dust, harbor an intricate web of chemical reactions that sculpt the materials essential for planet formation. Among the diverse array of chemical species within these disks, the methyl cation (CH3+) stands out as a key molecular fragment. Recent research has shed light on the intriguing formation of the methyl cation through photochem...

The space-time of general relativity theory consists of a connected Hausdorff manifold M of dimension 4 , called the space-time, which admits a metric tensor g of Lorentz signature ( + + + − ) . A tensor of particular importance from both the physical and mathematical viewpoint is the Weyl tensor C . This tensor has the property that if the metric g is replaced by a metric g ′ which is conformally related to it (so that g ′ = ϕ g for a nowhere-zero real-valued function ϕ on M ), then it is unchanged. If C is zero on M , then g is locally conformally related to a flat metric on M . The tensor C is given in components in terms of the curvature components R a b c d , the Ricci tensor components R a b ≡ R c a c b , and the Ricci scalar (and with square brackets denoting the usual skew-symmetrization of indices) by (a1) In the late 1940s and early 1950s, A.Z. Petrov developed some elegant algebraic techniques which led to the classification of the Weyl tensor and which now b...

♯recovering_all_articles_to_their_official_publisher_Karam_Ouharou For any point x ∈ M let N ǫ x be the image under ex p x of the ball of radius ǫ in K ⊥ x , for ǫ > 0 sufficiently small ; let B ( x,ǫ ) = { t · z | z ∈ N ǫ x and | t | < ǫ } . For some ǫ 0 ( x ) > 0, ǫ < ǫ 0 ( x ) implies that for all z ∈ N ǫ x , γ z (the integral curve of K with γ z (0) = z ) intersects N ǫ x precisely in z : For otherwise, there are sequences of points { z n } and { ̄ z n } in N ǫ x (any ǫ small enough) approaching x with γ z n ( t n ) = ̄ z n for some t n 6 = 0; we can assume all t n > 0. For ǫ sufficiently small, N ǫ x is achronal within B ( x,ǫ ) (viewed as a spacetime in its own right), so γ z n must exit B ( x,ǫ ) before returning to it and encountering ̄ z n ; hence, t n > 2 ǫ . For n sufficiently large, this means (since γ z n is not an arbitrary timelike curve but is constrained to be one of the K -curves) γ z n enters the future of x before exiting B ( x,ǫ ), so γ z n...