Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows andgeneral relativity. Recentworkby the author and his collaborators attempts to set the foundations for a study of weak solutions defined on Riemannian or Lorentzian manifolds and includes an investigation of the existence and qualitative behavior of solutions. The metric on the manifold may either ...

We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author’s recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.

Modelling of the point spread function of the UKIRT IRCAM3 array was conducted in order to test for any extended emission around the X-ray binary Cyg X-3. We found that the point spread function cannot be represented by a simple Gaussian, but modelling of the stars required additional functions, namely Lorentzian and exponential components. After modelling for the PSF, we found that Cyg X-3 cou...

We expand on the idea that spacetime signature should be treated as a dy-namical degree of freedom in quantum field theory. It has been argued that the probability distribution for signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is reviewed, and certain consistency constraints on the generalized signature (i.e. the tangent ...