In my speech, I will discuss the main problems of Conic Presentism (PS), as well as possible strategies to defend this position. First of all, I would like to point out that in PS the symmetry and transitivity of existence is not preserved. Next, it will be raised that the formulation of PS depends on the adoption of the time orientation of space-time, which is not found in the Special Relativity laws, but only in the boundary conditions. Finally, metaphysically interesting consequences of PS in the gravitational field described by general relativity will be indicated, such as the issue of the existence of objects in Schwarzschild space-time.