2020/01/02 by Thomas Schürmann, Schürmann, Thomas
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2001.02078
openalex publication_date 2020/01/02 · openalex created_date 2020/07/16 · openalex updated_date 2026/07/29
Prescribing both the areal-radius metric function F(r) and the scalar profile ϕ(r) generally overdetermines static Einstein-scalar reconstruction. The temporal and radial Einstein equations determine a redshift function and an algebraic radial source Valg(r), but do not by themselves impose the angular equation or guarantee a single-valued scalar potential. On a connected static interval we formulate the corresponding membership criterion for independently prescribed pairs: a potential-independent residual C[F,ϕ] must vanish, and Valg must descend across the full scalar image to one branch-independent C1 potential, with stationarity at values attained on constant-profile intervals. The compatibility and descent requirements are independent. As a positive benchmark, the criterion recovers the logarithmic Matos-Guzmán-Núñez scalar halo with its exponential potential. At a radially regular center we compute the leading scalar backreaction on F. Applied to a rational kink profile with rational curvature interpolation, exact compatibility forces the scalar amplitude to vanish for every integer n≥2, giving an ansatz-specific compatibility obstruction rather than a no-hair or classification theorem.