Definition of a photon surface in an invariant spin frame

D Dey, AA Coley, NT Layden�- Physical Review D, 2024 - APS
D Dey, AA Coley, NT Layden
Physical Review D, 2024APS
This paper defines the photon surface conditions using Cartan scalars within an invariant
spin frame, offering a comprehensive description of the local spacetime geometry. By
employing this approach, we gain novel insights into the geometry and dynamics of photon
surfaces, independent of the global spacetime structure. We first discuss the photon surface
conditions in a Petrov type-D spacetime manifold, and then we simplify those conditions
assuming the existence of spherical symmetry. Finally, employing the simplified, spherically�…
This paper defines the photon surface conditions using Cartan scalars within an invariant spin frame, offering a comprehensive description of the local spacetime geometry. By employing this approach, we gain novel insights into the geometry and dynamics of photon surfaces, independent of the global spacetime structure. We first discuss the photon surface conditions in a Petrov type-D spacetime manifold, and then we simplify those conditions assuming the existence of spherical symmetry. Finally, employing the simplified, spherically symmetric photon surface conditions, we explore the dynamics of photon surfaces in static, collapsing Lemaitre-Tolman-Bondi (LTB) spacetimes and Vaidya spacetimes. Notably, we show that photon surfaces can emerge from the central singularity during the collapse of an inhomogeneous dust cloud modeled by a LTB spacetime. This underscores the significance of our findings in comprehending the potential observational implications of the physics near the ultrahigh gravity region.
American Physical Society