Understanding photon sphere and black hole shadow in dynamically evolving spacetimes (1903.06376v2)

Abstract: We have derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been presented for Vaidya, Reissner-Nordstr\"{o}m-Vaidya and de-Sitter Vaidya spacetimes. It has been pointed out that evolution of the photon sphere depends crucially on the validity of the null energy condition by the in-falling matter and may present an observational window to even test it through black hole shadow. We have also presented the evolution of the photon sphere for slowly rotating Kerr-Vaidya spacetime and associated structure of black hole shadow. Finally, the effective graviton metric for Einstein-Gauss-Bonnet gravity has been presented, and the graviton sphere has been contrasted with the photon sphere in this context.

Photon Sphere and Black Hole Shadow in Dynamical Spacetimes

The paper under consideration explores the highly nuanced subject of photon spheres and black hole shadows within dynamically evolving spacetimes, extending the classical understanding grounded in General Relativity (GR) by incorporating dynamical elements. By deriving differential equations governing the evolution of photon spheres in non-stationary gravitational fields, the authors open up new vistas in understanding how these features can lead to observational evidence regarding the validity of certain energy conditions and possibly offer insights into higher-order gravitational theories.

The exploration begins with an analysis of dynamically evolving black holes, particularly focusing on the photon sphere, which acts as a pivotal region surrounding a black hole where photons can orbit infinitely without falling into the singularity or escaping to infinity. The interaction between the evolving spacetime metric and these photon spheres is quantified through differential equations that govern their dynamics, crucially depending on whether the spacetime respects the null energy condition (NEC).

Key Findings

1. Photon Sphere Evolution: The paper meticulously derives the evolution equation for the radius of the photon sphere in dynamical spacetimes, illustrating its relevance through numerical solutions in various contexts such as Vaidya, Reissner-Nordström-Vaidya, and de Sitter-Vaidya spacetimes. It is revealed that the evolution of the photon sphere is sensitive to the violation of NEC, a result that might be observationally significant.
2. Effect on Black Hole Shadow: Moving beyond photon spheres, this paper provides a framework for understanding how shadows, a potentially observable phenomenon, evolve in these dynamic scenarios. For researchers interested in astrophysical observations, this aspect of the research highlights the potential to probe spacetime characteristics more directly.
3. Rotating Black Holes: Incorporating rotation, the paper extends the analysis to Kerr-Vaidya spacetimes, albeit in the slow rotation limit. This extension includes deriving differential equations within this framework and discussing the apparent shadows cast by such black holes.
4. Higher-order Gravity Theories: Beyond the scope of GR, the effective graviton metrics within Einstein-Gauss-Bonnet gravity are considered. Here, the authors intricately show the divergence between photon and graviton spheres due to superluminal propagation in higher-order theories, indicating potential deviations that could provide observational tests for GR and its successors.

Implications and Future Directions

The implications of this paper are manifold. On a practical level, the evolution dynamics of photon spheres and shadows could refine the calibration of instruments designed to observe these phenomena, such as the Event Horizon Telescope. Moreover, understanding photon and graviton spheres in relation to NEC violation might provide novel insights into spacetime behavior during black hole accretion phases, potentially challenging some established astrophysical models.

The theoretical ramifications touch upon the verification of GR against alternative gravity models. The contrast between photon and graviton spheres in non-Einsteinian frameworks stresses the need for exploring gravitational theories beyond the classical GR paradigm. As observational technology advances, telescopes might not only confirm the presence of black hole shadows but also offer clues pointing to the signatures of phenomena unexplained by GR.

In conclusion, this paper enriches the theoretical landscape concerning black hole physics, proposing new mechanisms and critiquing established theories in light of dynamic spacetime interactions. Continuing research in this direction could bridge gaps between theory and observation, enabling us to discern new phenomena and perhaps unveil the interface where quantum and gravitational principles coalesce. Such investigations would likely inform future development in both fundamental physics and cosmological studies.