Phase Space of SdS Geodesics and using the Cosmological Horizon to Observe a Black Hole

TL;DR

This paper explores how the positive cosmological constant in Schwarzschild de Sitter spacetime allows observers to detect signals from near a black hole horizon by utilizing the blueshift effect at the cosmological horizon, analyzing geodesics and optimal observation strategies.

Contribution

It introduces a detailed analysis of SdS geodesics and demonstrates how the cosmological horizon can be used to observe highly redshifted signals from near the black hole horizon, revealing new observational strategies.

Findings

Existence of a critical curve with multiple circular orbits in SdS spacetime

Optimal observation occurs when the receiver is near the cosmological horizon and moving towards the black hole

Cosmological constant enhances observability by a factor up to three for certain photon emissions

Abstract

Light propagating from near a black hole horizon to the outside world is highly redshifted. In the limit that the emitter passes through the horizon, the redshift becomes infinite. In this sense the near horizon region is unobservable, as emission energies fall below some detectability bound. However, in Schwarzschild de Sitter (SdS) spacetime there is a second, cosmological, horizon due to the positive cosmological constant. Judiciously placed observers can take advantage of the blueshift due to this horizon. The frequency of signals emitted from near the black hole can be shifted back upward to an observable value. This effect is computed for a variety of accelerated and geodesic observers. An analysis of radial and circular geodesics in SdS is a key component of the paper. We find a ``cresting-wave" shaped critical curve in the SdS-geodesic parameter space such that under the curve there are three circular orbits, on the curve there are two orbits, and elsewhere there is one. It is found that the best strategy for observing photons from an emitter falling into the black hole is for the receiver to be near the cosmological horizon and also moving towards the black hole. For photons emitted from the smallest circular orbit and received at the largest circular orbit, the nonzero cosmological constant enhances observations by a factor that varies from zero to three.