Black holes against the universe – particle and photon orbits in McVittie spacetimes

Brien Nolan

Brien Nolan is a Senior Lecturer in the School of Mathematical Sciences, Dublin City University

Black holes have a potential technological application that is frequently overlooked: they allow you to look at the back of your own head. This could be useful for checking that your tie is properly tucked into your shirt collar, or – perhaps more relevant for physicists – that your pony tail is straight. This technology relies on the fact that there exist circular photon orbits in all members of the Kerr-Newman-de Sitter family of spacetimes for which the parameters (mass, charge and cosmological constant) correspond to a black hole.

The question arises as to whether this characteristic feature of electro-vac black holes carries over to more general settings – for example, to the case of black holes embedded in cosmological backgrounds. On the other hand, the question of the existence of closed or bound orbits provides a tool that aids the interpretation of spacetime metrics purporting to represent black holes in cosmological backgrounds. Going further, one sees that the existence of bound orbits around a black hole in a cosmological background would influence cosmological observations. This would arise, for example, through the calculation of the angular diameter distance, where the strong local effects of the black hole would have to be taken into account. For massive particles, there is also the possibility of the formation of accretion disks in cosmological backgrounds.

In our article we have studied this question – the existence of circular or bound particle and photon orbits – in the family of McVittie spacetimes. McVittie spacetimes represent an embedding of the Schwarzschild field in isotropic cosmological backgrounds. Depending on the scale factor of the background, and the presence or otherwise of a cosmological constant, the resulting spacetime may contain black and white hole horizons, as well as other interesting boundary features. By using center manifold (and other) methods from dynamical systems, we have found that in physically relevant cases, circular orbits are absent, but bound photon and particle orbits exist. These orbits are asymptotic at late times to circular orbits of Schwarzschild or Schwarschild-de Sitter spacetime. Thus there are always particles that are not swept up in the accelerating cosmological expansion, but that opt for the comfort of a stable orbit around the central black hole.

Read the full article in Classical and Quantum Gravity:
Particle and photon orbits in McVittie spacetimes
Brien C Nolan
2014 Class. Quantum Grav. 31 235008

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