Black Holes in an Expanding Universe (0912.2809v3)

Abstract: An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state. It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter (the ratio of the energy density of U(1) fields to that of the scalar field). The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature.

Black Holes in an Expanding Universe: An Expert Review

The paper "Black Holes in an Expanding Universe" by Gary W. Gibbons and Kei-ichi Maeda presents a comprehensive analysis of black holes within the framework of an expanding cosmological background, specifically the Friedmann-Lemaître-Robertson-Walker (FLRW) universe. This investigation is rooted in the Einstein-scalar-Maxwell system and employs a model wherein two Maxwell-type U(1) fields are coupled to a scalar field with an exponential potential. The authors succeed in deriving an exact solution which encapsulates maximally charged black holes in a dynamic cosmological setting, a problem that has remained intriguing in both astrophysics and theoretical physics contexts.

Overview of the Solution

The research introduces a model where black holes co-exist with an underlying expanding universe governed by an arbitrary equation of state, $P=w \rho$, within the range $-1 \leq w \leq 1$. The importance of this work is underscored by its ability to yield a regular horizon where gravitational forces are balanced against the repulsive forces originating from U(1) fields on the scalar field. The paper covers the notable achievement of finding a static horizon through this balance, an impressive feature given the cosmological dynamics involved.

Analytical Exploration and Implications

The solution derived in the paper features a multi-black hole system that asymptotically approaches a flat FLRW spacetime without introducing a deficit angle, and critically, no singularity exists outside the event horizons. This is a notable departure from earlier models, such as the McVittie solution, which have been unable to accurately describe a dynamic black hole processes in an expanding universe due to various disqualifications such as energy condition violations.

The paper is particularly notable for addressing the theoretical implications and potential applications in AI within cosmological contexts. The use of self-similar solutions suggests that they may provide insight into accelerating universes, an area ripe for further exploration given the current interest in phenomena like dark energy.

Future Directions and Questions

Several key questions for future work remain: extending the current solutions to more realistic models that involve rotations, understanding how black hole thermodynamics can be applied or extended in these dynamic contexts, and exploring collisions within these time-dependent solutions. The authors postulate connections with intersecting brane systems in higher-dimensional supergravity models, suggesting potential avenues for linking these results to broader frameworks in string theory and quantum gravity.

Strong Numerical Results

Numerically, the black hole temperatures and horizon radii provide critical insights into the dynamic nature of these systems. For instance, the surface gravity and corresponding temperatures on the horizons are calculated, revealing insights into the thermodynamic behavior of these black holes within an expanding universe.

Conclusion

Overall, the paper contributes significantly to the understanding of black holes within cosmological models. The complex interplay between gravitational forces and charged fields introduces a dynamic equilibrium that speaks to the rich possibilities of research at the intersection of general relativity, cosmology, and quantum field theory. The conclusions drawn offer a comprehensive pathway for further exploration, particularly as they may apply to future developments in AI and the modeling of cosmological phenomena.