The surprising behavior of black holes in an expanding universe

A physicist studying black holes discovered that in an expanding universe, Einstein’s equations require that the rate of expansion of the universe at the event horizon of each black hole be a constant, the same for all black holes. In turn, this means that the only energy at the event horizon is dark energy, the so-called cosmological constant. The study is published on the arXiv preprint server.

“Otherwise,” said Nikodem Popławski, a lecturer at the University of New Haven, “the pressure of matter and the curvature of space-time would have to be infinite at a horizon, but that’s not physical.”

Black holes are a fascinating subject because they are the simplest things in the universe: their only properties are mass, electric charge, and angular momentum (spin). Yet their simplicity gives rise to a fantastic property: they have an event horizon located at a critical distance from the black hole, an unphysical surface around it, spherical in the simplest cases. Anything closer to the black hole, that is, inside the event horizon, can never escape the black hole.

Black holes were predicted in 1916 by Karl Schwarzschild while serving as a German soldier on the Russian front, while suffering from a painful autoimmune skin disease, pemphigus.

Using Einstein’s equations of general relativity, he assumed a massive, non-rotating, perfectly round object in an otherwise empty and unchanging universe and discovered the event horizon. The radius of the event horizon is proportional to the mass of a black hole. On the horizon, not even light, the fastest object in the universe, can escape the hole.

Schwarzschild also discovered an apparent singularity at the center of the black hole, a place of infinite density where Einstein’s laws of gravity seem to break down.

Astronomers have since discovered that most galaxies appear to have a supermassive black hole at their center; for the Milky Way, it is Sagittarius A*, with a mass more than four million times that of the sun. A black hole was only directly photographed in 2019, a black spot surrounded by a halo of light, located in the center of the galaxy Messier 87, 55 million light years from Earth.

Beyond Schwarzschild, Popławski assumed a massive object with central symmetry in an expanding universe. In this case, the solution to Einstein’s equations for the structure of space-time around mass was first obtained in 1933 by the British mathematician and cosmologist George McVittie.

McVittie discovered that near mass, spacetime is like Schwarzschild, with an event horizon, but that far from mass, the universe expands like our universe today. The Hubble parameter, also called the Hubble constant, specifies the rate of expansion of the universe.

Popławski used McVittie’s solution to discover that the rate of expansion of space at the event horizon must be a constant, related only to the cosmological constant (which can be interpreted as the energy density of the vacuum of spacetime). Today we know this as the density of dark energy. In other words, the only energy at the horizon is dark energy. The consequence, he said, is that different parts of the universe are expanding at different rates.

In fact, something similar was found with the so-called “Hubble tension”, a statistically significant discrepancy between two different measured values ​​of the Hubble parameter, depending on whether one uses “late universe” measurements or “early universe” techniques based on measurements of the cosmic microwave background. In his work, Popławski stated that this discrepancy “is a natural consequence of a correct analysis of the spacetime of a black hole in an expanding universe within the framework of Einstein’s theory of general relativity”.

Furthermore, his equations show that one of the consequences of the universe expanding at different rates is that the cosmological constant – and therefore the value of dark energy – must be positive. Otherwise, without this constant, says Popławski, “a closed universe would be oscillatory and could not create cosmic voids.”

“This is the simplest explanation for the current acceleration observed in the universe.”

For a star, say, the universe is also expanding at its surface limit, but the body is not expanding because it is gravitationally and electromagnetically bound.

An event horizon, however, is a mathematically abstract thing, not made of matter or energy but simply of points in space, so a constant expansion rate of space is not surprising. The event horizon itself (and thus a black hole) is not expanding; points in space outside the horizon are moving away from it.

Real black holes rotate, but if the rotation is generally slow, Popławski’s conclusions should also apply to them with a good approximation. But measuring the Hubble parameter at an event horizon is currently impossible unless new techniques are developed.

An observer at the event horizon could in principle measure the Hubble parameter there, but would forever be unable to communicate its value to the rest of the universe as it passes beyond the event horizon, and no information cannot be sent back through it.

This ties in, Popławski said, with a hypothesis he published in 2010: that every black hole is actually a wormhole (an Einstein-Rosen bridge) to a new universe on the other side of its event horizon.

“The event horizon is a gateway from one universe to another,” he said. “This gate does not expand as the universe expands… If this happens for the event horizon of the universe-forming black hole, it should also work for the event horizons of other black holes in this universe.”

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