The Surprising Behavior of Black Holes in the Expanding Universe

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

“Otherwise,” said Nikodem Popławski, a distinguished lecturer at the University of New Haven, “the pressure of matter and the curvature of spacetime would have to be infinite at the horizon, but that’s unphysical.”

Black holes are a fascinating subject because they involve the simplest things in the universe: their only properties are mass, electric charge, and angular momentum (spin). Yet their simplicity gives rise to fantastic properties – they have an event horizon at a critical distance from the black hole, an unphysical surface around it, spherical in the simplest cases. Anything closer to the black hole, i.e. 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 the painful autoimmune skin disease pemphigus.

Using Einstein’s equations of general relativity, he postulated 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 the black hole. Inside the horizon, not even light, the fastest object in the universe, can escape through the hole.

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

Astronomers have since discovered that most galaxies 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 not directly imaged until 2019, a black spot with a halo of light around it, located at the center of the galaxy Messier 87, 55 million light-years from Earth.

Popławski went beyond Schwarzschild and postulated a massive, centrally symmetric object in an expanding universe. In this case, the solution to Einstein’s equations for the structure of space-time around matter was first obtained in 1933 by the British mathematician and cosmologist George McVittie.

McVittie discovered that near matter there is a Schwarzschild-like space-time, with an event horizon, but far from matter the universe expands like our universe today. The Hubble parameter, also called the Hubble constant, indicates the rate at which the universe is expanding.

Popławski used McVittie’s solution to find 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 dark energy density. This means that the only energy on 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 has been found for the so-called “Hubble tension”, which is a statistically significant difference between two different measured values ​​of the Hubble parameter depending on whether “late universe” measurements or “early universe” techniques based on measurements of the cosmic microwave background are used . Popławski said in his paper that this contradiction “is a natural consequence of the correct analysis of the spacetime of a black hole in an expanding universe within Einstein’s general theory of relativity”.

Furthermore, his equations show that a consequence of the universe expanding at different rates is that the cosmological constant—and thus the value of dark energy—must be positive. Otherwise, without this constant, Popławski said, “a closed universe would oscillate and not be able to form cosmic voids.”

“It is the simplest explanation for the observed current acceleration of the universe.”

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

However, the event horizon is a mathematically abstract thing, it is nothing composed of matter or energy, but only of points of space, so the constant rate of expansion of space there is not surprising. The event horizon (and thus the black hole) itself is not expanding; points of space outside the horizon move away from it.

Real black holes rotate, but if the rotation is typically slow, Popławski’s conclusions should also apply to them to a good approximation. But measuring the Hubble parameter at the 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 falls beyond the event horizon, and no information can be sent across it.

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

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

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