For decades, black holes have fascinated scientists and nonscientists alike. Their ominous voids, like an open pair of jaws, has inspired a whole wave of science-fiction featuring the phenomenon. Physicists have also been similarly inspired, specifically to understand the dynamics of what is happening inside of the black hole, especially for objects thatmay fall in. The historical theories about black holes are closely linked to those within quantum physics and they suggest interesting phenomena. “The best models of black holes we have in general relativity, like the Kerr metric or the Reissner-Nordström metric, actually make some pretty crazy predictions,” explained JILA graduate student Tyler McMaken. “After you fall in, you eventually reach a spot, called the inner horizon, where we can enter into a wormhole, see a naked singularity [A region in space-time at which matter is infinitely dense], time-travel, and do a bunch of things that go against what we think should be physically possible.” To better understand the quantum mechanics of these black hole models, McMaken and JILA Fellow Andrew Hamilton and looked into the quantum effects that may be happening around and inside a black hole. From their research, they found that there was a divergence of energy into multiple levels at the inner horizon of the black hole, suggesting that quantum effects play a crucial role in how to model realistic black holes. “The exciting part of this research is the discovery that quantum effects save the day—as you approach the inner horizon, you're met with a wall of diverging energy from Hawking radiation, so that any weird, causality-violating parts of the spacetime are completely blocked off and replaced with a singularity,” McMaken added. This diverging energy split the radiation into multiple levels. “Without a full theory of quantum gravity, we won’t know exactly what happens at this singularity, but we do know that just like the Big Bang singularity, or the singularity we might find in simpler spherical black holes, it marks the end of spacetime as we know it as the curvature exceeds the Planck scale.” The results of the study have been submitted by McMaken and Hamilton for publication in the journal Physical Review D.
Looking into a Black Hole
The concept Hamilton and McMaken started with for their research seemed relatively straightforward. “We’re trying to figure out what happens if you add the effects of quantum field theory to black holes,” explained McMaken. As a marker for how quantum field theory would affect things falling into the black hole, Hamilton and McMaken focused on the detection of Hawking radiation. Hawking radiation is created by the interactions of particles and antiparticles that surround the black hole. According to McMaken: “You have a sea of virtual particles and antiparticles that pop into existence from the quantum vacuum and then annihilate each other. Hawking radiation is what happens when one particle is just outside the horizon of the black hole, while the other gets absorbed inside the black hole [a Hawking pair]. They never get the chance to meet up and cancel each other out again.” As McMaken explained further, most physicists are interested in looking at Hawking radiation produced right at the horizon and detected at a far distance from a black hole. But these Hawking pairs are being ripped apart everywhere in the spacetime, and McMaken and Hamilton wanted to look at where the radiation is happening the most, right at the edge of the black hole’s inner horizon.
While Hawking radiation seemed to be a straightforward proxy for understanding the semiclassical behavior of the system, actually calculating the measured Hawking radiation was a bit more complicated. “Though we think of Hawking radiation in terms of particle-antiparticle pairs, that's actually not how it's usually calculated,” McMaken stated. “Instead, we think in terms of waves moving through the quantum field. When those waves become exponentially red-shifted, or stretched apart, then we detect this as the radiation.” From their models, Hamilton and McMaken found something rather interesting. “Close to the inner horizon [of the black hole], those waves start blue-shifting, or getting squashed, until you see a diverging amount of energy there.”
Falling into the Black Hole
This energy divergence, while at first confusing to the researchers, ended up being a crucial part of a black hole faller-in’s journey. “Conceptually, if you're falling into a black hole, you’ve probably heard that you will get ‘spaghettified,’” McMaken said. “So if you're falling in feet first, then the gravity is going to pull stronger at your feet than it will at your head, and you'll end up getting stretched out like a spaghetti noodle. That same force is going to pull apart the Hawking pairs.” While this did not sound like a comfortable process, it only got worse as one traveled along. “But for realistic black holes, which are rotating and accreting matter, once you get close enough, then the opposite starts to happen—instead of getting stretched out, you'll end up getting squashed. So, the forces at your head will end up getting stronger and stronger than those at your feet, until you get squished up like a pancake. I guess you could call it ‘pancakification.’” This sudden shift in force was where McMaken and Hamilton saw the divergence in Hawking radiation. As McMaken explained, “there's some amazing effect, where the particles have such a large amount of energy that they still manage to escape the event horizon even though gravity is trying to squash them back together. And we end up calling this a negative temperature.” The idea of a negative temperature comes from Stephen Hawking, who proposed that the temperature of a black hole is related to its mass. Because black holes can have a negative mass (as they are absorbing other masses), they may also have a negative temperature. While the concept of negative temperature shows up in many different areas of physics, the researchers still aren't entirely sure exactly what that means for the black hole system’s dynamics, even though they can observe and measure it. “Something has to happen there,” McMaken stated. “And exactly what it is, is going to inform us a lot about quantum gravity as a theory.”
The results that Hamilton and McMaken found also have some interesting implications for the field of astrophysics. “On the astrophysics side, there are some interesting things that are perhaps worth exploring,” McMaken added. “We’ve mostly been interested in how we can consistently model the inside of a black hole, which gives helpful insights about quantum gravity but not so much for observations. But one of the things that we mentioned in our paper is that this negative temperature can be detected outside the black hole in certain cases. If you have a high enough charge—or by analogy if the black hole is spinning fast enough—then you should start to see negative temperatures even above the event horizon, which might affect how particles in the accretion disk interact with it.” While this study revealed a whole new batch of questions to be answered, it also upheld the black hole’s mysterious and strange reputation within the scientific community.
Written by Kenna Hughes-Castleberry, JILA Science Communicator