Here’s what you’ll learn when you read this story:
Black holes do not appear to develop measurable tidal distortions in response to outside influences carried by bosonic fields, so their tidal Love number is zero in those cases.
A new study suggests that the situation may differ for fermionic fields, including massless, neutrino-like Dirac fields, for which the tidal Love number may be nonzero.
If confirmed, the finding could open a new way to probe black holes, their interactions with fundamental fields, and possibly their internal structure.
Black holes tend to defy physics in a number of ways, leaving behind paradoxes and an overall breakdown of known physics in their wake. The same is true regarding the ways that tidal forces interact with black holes from external gravitational sources. This interaction is quantified by what’s known as a “tidal Love number,” and for decades, scientists have known that the tidal Love number for black holes is precisely zero, nada, zilch. This means that a black hole experiences no deformations when it comes into contact with outside gravitational influences. However, a new study published in the journal Physical Review D suggests that under certain conditions, black holes break that “zero” rule, in keeping with their reputation as the supermassive scientific headaches of the universe.
Love numbers were first formulated in 1909 by British mathematician Augustus Edward Hough (A.E.H.) Love, who wanted to understand the tidal deformation experienced by the Earth as it’s pulled on gravitationally by the Moon and the Sun. Today, these Love numbers help scientists explore the internal structure of objects as they shift and stretch due to tidal forces. But black holes—unlike Earth, or even ultra-dense objects like neutron stars—have an atypical Love number (to say the least).
“In general relativity, black holes exhibit a remarkable feature: their tidal Love numbers—associated with the conservative response to static tidal fields—vanish identically,” the authors wrote. “This result stands in sharp contrast with the behavior of other compact objects, which generically have nonzero tidal Love numbers […] the tidal Love numbers are nonzero also for black holes surrounded by matter distributions, for black holes in modified gravity theories and asymptotically nonflat spacetimes, and finally for higher-dimensional black holes.”
However, this study decided to analyze the Love number of black holes from another perspective: a fermionic one. Typically, Love numbers are derived from bosonic (force-carrying) sources, which include things like gravitational waves, electromagnetic fields, or scalar fields. But instead, the researchers behind this study analyzed Kerr black holes—uncharged black holes with angular momentum described by Einstein’s Theory of Relativity—using fermionic sources, such as the massless neutrino-like Dirac field (a mathematical field in quantum field theory).
The difference between the two approaches boils down to what are known as “ladder symmetries.” These symmetries essentially force a zero solution for bosonic perturbations, but the fermionic fields evade this constraint because their lowest multipole moment (a value that helps describe the gravitational structure of black holes) “admits a regular decaying solution,” according to the authors. This suggests that the black holes might contain fermionic “hair”—similar to a theoretical scenario known as electroweak hair, which describes a cloud of W and Z bosons from which a given black hole can extract energy and angular momentum.
“Our results highlight the distinctive role of fermions in potentially circumventing these theorems, and open new directions to probe the interplay between fundamental fields, black-hole structure, and strong-gravity phenomenology,” the authors wrote. If their research is confirmed, it could open a new avenue for exploring one of the most enigmatic celestial objects in the universe.
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