Figure 1: A photo showing the merging of two black holes into one. This event - a black hole merger - produced the first ever inductive evidence for gravitational waves in 2015.
Source Credit: Laser Interferometer Gravitational-Wave Observatory Gallery (LINK)
In the 1970s, the renowned theoretical physicist Stephen Hawking proposed the Black Hole Area Law (it then became one of the four laws of black hole thermodynamics) which, in mathematical terms, is stated as the following: “The surface area of a black hole, assuming the weak energy condition, is a non-decreasing function of time–that is to say, dA/dt ≥ 0.” Let us break this law down. First, the surface area of a black hole is the area of the region encompassed by the black hole’s event horizon–the boundary at which even light can no longer escape the gravity of the black hole (this is why the surface area of the black hole is often referred to as the ‘horizon area’). Next, the weak energy condition implies that the local energy density of any system under consideration must be nonnegative;in other words, the amount of energy per volume must be greater than or equal to zero. Finally, to say that the surface area is a ‘non-decreasing function of time’ is the same as saying that as time progresses, the horizon area of a black hole will never decrease: it will only ever increase or stay the same.
Speaking in terms of relativity, the law asserts that the surface area that the black hole gains from absorbing mass-energy from its surroundings will always outsize the loss of surface area due to the absorbed mass-energy increasing the spin of a black hole.
In order to gather inductive evidence for this law, Maximiliano Isi, a researcher at the Massachusetts Institute of Technology, along with his team published a paper on May 26, 2021, in which they used data from a black hole merger event (in which two black holes merged into one) to assess whether or not the horizon area of the merged black hole was larger than the sum of the horizon areas of the two black holes that merged together. The investigation yielded a positive result (with a confidence level of 95%), thereby upholding Hawking's surface area law.
However, there are still uncertainties in the law. According to Matt Visser, a professor of mathematics at Victoria University of Wellington, “The very fact that Hawking evaporation occurs at all violates the area increase theorem...for classical black holes. This implies that the quantum process underlying the Hawking evaporation process must also induce a violation of one or more of the input assumptions used in proving the classical area increase theorem...” In Hawking radiation, a pair of virtual particles appear at the event horizon of a black hole. One gets absorbed by the black hole, and the other escapes out into the universe. What this implies is that over very large spans of time, even black holes will eventually evaporate, which goes against Hawking's law which purports that horizon area never decreases. Though this topic is interesting, in order to get a better perspective into this issue, there is still a need to further develop our theories of quantum gravity.
Q&A:
Sally: Are there any recent discoveries that support or compromise the Black Hole Area Law? Or are there other laws that deal with similar forms of energy, density, and time that may help us believe that this law is realistic?
As mentioned in the article, the very existence of Hawking radiation threatens the black hole area law by purporting its evaporation over long periods of time. One law that is similar in nature with the black hole area law is the second law of thermodynamics, which states that entropy is a nondecreasing function of time (not on the local scale, but on the universal scale). This law proves useful in the proof of the black hole area theorem (under certain conditions), thus providing some realist evidence for the law.
Xavier: How will an increased understanding of black holes impact the field of science and its future?
Not only will the knowledge of black holes be accumulated for the sake of itself, but we might be able to answer the question regarding the information paradox at the black hole. When a black hole sucks in mass-energy, it is believed that information about the object is forever lost, contrary to the quantum mechanical results that state that information is never lost. By increasing our understanding of black holes, we might be able to refine such theories of science.
Wooseok: It seems like some of the laws go against each other - which one is most widely believed among scientists in modern day? Is there a specific reason why?
These consequences aren’t consistent because our theories of general relativity and quantum mechanics aren’t compatible. If, in the future, we are able to devise a consistent theory of quantum gravity or provide sufficient evidence for other theoretical frameworks like string theory, we may be able to make these theoretical consequences compatible. Conclusively, whether or not one is favored over the other is a meaningless question.
Hannah: You used the terms quantum gravity and quantum mechanics but what exactly do they mean? And is research on this topic ongoing?
Quantum gravity is the hypothetical theoretical framework that bridges the gap between gravity and quantum mechanics. As of now, there is no consistent theory of quantum gravity. However, by persistently continuing research like this, we may be able to solve this problem in the future.
Works Cited:
Carlip, S. (2014). Black hole thermodynamics. International Journal of Modern Physics D, 23(11), 1430023. https://doi.org/10.1142/s0218271814300237
Jennifer Chu | MIT News Office. (n.d.). Physicists observationally confirm Hawking's black hole theorem for the first time. MIT News | Massachusetts Institute of Technology. https://news.mit.edu/2021/hawkings-black-hole-theorem-confirm-0701.
Isi, M., Farr, W. M., Giesler, M., Scheel, M. A., & Teukolsky, S. A. (2021). Testing the Black-Hole Area Law with GW150914. Physical Review Letters, 127(1). https://doi.org/10.1103/physrevlett.127.011103
Lesourd, M. (2018). A remark on the energy conditions for Hawking’s area theorem. General Relativity and Gravitation, 50(6). https://doi.org/10.1007/s10714-018-2377-1
Spindel, R. (2011). Hawking radiation. Scholarpedia, 6(12), 6958. https://doi.org/10.4249/scholarpedia.6958
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