The event horizons of black holes that are far from equilibrium can now be described by the first and second laws of thermodynamics thanks to new work by theoretical physicists at Pennsylvania State University in the US. The result augments the work of the late Stephen Hawking and others who showed in the 1970s that these classical concepts have applications in idealized, static black holes.

Black holes are objects so dense that their gravitational pull prevents anything – even light – from escaping them. The “point of no return” of any object falling into a black hole is called the event horizon, and it represents the black hole’s mathematically defined “edge”.

Although black holes can be described using concepts from quantum mechanics and Einstein’s general theory of relativity, some 50 years ago physicists like Hawking and Jacob Bekenstein showed that the equations governing them are also astonishingly similar to the fundamental laws of thermodynamics. “This seminal observation sparked a rethinking of black holes in thermodynamics terms,” explains Abhay Ashtekar, a physicist at Penn State’s Eberly College who led the new study. In particular, Ashtekar says it meant that black holes could be assigned an entropy that is equal to the area of their event horizon.

The problem, he continues, is that technically, these relationships are only valid for black holes in equilibrium – that is, those that are stable and do not change over time. In contrast, real astrophysical black holes are constantly changing: they form, merge and eventually evaporate because of quantum effects.

“In these dynamical objects, event horizons are ‘teleological’, meaning that we need to know how a black hole will behave for all of eternity to be able to define its entropy today,” Ashtekar explains. “This notion of black hole entropy is therefore physically untenable. Indeed, this limitation was already recognized in the 1990s and it has been the elephant in the room since then.”

Extending the laws of thermodynamics

In their new work, Ashtekar and colleagues sought to overcome this limitation by replacing static event horizons with an alternative concept known as dynamical horizon segments. These segments are characterized by the physical properties of a black hole at a given moment in time, and other researchers have employed them in numerical simulations of black hole mergers and gravitational collapse. Indeed, Ashtekar and various colleagues had previously shown that dynamical horizons were a physically admissible replacement for event horizons.

However, Ashtekar says that these earlier studies had not addressed two central questions. These involved defining intensive parameters – analogues of pressure and temperature in ordinary thermodynamics systems such as gases – and defining the energy of a black hole by itself in a highly curved region of space-time at a given instant.

“Our study now shows that Einstein’s equations imply that these dynamical horizons also satisfy equations very similar to the first and second laws of thermodynamics,” Ashtekar tells Physics World. “What is more, the change in thermodynamical quantities of these horizons at any given moment in time are caused directly by fluxes of energy and changes in the angular momentum of the black hole at that instant.”

The researchers’ new calculations show that even when black holes are very far from equilibrium, their evolution defines specific trajectories in the space of different equilibrium states. “This allows us to transport observables from these states to instantaneous non-equilibrium ones,” explains Ashtekar. “Such a procedure cannot be applied to conventional thermodynamics systems; black holes are very special in this regard.”

Event horizons “entirely absent” when quantum effects are included

According to team member Daniel Paraizo, the new work treats the event horizon as a dynamical horizon segment that forms in a gravitational collapse and then evaporates because of quantum effects. Intriguingly, Paraizo says that within this framework, event horizons vanish entirely when quantum effects are included – a fact which, he says, “removes a great deal of confusion currently surrounding the issue of information loss from a black hole, for example”. This same finding, he notes, also supports an idea that Hawking advocated shortly before his death in 2018: the possibility that a “true” event horizon never actually forms.

The Penn State researchers now plan to build on their present work with theories involving both classical and quantum gravity. Team member Jonathan Shu says that such theories may provide a thermodynamic explanation of several puzzling features that have been observed in numerical simulations of black hole mergers. “We have also already extended our results to theories of gravity beyond general relativity,” he reveals. “For quantum gravity, dynamical horizon segments have been successfully deployed in the so-called semi-classical phase of black hole evaporation and work is underway to address still unanswered questions about the final stages of the process using a theory known as loop quantum gravity.”

The researchers report their work in Physical Review Letters. Ashtekar will also be speaking on this subject at Penrose Fest@95, which is due to be held in Oxford, UK in September.

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Tissue engineering offers a means to restore, maintain or replace biological tissues. But it is difficult to grow blood vessels using conventional fabrication techniques like 3D printing, as they are typically not precise enough to print fine capillaries and veins. A team of engineers from the Massachusetts Institute of Technology (MIT) has now developed a new approach to do just that, by using mechanical forces. Their blood-vessel-on-a-chip could be the first step in the scalable production of vascular networks that could then be implanted in the body to replace tissue that has been damaged by disease or injury.

The researchers, led by Ritu Raman, made their chip by filling a Petri dish with a gel containing nutrients and cell-growth factors. They then embedded a small magnet into the gel. Finally, they introduced a thin, hollow tube into the gel and coated the inside of the tube with live endothelial cells – the cells that naturally line blood vessels in the body.

Once anchored onto the inner walls of the tube, the endothelial cells began sprouting new, capillary-like vessels in the gel. And when the researchers moved the embedded magnet back and forth in different directions and by varying degrees, they found that the mechanical forces created by the moving magnet could stretch the vessels and increase the number of new capillaries that grew, as well as their length.

‘Steering’ blood vessel growth

“We also showed that blood vessel growth, or angiogenesis, could be directionally patterned using the mechanical forces created by the magnet and that these directions could change dynamically over time,” explains Raman. “This allows us to ‘steer’ blood vessel growth in all three spatial directions (x, y, z) and make complex geometries (like L-shaped branches) that would not be possible to fabricate using conventional methods.”

The researchers had previously demonstrated that biological cells are highly responsive to mechanical forces in the body, but they did not know how different types of forces – for example, stretching in different directions and at different degrees and frequencies – impacted the 3D structure of blood vessels. The main obstacle lay in developing a coupled magnet system to precisely stretch blood vessels in different directions. To achieve this, they designed a method for mechanically stimulating tissues, dubbed “magnetic matrix actuation”.

In their new work, which is detailed in PNAS, they went a step further and developed a method to accurately yet non-invasively stretch 3D blood vessel tissues they had built in the laboratory.

To better understand the effect of mechanical forces on angiogenesis, the MIT team decided to look into the role of a gene known as PIEZO1, which is just one of the many mechanically sensitive genes in the body. They built on the work of molecular biologist Ardem Patapoutian, who received the 2021 Nobel Prize in Physiology or Medicine for discovering that ion channels in cells open and close in response to mechanical pressure. One such ion channel is PIEZO1, which is regulated by the PIEZO1 gene.

By suppressing this PIEZO1 gene in the endothelial cells they studied, the researchers indeed observed that significantly fewer new blood vessels grew in the gel. This, they say, provides evidence that the applied mechanical forces in their experiment may have been opening the PIEZO1 ion channel in the endothelial cells, so triggering the new blood vessel growth.

“My group has always been interested in engineering artificial tissues that can be implanted in the body to repair damage caused by disease or traumatic injury, but such artificial tissues require integrated networks of blood vessels in order to function,” says Raman. “We hope that our method for precisely fabricating complex networks of blood vessels within engineered tissues will enable the development of such implants,” she tells Physics World.

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