Charged Black Hole Solution in Hoyle Narlikar Gravity and its Thermodynamic Properties

Deep in the heart of modern physics lies a persistent puzzle: why is the universe expanding at an ever-increasing speed? For decades, the standard rules of gravity, established by Albert Einstein, have struggled to explain this cosmic acceleration without invoking mysterious, invisible substances like dark energy. While some scientists propose adding new ingredients to the cosmic recipe, others have turned their attention to the recipe itself, asking if the laws of gravity need to be rewritten. One such alternative theory, known as Hoyle–Narlikar gravity, suggests that the universe does not just expand, but continuously creates new matter as it grows. This idea, which relies on a special "creation field" that carries negative energy, offers a different way to understand the cosmos. To see if this theory holds water, researchers must test it in the most extreme environments possible: the dense, invisible cores of black holes. By examining how these theories behave under such intense conditions, scientists can determine if the creation field is a viable description of reality or merely a mathematical curiosity.

In a recent study, a team of mathematicians in India set out to explore this very question by constructing a new model of a charged black hole within the framework of Hoyle–Narlikar gravity. Unlike the standard models that assume a black hole is a simple, empty void, this team imagined a black hole surrounded by an electric charge, a common feature in theoretical physics that acts as a source of energy. They began by writing down the equations that describe how space and time curve around such an object when the creation field is present. The result was a new, complex description of the black hole's geometry, which they found to be a generalization of the famous Reissner–Nordström solution, a classic model used in Einstein's theory. When the researchers removed the specific effects of the creation field from their equations, their new model smoothly transformed back into the standard Einsteinian version, confirming that their work was consistent with established physics while offering something new.

The team then turned their attention to the horizons of this black hole, the invisible boundaries beyond which nothing can escape. By analyzing their new equations, they discovered that the structure of these horizons depends heavily on the strength of the creation field and the amount of electric charge. In some scenarios, the black hole possesses two distinct boundaries: an inner edge and an outer edge. In others, these boundaries merge into a single line, or disappear entirely, leaving behind a "naked singularity," a point of infinite density exposed to the rest of the universe. This last possibility is significant because, in standard physics, nature is thought to hide such singularities behind event horizons. The researchers found that if the electric charge becomes too strong, the event horizon vanishes, suggesting that the creation field could fundamentally alter the fate of a black hole, potentially exposing its core to the cosmos.

Having mapped the shape of this new black hole, the researchers investigated its thermal behavior, asking how it would feel if one could measure its temperature. In the world of black holes, temperature is linked to the surface gravity at the event horizon. The team calculated this temperature and found a striking pattern: for small black holes, the temperature could be negative, a state that implies thermodynamic instability and suggests such small objects might not exist in a stable form. However, as the black hole grows larger, the temperature rises, becomes positive, and eventually stabilizes. This indicates that while tiny black holes in this theory might be chaotic and short-lived, large black holes settle into a calm, stable state. This finding is crucial because it suggests that the universe could naturally favor the existence of large, stable black holes under these modified laws of gravity.

To confirm this stability, the scientists looked at how the black hole would react to small changes in its energy, a property known as specific heat. If a system has a positive specific heat, it can absorb energy without flying apart; if it is negative, it is unstable. Their calculations showed that for small black holes, the specific heat is negative, confirming the instability seen in the temperature analysis. But as the black hole's size increases, the specific heat turns positive, signaling a transition to a stable phase. Furthermore, they calculated the Gibbs free energy, a measure of the system's overall tendency to settle into a stable state. They found that for large black holes, this energy becomes negative, which is the mathematical signature of a globally stable system. In plain terms, this means that once a black hole in this theory grows beyond a certain size, it becomes a robust, enduring object that resists falling apart.

The study concludes that within the framework of Hoyle–Narlikar gravity, charged black holes undergo a distinct transformation as they grow. They begin as unstable, perhaps non-existent entities with negative temperatures, but as they expand, they cross a threshold into a regime where they are both locally and globally stable. This stability is not just a minor detail; it is a fundamental property that ensures these massive objects can persist in the universe. The researchers found that this behavior is a direct consequence of the creation field and the electric charge working together. While the theory still requires further testing against observations, this work provides a clear, mathematical demonstration that Hoyle–Narlikar gravity can support the existence of large, stable black holes, offering a fresh perspective on how the universe might be structured at its most extreme limits.