New Black Hole Solutions Emerge from Quantum Gravity Calculations.

Research identifies novel black hole solutions within a modified theory of gravity, utilising the Vilkovisky-DeWitt effective action to correct Einstein’s equations. These solutions, analogous to those found with quadratic gravity, demonstrably exist both near the event horizon and at large distances from the black hole.

The enduring mystery of black holes continues to yield to theoretical investigation, with recent work focusing on how quantum effects modify their established properties. Researchers are increasingly employing effective action techniques, approximations used in quantum field theory to simplify complex calculations, to explore deviations from classical general relativity in extreme gravitational environments. A team at the University of Sussex, comprising Xavier Calmet, Andrea Giusti, and Marco Sebastianutti, present a study detailing novel black hole solutions derived using the Vilkovisky-DeWitt effective action, a specific approach to calculating quantum corrections to gravity. Their work, titled ‘Black Hole Solutions in Quantum Gravity with Vilkovisky-DeWitt Effective Action’, identifies these solutions both near the event horizon, the boundary beyond which nothing can escape a black hole’s pull, and at large distances from the singularity, offering insights into how quantum gravity may alter our understanding of these cosmic objects.
Researchers are investigating quantum corrections to Einstein’s equations, employing the Vilkovisky action to systematically calculate how quantum effects modify classical gravity. The Vilkovisky action, a mathematical tool, allows for the computation of quantum corrections to the Einstein-Hilbert action, the foundation of general relativity, and subsequent exploration of resulting black hole geometries. This approach reveals deviations from general relativity in extreme conditions, particularly concerning the identification of novel black hole solutions.

The study establishes the existence of black hole solutions distinct from the well-known Schwarzschild and Kerr solutions, suggesting a more complex spacetime structure than previously understood, manifesting near the event horizon and at large distances from the black hole. A key finding introduces terms related to non-metricity into the gravitational action, describing a failure of the metric tensor to remain constant during parallel transport. In general relativity, the metric defines distances and angles; non-metricity indicates a departure from this fundamental assumption, suggesting spacetime itself may exhibit more intricate properties at the quantum level, potentially influencing matter and energy in strong gravitational fields.

Incorporating quantum gravity effects, specifically through the Vilkovisky action, modifies established black hole solutions, revealing deviations from the standard Schwarzschild metric and manifesting as alterations to both the black hole’s mass and the cosmological constant. These modifications suggest a more complex relationship between gravity and spacetime than previously understood, challenging the classical description of black holes and establishing solutions where the event horizon does not coincide with the traditional Schwarzschild radius. This displacement indicates a fundamental shift in the geometry surrounding these objects, potentially influencing how matter interacts with and falls into the black hole, and identifies an effective stress-energy tensor arising from the quantum corrections, suggesting quantum effects contribute to the gravitational field.

Calculations reveal the obtained solutions remain valid both near the event horizon and at large distances from the black hole, strengthening their plausibility and potential relevance to real astrophysical scenarios, aligning with previous work on asymptotically safe gravity. This framework posits that gravity remains well-defined at all energy scales, avoiding the infinities that plague other approaches to quantum gravity.

Researchers build upon prior work by Barvinsky, Vilkovisky, Lu, Perkins, Pope, and Stelle, extending investigations into higher-order quantum corrections, and contribute to the broader effort of developing a consistent theory of quantum gravity. The findings offer theoretical predictions that may eventually test through observations of gravitational waves or other astrophysical phenomena, furthering our understanding of the universe’s most extreme environments.

Future work should explore the stability of these modified black hole solutions, determining whether they can withstand perturbations and remain physically realistic over time, and investigate the implications of a non-constant cosmological constant for cosmological models, potentially offering new insights into the accelerating expansion of the universe and the nature of dark energy. A key avenue for future research involves connecting these theoretical findings to observable phenomena, with precise calculations of gravitational wave signatures emitted by these modified black holes providing a pathway for testing the model against data from gravitational wave detectors.

Researchers analyse the behaviour of matter accreting onto these black holes, revealing subtle differences compared to predictions based on classical general relativity, and expand the current framework to include higher-order quantum corrections. While the Vilkovisky action provides a valuable first-order approximation, incorporating additional quantum effects could refine the solutions and provide a more complete picture of quantum gravity’s influence on black hole physics, requiring significant computational effort but potentially yielding substantial theoretical rewards. This research, funded by the National Science Foundation, represents a significant step forward in our understanding of the fundamental nature of gravity and the universe, and opens up new avenues for exploration in theoretical physics. The team plans to continue their research, focusing on developing more accurate models of black holes and exploring the implications of their findings for cosmology and astrophysics.