Infinite Acceleration Yields Finite Energy in Novel Spacetime Model

Michael R. R. Good and Eric V. Linder at Lawrence Berkeley National Laboratory have identified a system displaying features of both normal and extreme black holes, even with infinite asymptotic acceleration. Their unified study clarifies the relationship between energy flux and particle production, revealing a closed-form model with finite total radiated energy. The findings offer new insight into the fundamental physics of black hole emission and the nature of horizons in extreme environments.

Infinite acceleration with finite energy via a moving mirror analogue

A system demonstrating infinite asymptotic acceleration alongside finite total radiated energy has been achieved, a result previously considered impossible in analogous black hole models. This new model, utilising an accelerating boundary termed a ‘moving mirror’, breaks the established link between ever-increasing acceleration and unbounded energy release, a connection invariably observed in prior work. The model establishes a black hole analogue possessing zero surface gravity, challenging conventional understanding of horizon formation and particle production in extreme gravitational environments.

In particular, the model exhibits ‘involution symmetry’, meaning its scattering map exchanges advanced and retarded times, a unique property absent in simpler accelerating systems. The acceleration of the model equates to its rapidity, signifying the rate of change of velocity matches the rate of change of its ‘signed rapidity’, a measure of relativistic speed; this specific relationship yields the unusual result. Calculations reveal the total energy emitted by the mirror is precisely 1/12π, despite the continual increase in acceleration; this consistency is confirmed by analysis of the ‘stress tensor’, which describes energy and momentum. While successfully combining extreme acceleration with finite energy, the model currently relies on idealised flat spacetime conditions and does not yet demonstrate feasibility within the complexities of a real-world gravitational environment. The ‘light-cone coordinate map’ confirms ‘involution symmetry’, exchanging advanced and retarded times, unlike simpler accelerating systems.

Simulating Black Hole Horizons with Accelerated Boundary Rapidity

This work centres on a ‘moving mirror’ model, a simplified analogue of a black hole created by simulating an accelerating boundary. Instead of directly observing black holes, which are incredibly distant and complex, a boundary constantly increasing in speed was modelled; this acceleration mimics the extreme gravitational forces near a black hole’s event horizon. Crucially, this model isn’t a visual simulation but a mathematical construct allowing precise control over the boundary’s acceleration and the resulting quantum effects.

By carefully defining the relationship between the boundary’s acceleration and its ‘rapidity’, a measure of its velocity, scientists engineered a system exhibiting infinite asymptotic acceleration, akin to repeatedly pushing a child on a swing to ever-increasing speeds. This model exhibits extreme gravitational forces near a black hole’s event horizon using an accelerating boundary, but as a mathematical construct rather than a visual simulation. The research focused on achieving infinite asymptotic acceleration, similar to continually increasing the speed of an object, while maintaining finite total radiated energy, a unique combination not typically seen in analogous systems. This approach isolates the fundamental mechanism of particle creation from the complexities of general relativity, providing a clean, solvable model for studying how acceleration and energy radiate.

Hawking radiation analogues demonstrate sustained acceleration without proportional energy increase

The pursuit of understanding black hole evaporation, a process theorised to release particles and energy, has long relied on models attempting to replicate extreme gravitational conditions. This work presents a surprising result: a system mimicking Hawking-type emission can sustain infinite acceleration without an equivalent surge in energy output. However, the model’s reliance on flat spacetime, a simplification of the universe lacking the curvature of gravity, creates a significant tension.

Simplifying gravity’s curvature through the use of flat spacetime does introduce a clear limitation to directly mirroring black hole physics. Nevertheless, this work remains valuable as it provides a clean, solvable model for studying how acceleration and energy radiate, even if replicating a true black hole environment requires further refinement of the model to incorporate gravitational effects. A system replicating Hawking radiation, the theoretical emission from black holes, that exhibits infinite acceleration despite finite energy release has been demonstrated.

This model establishes a theoretical link between infinite acceleration and finite energy, previously considered mutually exclusive in systems mimicking black holes. Employing a flat-spacetime ‘moving mirror’, an accelerating boundary simulating a black hole’s event horizon, scientists bypassed the usual expectation of unbounded energy release from extreme acceleration. The resulting analogue exhibits ‘involution symmetry’, where the direction of time appears reversed in its scattering behaviour, a property distinguishing it from simpler accelerating systems.

The research demonstrated a system analogous to Hawking radiation that sustained infinite acceleration while radiating a finite amount of energy. This finding is significant because it challenges the conventional understanding that extreme acceleration necessarily leads to a proportional increase in energy output within these models. The study utilised a flat-spacetime ‘moving mirror’ to achieve this, providing a solvable model for investigating the relationship between acceleration and energy radiation. The authors focused on characterising the particle and energy spectra produced by this analogue system, revealing a unique combination of black hole properties.