[Paper Review] Strange Horizons: Understanding Causal Barriers Beyond General Relativity

Bethan Cropp|arXiv (Cornell University)|Nov 1, 2016

Quantum Electrodynamics and Casimir Effect100 references4 citations

TL;DR

This thesis investigates causal barriers in modified gravity theories beyond general relativity, focusing on universal horizons in Lorentz-violating frameworks like Einstein-Æther and Hołava-Lifshitz gravity. Using ray tracing and surface gravity analysis, it identifies distinct surface gravities for universal and Killing horizons, demonstrates peeling behavior of rays near universal horizons, and explores the thermodynamic consistency and potential Hawking radiation of these horizons, while proposing a novel analogue model using relativistic Bose-Einstein condensates to simulate universal horizons.

ABSTRACT

This thesis explores two avenues into understanding the physics of black holes and horizons beyond general relativity, via analogue models and Lorentz violating theories. Analogue spacetimes have wildly different dynamics to general relativity; this allows the possibility of non-Killing horizons in stationary solutions. In the case of non-Killing horizons different definitions of surface gravity are truly different quantities. This also has application to modified theories of gravity, where there is no reason to expect all horizons to be Killing horizons. In Lorentz violating theories, the situation becomes even stranger, as Killing horizons are at best low energy barriers, but for superluminal dispersion relations a true causal barrier, the universal horizon, may be present. We investigate the nature of these universal horizons via a ray tracing study, and delve into what happens near both the universal and Killing horizons. From this study we determine the surface gravity of universal horizons by the peeling properties of rays near the horizon and discuss whether, and at what temperature these horizons radiate. Finally, we combine our investigations of universal horizons and analogue spacetimes, and ask why we have not seen a universal horizon in studies of analogue gravity.

Motivation & Objective

• To understand the nature of causal barriers in modified gravity theories where Killing horizons are not sufficient to describe black hole behavior.
• To investigate the existence and properties of universal horizons—causal barriers in Lorentz-violating theories like Einstein-Æther gravity.
• To determine whether universal horizons can support Hawking radiation and at what temperature, given their distinct surface gravity.
• To bridge analogue gravity models with universal horizon physics by introducing a relativistic Bose-Einstein condensate coupled to an Æther field.
• To resolve inconsistencies in existing radiation calculations by identifying key challenges in boundary conditions and pole structures near universal horizons.

Proposed method

• Employed ray tracing in Einstein-Æther black hole spacetimes to study the behavior of physical trajectories near universal and Killing horizons.
• Defined and computed surface gravity via the peeling rate of null rays near the universal horizon, distinguishing it from standard metric-based definitions.
• Analyzed modified dispersion relations and conserved energy-like quantities to model non-geodesic ray trajectories in Lorentz-violating spacetimes.
• Used the near-horizon limit of the ray equations to extract surface gravity values for both universal and Killing horizons.
• Proposed a relativistic Bose-Einstein condensate model with a Proca field to couple to a preferred frame (Æther), enabling simulation of universal horizons in analogue systems.
• Evaluated the thermodynamic consistency of universal horizons by examining adiabaticity and Euclidean continuation techniques in the context of Hawking radiation.

Experimental results

Research questions

• RQ1 What is the surface gravity of a universal horizon, and how does it differ from that of a Killing horizon in Lorentz-violating gravity?
• RQ2 Can universal horizons support Hawking radiation, and if so, at what temperature, given their non-geodesic causal structure?
• RQ3 Why have universal horizons not yet been observed in standard analogue gravity models, and how can the preferred frame be decoupled from the fluid flow?
• RQ4 How do the pole structures and boundary conditions in wave equation solutions differ at universal versus Killing horizons, and what are the implications for radiation calculations?
• RQ5 Can a relativistic Bose-Einstein condensate system be engineered to realize a universal horizon through coupling to a Proca field and a preferred frame?

Key findings

• The surface gravity of a universal horizon was determined via the peeling rate of rays near the horizon, yielding a distinct and measurable value different from the standard metric-based surface gravity.
• Rays near the universal horizon peel off due to the non-geodesic nature of the causal structure, indicating a surface gravity associated with this peeling process.
• Low-energy rays linger near the Killing horizon, suggesting a separate, potentially thermal, process may occur there, possibly involving mode conversion.
• The analysis of the transplanckian problem and adiabaticity suggests that Hawking radiation at the universal horizon is theoretically possible, though boundary condition selection remains a key challenge.
• The calculation of radiation via the tunnelling method supports a finite temperature for the universal horizon, but collapse scenario models cast doubt on the robustness of this picture.
• A novel framework using a relativistic Bose-Einstein condensate coupled to a Proca field provides a promising path toward realising an analogue universal horizon, as it allows independent control of geometry and preferred frame.