Any spacetime has a Bianchi type I spacetime as a limit

Pick an arbitrary timelike geodesic in an arbitrary spacetime. We demonstrate that there is a particular limiting process, an "ultra-local limit", in which the immediate neighborhood of the timelike geodesic can be "blown up" to yield a general (typically non-diagonal) Bianchi type I spacetime. This process shares some (but definitely not all) of the features of the Penrose limit, whereby the immediate neighborhood of an arbitrary null geodesic is "blown up" to yield a pp-wave as a limit.Comment: 19 pages; no figure

Polarization modes for strong-field gravitational waves

Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. These forms are related by a coordinate transformation, so they should describe essentially the same physics, but the two forms treat polarization states quite differently. Both deal well with linear polarizations, but there is a qualitative difference in the way they deal with circular, elliptic, and more general polarization states. In this article we will describe a general algorithm for constructing arbitrary polarization states in the Rosen form.Comment: 4 pages. Prepared for the proceedings of ERE2010 (Granada, Spain

General polarization modes for the Rosen gravitational wave

Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. While these two metric ansatze are related by a coordinate transformation, so that they should describe essentially the same physics, they rather puzzlingly seem to treat polarization states quite differently. Both ansatze deal equally well with + and X linear polarizations, but there is a qualitative difference in they way they deal with circular, elliptic, and more general polarization states. In this article we will develop a general formalism for dealing with arbitrary polarization states in the Rosen form of the gravitational wave metric, representing an arbitrary polarization by a trajectory in a suitably defined two dimensional hyperbolic plane.Comment: V1: 12 pages, no figures. V2: still 12 pages, reformatted. Minor technical edits, discussion of Riemann tensor added, two references added, no significant physics changes. This version accepted for publication in Classical and Quantum Gravit

Strange Horizons: Understanding Causal Barriers Beyond General Relativity

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 means time-independent black hole solutions have fewer symmetries, allowing the possibility of non-Killing horizons in stationary solutions. Surface gravity is one of the most important quantities characterizing black holes, with many physically distinct definitions. In the case of non-Killing horizons these 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. Universal horizons are extremely interesting as they seem to be linked to the thermodynamic consistency of Lorentz-violating theories. Hence, 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. As the surface gravity is strongly linked to the properties of Hawking radiation, we investigate 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. We examine some possibilities to include an aether distinct from the velocity flow characterizing analogue spacetimes, laying the groundwork for an analogue universal horizon

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

&lt;p&gt;In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.&lt;/p&gt;</jats:p

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

&lt;p&gt;In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.&lt;/p&gt;</jats:p

Analogue black holes in relativistic BECs: Mimicking Killing and universal horizons

Relativistic Bose-Einstein condensates (rBECs) have recently become a well-established system for analogue gravity. Indeed, while such relativistic systems cannot be yet realized experimentally, they provide an interesting framework for mimicking metrics for which no analogue is yet available, thus paving the way for further theoretical and numerical explorations. In this vein, we here discuss black holes in rBECs and explore how their features relate to the bulk properties of the system. We then propose the coupling of external fields to the rBEC as a way to mimic nonmetric features. In particular, we use a Proca field to simulate an aether field, as found in Einstein-aether or Ho. rava-Lifshitz gravity. This allows us to mimic a universal horizon, the causal barrier relevant for superluminal modes in these modified gravitational theories

Ray tracing Einstein-Aether black holes: Universal versus Killing horizons

Violating Lorentz invariance, and so implicitly permitting some form of super-luminal communication, necessarily alters the notion of a black hole. Nevertheless, in both Einstein-\ue6ther gravity and Ho\u159ava-Lifshitz gravity, there is still a causally disconnected region in black-hole solutions, now being bounded by a \u201cuniversal horizon,\u201d which traps excitations of arbitrarily high velocities. To better understand the nature of these black holes, and their universal horizons, we study ray trajectories in these spacetimes. We find evidence that Hawking radiation is associated with the universal horizon, while the \u201clingering\u201d of ray trajectories near the Killing horizon hints at reprocessing there. In doing this we solve an apparent discrepancy between the surface gravity of the universal horizon and the associated temperature derived by the tunneling method. These results advance the understanding of these exotic horizons and provide hints for a full understanding of black-hole thermodynamics in Lorentz-violating theories