Black hole tidal charge constrained by strong gravitational lensing

Spherically symmetric brane black holes have tidal charge, which modifies both weak and strong lensing characteristics. Even if lensing measurements are in agreement with a Schwarzschild lens, the margin of error of the detecting instrument allows for a certain tidal charge. In this paper we derive the respective constraint on the tidal charge of the supermassive black hole (SMBH) in the center of our galaxy, from the radius of the first relativistic Einstein ring, emerging in strong lensing. We find that even if general relativistic predictions are confirmed by high precision strong lensing measurements, SMBHs could have a much larger tidal charge, than the Sun or neutron stars

Gravitational Lensing with a Large Deflection Angle as a Probe of General Relativity and the Galactic Center

Gravitational lensing is an important tool for the study of gravity. In this thesis, we use gravitational lensing in the strong field to study a variety of phenomena. We begin with an overview of gravitational lensing in the weak and strong deflection limits, including a formalism for the study of light that passes close enough to a black hole to loop around it several times before reaching the observer. We move on to discuss recent developments in the study of ``braneworld models which present an interesting framework for the effect of extra dimensions on gravity. We also discuss several potential black hole metrics in the Randall-Sundrum II braneworld model. We then numerically study a variety of lensing scenarios involving braneworld black holes, including a new form of the ``tidal Reissner-Nordstrom metric and find that a braneworld metric will produce results theoretically differentiable from a Schwarzschild black hole. The analytical formalism we review is found to be an accurate reproduction of the numerical results. We outline a test for the application of this analytical formalism to an arbitrary static, spherically symmetric spacetime. We then study the effects of gravitational lensing on the S stars orbiting Sgr A* in the galactic center. We show that modifying the metric for the black hole at Sgr A* will produce different image properties for the lensed S stars. We catalogue these image properties as a function of the metric and comment on the observational prospects for these images and the specifics of their properties. Finally, we suppose that the dark mass at the galactic center is a boson star and offer evidence that this will create observationally significant lensing events for nearby stars

Modular decomposition techniques for stored-logic digital filters

Digital filtering is an important signal processing technique whose theory is now well established. At present, however, there are no well-defined and systematic methods available for realising digital filters in hardware. This project aims to develop such methods which are general and technology independent, and adopts a systems and sub-systems design philosophy. The realisation problem is approached in a new way using concepts from finite-automata theory and implementing complete digital filter sections as stored-logic units. Two methods are introduced and developed. [Continues.

Relativistic Images in Randall-Sundrum II Braneworld Lensing

In this paper, we explore the properties of gravitational lensing by black holes in the Randall-Sundrum II braneworld. We use numerical techniques to calculate lensing observables using the Tidal Reissner-Nordstrom (TRN) and Garriga-Tanaka metrics to examine supermassive black holes and primordial black holes. We introduce a new way tp parameterize tidal charge in the TRN metric which results in a large increase in image magnifications for braneworld primordial black holes compared to their 4 dimensional analogues. Finally, we offer a mathematical analysis that allows us to analyze the validity of the logarithmic approximation of the bending angle for any static, spherically symmetric metric. We apply this to the TRN metric and show that it is valid for any amount of tidal charge.Comment: 13 pages, 3 figures; Accepted for Publication in Physical Review

Strong Gravitational Lensing by Sgr A*

In recent years, there has been increasing recognition of the potential of the galactic center as a probe of general relativity in the strong field. There is almost certainly a black hole at Sgr A* in the galactic center, and this would allow us the opportunity to probe dynamics near the exterior of the black hole. In the last decade, there has been research into extreme gravitational lensing in the galactic center. Unlike in most applications of gravitational lensing, where the bending angle is of the order of several arc seconds, very large bending angles are possible for light that closely approaches a black hole. Photons may even loop multiple times around a black hole before reaching the observer. There have been many proposals to use light's close approach to the black hole as a probe of the black hole metric. Of particular interest is the property of light lensed by the S stars orbiting in the galactic center. This paper will review some of the attempts made to study extreme lensing as well as extend the analysis of lensing by S stars. In particular, we are interested in the effect of a Reissner-Nordstrom like 1/r^2 term in the metric and how this would affect the properties of relativistic images.Comment: 13 pages, 9 figures. Submitted as invited review article for the GR19 issue of CQ