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M. Hortacsu

Publications and source records attributed to M. Hortacsu.

At least 19 recordsLinked to original sources
arXiv2021

A massless scalar particle coupled to the Wahlquist metric

We study the solutions of the wave equation where a massless scalar field is coupled to the Wahlquist metric, a type-D solution. We first take the full metric and then write simplifications of the metric by taking some of the constants in the metric null. When we do not equate any of the arbitrary constants in the metric to zero, we find the solution is given in terms of the general Heun function, apart from some simple functions multiplying this solution. This is also true, if we equate one of the constants $Q_0$ or $a_1$ to zero. When both the NUT-related constant $a_1$ and $Q_0$ are zero, the singly confluent Heun function is the solution. When we also equate the constant $ν_0$ to zero, we get the double confluent Heun-type solution. In the latter two cases, we have an exponential and two monomials raised to powers multiplying the Heun type function. Thus, we generalize the Batic et al. result for type-D metrics for this metric and show that all variations of the Wahlquist metric give Heun type solutions.

gr-qc↗
arXiv2021

The radial Teukolsky equation for Kerr-Newman-de Sitter geometry: Revisited

We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.

gr-qc↗
arXiv2020

The zero mass limit of Kerr and Kerr-(anti-)de Sitter space-times: Revisited

We continue studying the zero mass limit of the Kerr- (Anti) de Sitter space-times by investigating the possibility of special values of the frequencies to have polynomial solutions for the radial wave equation, compute reflection coefficient for waves coming from and going to the cosmological horizon and see whether there is Hawking radiation for de Sitter geometry. We used the Parikh-Wilczek method to study this property and could not find Hawking radiation.

gr-qc↗
arXiv2018

Heun Functions and Some of Their Applications in Physics

Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is one of these examples, which recently is often encountered in problems in general relativity and astrophysics. Its special and confluent forms take names as Mathieu, Lamé and Coulomb spheroidal equations. For these equations whenever a power series solution is written, instead of a two-way recursion relation between the coefficients in the series, we find one between three or four different ones. An integral transform solution using simpler functions also is not obtainable. The use of this equation in physics and mathematical literature exploded in the later years, more than doubling the number of papers with these solutions in the last decade, compared to time period since this equation was introduced in 1889 up to 2008. We use SCI data to conclude this statement, which is not precise, but in the correct ballpark. Here this equation will be introduced and examples for its use, especially in general relativity literature will be given.

math-ph↗
arXiv2008

2+1 dimensional solution of Einstein Cartan equations

In this work a static solution of Einstein-Cartan (EC) equations in 2+1 dimensional space-time is given by considering classical spin-1/2 field as external source for torsion of the space-time. Here, the torsion tensor is obtained from metricity condition for the connection and the static spinor field is determined as the solution of Dirac equation in 2+1 spacetime with non-zero cosmological constant and torsion. The torsion itself is considered as a non-dynamical field.

gr-qc↗
arXiv2008

Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution

Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun's equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an appendix which gives a new example where one encounters a form of the Heun equation.

gr-qc↗
arXiv2007

Gauged System Mimicking the Gürsey Model

We comment on the changes in the constrained model studied earlier when constituent massless vector fields are introduced. The new model acts like a gauge-Higgs-Yukawa system, although its origin is different.

hep-th↗
arXiv2007

Heun and Mathieu functions as solutions of the Dirac equation

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.

gr-qc↗
arXiv2007

Dirac Equation in the Background of the Nutku Helicoid Metric

We study the solutions of the Dirac equation in the background of the Nutku helicoid metric. This metric has curvature singularities, which necessitates imposing a boundary to exclude this point. We use the Atiyah-Patodi-Singer non local spectral boundary conditions for both the four and the five dimensional manifolds.

gr-qc↗
arXiv2007

Another Model with Interacting Composites

We show that we can construct a model in 3+1 dimensions where it is necessary that composite vector particles take place in physical processes as incoming and outgoing particles . Cross-section of the processes in which only the constituent spinors take place goes to zero. While the spinor-spinor scattering goes to zero, the scattering of composites gives nontrivial results.

hep-th↗
arXiv2007

Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces

We give examples where the Heun function exists in general relativity. It turns out that while a wave equation written in the background of certain metric yields Mathieu functions as its solutions in four space-time dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations.

gr-qc↗
arXiv2006

A Model with Interacting Composites

We show that we can construct a model in 3+1 dimensions where only composite scalars take place in physical processes as incoming and outgoing particles, whereas constituent spinors only act as intermediary particles. Hence while the spinor-spinor scattering goes to zero, the scattering of composites gives nontrivial results.

hep-th↗
arXiv2003

Notes on Choptuik Phenomena

We review the work going on in black-hole physics during the last ten years, called the Choptuik Phenomenon.

gr-qc↗
arXiv2003

Properties of Solutions in 2+1 Dimensions

We solve the Einstein equations for the 2+1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.

gr-qc↗
arXiv2002

Three Dimensional Gravity in the Presence of Scalar Fields

We study a scalar field in curved space in three dimensions. We obtain a static perturbative solution and show that this solution satisfies the exact equations in the asymptotic region at infinity. The new solution gives rise to a singularity in the curvature scalar at the origin. Our solution, however, necessitates the excising the region near the origin, thus this naked singularity is avoided.

gr-qc↗
arXiv2001

Explicit Examples on Conformal Invariance

We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.

hep-th↗