# M. HortacsuMimar Sinan Fine Arts University · Department of Physics

M. Hortacsu

PhD

## About

105

Publications

4,957

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

801

Citations

Introduction

I try to obtain exact solutions of fields in the background certain metrics in general relativity by solving their respective linear differential equations, i.e. I study semi classical gravity.

Additional affiliations

Education

September 1966 - December 1971

September 1962 - June 1966

**Robert College Engineering School**

Field of study

- Electrical Engineering

## Publications

Publications (105)

Here we continue studying the Wahlquist metric. We know that the wave equation written for a zero mass scalar particle in the background of this metric gives Heun type solutions. To be able to use the existing literature on Heun functions, we try to put our wave equation to the standard form for these functions. Then we calculate the reflection coe...

Here we continue studying the Wahlquist metric. We know that the wave equation written for a zero mass scalar particle in the background of this metric gives Heun type solutions. To be able to use the existing literature on Heun functions, we try to put our wave equation to the standard form for these functions. Then we calculate the reflection coe...

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 solut...

We use Heun-type solutions given in Suzuki et al. (Prog Theor Phys 100:491, 1998) for the radial Teukolsky equation written in the background metric of the Kerr–Newman–de Sitter geometry to calculate reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.

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 solut...

We use the Heun type solutions given in \cite{Suzuki} and a new generated that equation for the radial Teukolsky equation for Kerr-Newman-de Sitter geometry to calculate reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.

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 and compute the reflection coefficients at the origin for waves coming from the infinity for the AdS and from the cosmological horizon in th...

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...

Here we want to report an unfortunate misprint in the last equation, eq.(28), in our paper The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes , which was published in General Relativity and Gravitation, [1].

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 coefficien...

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge–Kutta method. From the numerical solution, we make an ansatz for the rota...

Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the cl...

Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the cl...

We find confluent Heun solutions to the radial equations of two Halilsoy-Badawi metrics. For the first metric, we studied the radial part of the massless Dirac equation and for the second case, we studied the radial part of the massless Klein-Gordon equation.

We couple a conformal scalar field in (2+1) dimensions to Einstein-Cartan gravity. The field equations are obtained by a variational principle. Einstein-Cartan equations are not solved analytically. These equations are solved numerically with 4th order Runge-Kutta method.

After a brief introduction to Heun type functions we note that the actual solutions of the eigenvalue equation emerging in the calculation of the one loop contribution to QCD from the Belavin-Polyakov-Schwarz-Tyupkin instanton and the similar calculation for a Dirac particle coupled to a scalar $CP^1$ model in two dimensions can be given in terms o...

Most of the theoretical physics known today is described using a small number
of differential equations. If we study only 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 c...

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...

The 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 equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on t...

This paper contains some errors. Please see the PDF for details.

This paper contains some errors. Please see the PDF for details.

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.

We show that when a model, which is equivalent to the Gürsey model
classically, is gauged with a SU(N) field, we get indications of a
nontrivial field theory.

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.

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 f...

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 composite...

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. Comment: 9 Pages

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

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.

We study examples where conformal invariance implies triviality of the underlying quantum field theory.

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.

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...

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.

{We study vacuum fluctuations of different gravitational waves by taking a detour in de Sitter space in the intermediate steps. We find finite contributions when the coupling constant is dimensionless, whereas null result persists in the cases with dimensional coupling constants. We also test our method for exactly solvable cases, and show that no...

We show spurious effects in perturbative calculations due to different
orderings of inhomogeneous terms while computing corrections to Green functions
for two different metrics. These effects are not carried over to physically
measurable quantities like the renormalized value of the vacuum expectation
value of the stress-energy tensor.

The author shows that quantum fluctuations, in particular vacuum polarization, vanish in the background of the spherical shock wave solution of the Einstein field equations, recently found by Nutku (1991). This result is due to the smoothness properties of the new solution.

By integrating exactly the effective Bose field theory which describes the s-wave fermion-magnetic monopole system, the authors show that the condensate around a gauge theory monopole is electrically neutral. So the fermion-monopole scattering is of pure helicity flip due to the chiral condensate.

We show that quantum fluctuations, in particular vacuum polarization, vanish in the background of the spherical shock wave solution of the Einstein field equations recently found by Nutku. This work extends previous work on the similar problem, concluding that one can not change the null result previously obtained by using more general solutions.

We extend the work done for cosmic strings on the perturbative calculation of vacuum polarization of a massless field in the space-time of multiple cosmic strings and show that for a more general class of locally flat metrics, the one-loop calculation does not introduce any new divergences to the vev of the energy of a scalar particle or a spinor p...

Physical properties of gravitational instantons which are derivable from minimal surfaces in 3-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi Type $VII_0$, or E(2)...

We study two constrained scalar models. While there seems to be equivalence when the partially integrated Feynman path integral is expanded graphically, the dynamical behaviour of the two models are different when quantization is done using Dirac constraint analysis.

We compare the exact and perturbative results in two metrics and show that
the spurious effects due to the perturbation method do not survive for
physically relevant quantities such as the vacuum expectation value of the
stress-energy tensor.

We review our previous work on the the calculation of the stress-energy tensor for a scalar particle in the background metric of different types of spherical impulsive, spherical shock and plane impulsive gravitational waves.

We show that the vacuum expectation value of the stress-energy tensor of a scalar particle on the background of a spherical gravitational shock wave does not give a finite expression in second-order perturbation theory, in contrast to the case seen for the impulsive wave. No infrared divergences appear at this order. This result shows that there is...

Quantum fluctuations for a massless scalar field in the background metric of spherical implusive gravitational waves propagating through Minkowski and de Sitter spaces are investigated. It is shown that there exist finite fluctuations for de Sitter space.

We propose a method for calculating vacuum fluctuations on the background of a spherical impulsive gravitational wave which results in a finite expression for the vacuum expectation value of the stress-energy tensor. The method is based on first including a cosmological constant as an auxiliary constant. We show that the result for the vacuum expec...

We study the interaction of a massless quantized spinor field with the gravitational filed of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force attraction...

Unruh's detector calculation is used to study the effect of the defect angle
$\beta$ in a space-time with a cosmic string for both the excitation and
deexcitation cases. It is found that a rotating detector results in a non-zero
effect for both finite (small) and infinite (large) time.

We extend the work done for cosmic strings on the perturbative calculation of vacuum polarization of a massless field in the space-time of multiple cosmic strings and show that for a more general class of locally flat metrics the one loop calculation do not introduce any new divergences to the VEV of the energy of a scalar particle or a spinor part...

We know that plane waves do not give rise to vacuum fluctuations [1,2].
One may check whether the same result is true also for spherical waves.
A while ago, in the year 1988, Prof. Yavuz Nutku gave me his metric
which was not published yet, and asked me to calculate the vacuum
fluctuations in the background of this metric. He published his metric,...

We calculate the Bogolubov coefficients for aC
(0) metric which describes the snapping of a cosmic string. In this background, we show that there are noregular solutions with particle interpretation, but we find ageneralized solution with integrable discontinuity, which exhibits particle creation. We also find a regular solution if we allow wave pa...

The role of the identification of the vacuum and non-vacuum space-times in the computation of vacuum fluctuations in the presence of a cosmic string is discussed and an alternative interpretation of the renormalization is proposed. This procedure does not give rise to vacuum fluctuations.

We calculate the Bogolubov coefficients for a metric which describes the snapping of a cosmic string. If we insist on a matching condition for all times {\it and} a particle interpretation, we find no particle creation.

The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a ‘‘rotating’’ cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is...

It is shown how a constraint imposed by the physical relevance of the solutions reduces the dimension of space–time. The C(0) metric given by Nutku is used to describe gravitational shock waves and the trivial case is looked at. It is found that imposing triviality on the solutions reduces the dimension of space–time by one.

It is shown that quantum fluctuations, in particular vacuum polarization, vanish in the background of a spherical impulsive wave solution of the Einstein field equations, recently found by Nutku and Penrose. The calculation is done in first‐order perturbation theory but arguments are given why it should persist to all orders.

The author shows that quantum fluctuations, in particular vacuum polarisation, exist in the background of the spherical impulsive wave solution of the Einstein field equations, found by Nutku and Penrose (1990).

We find that Green's functions for two C
0 metrics are not of the Hadamard form.

We present a static solution to the classical field equations of a purely spinorial model with SO(2n) internal symmetry in 2n dimensions. The model contains composite vector fields which have solutions of the Wu-Yang monopole type.

The author shows that quantum fluctuations, in particular vacuum polarisation, exist in the background of the spherical impulsive wave solution of the Einstein field equations, found by Nutku and Penrose (1990).

We calculate the propagator in the scale invariant gauge theories in d=6 in the background of classical solutions. We find that the propagator between different fields is not zero.

We construct monopole solutions of the alternative scale invariant pure Yang-Mills models in six dimensions. and Technological Research Council of Turkey.

We investigate the eigenmodes for fluctuations about the instantonlike solutions of the generalized Liouville equation. We find that the scalar equation gives positive-definite eigenvalues whereas zero modes can be formed in one sector for the spinor case.

A scheme is suggested for the quantization of the recently proposed scale-invariant gauge theories in higher dimensions. The model is minimally coupled to a spinor field. Regularization algorithms are proposed.

The effective s-wave fermion-monopole theory, with massive quarks and non-abelian colour interactions near the monopole core taken into account, is solved in the approximation scheme. The zero energy four-point function vanishes rapidly at the origin, hinting that the massive quarks may not reach the monopole core to trigger catalysis.

We present a static solution to the classical field equations of a purely spinorial model with SU(2) internal symmetry. The model contains composite vector and pseudovector gluon fields. The solution for the vector field is precisely that of the Wu-Yang monopole.

Magnetic monopoles1 have received a great deal of renewed attention over the past few years. Indeed any nonabelian gauge theory2 has a magnetic monopole solution. In its simplest form this solution is the Wu-Yang monopole3 with a singularity at the site of the monopole. The mechanism of spontaneous symmetry breaking can be utilized4 to smear this s...

The authors show that, in the framework of a purely fermionic model, the smallest gauge group which has acceptable fermion representations is SU(16). The simplest embedding of SU(5) into SU(16) implies a maximum number of three chiral families of fermions.

The authors calculate the electron-positron annihilation cross section and the electromagnetic quark structure function in a pure fermionic model with composite gluons. They find that the parton-model result is not modified.

Non-abelian gauge theories are obtained as effective theories of certain models which at the lagrangian level contain only spinor fields.

Summary The functional determinant in the meron background is calculated and the results are contrasted with those obtained when an
instanton background is used.

Summary The index theorem of Atiyah-Patodi and Singer is applied to the case with a meron background where naively an ambiguity seems
to exist.

A pure spinor model with a non-polynomial interaction with global SU(n) symmetry is quantized in the path integral formalism. The model is found to be asymptotically free.

The Gürsey model, a conformally invariant pure spinor model in four dimensions, is quantized to result in an asymptotically free theory.

We show that the meron solutions are stable in pure spinor models.

We calculate the quark and pion structure functions in CPn−1 models with quarks using 1/N expansions. We find that the quark structure function, in the lowest order in 1/N, is just the free parton result with a modified coupling constant. The pion structure function resembles the phenomelogically successful fit but contains correction terms which m...

As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of “box-quantization”: the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ5 symmetry, apart from t...

We perform the /N expansion in two-dimensional field theoretical models with non-isoscalar gluons by summing the planar diagrams and by using saddle-point techniques. We find agreement in these two approaches.

This is our reply to Patrascioiu's criticism of our calculation of the fermionic functional determinant in two-dimensional QED.

We calculate the determinant of the model in the presence of the instanton solution.
Si calcola il determinante del modello in presenza della soluzione istantonica.
Мы вычисляем детерминант для модели с инстантонным решением.

We obtain a closed expression for the functional determinant of the Dirac operator in two-dimensional QED by confronting results on cluster decomposition with direct fermion integration in the presence of Atiyah-Singer zero modes. The result is shown to be identical with the one obtained from the f-function definition and the use of the modified an...

We calculate the determinant in a model where a scalar model with instantons is coupled to fermions in a minimum way. We find that the infrared divergence existing in the pure scalar model is removed.

We show that, in a generalized version of the non-linear O(N) sigma-model, particle production occurs. It therefore cannot have a factorizing S-matrix.

We explicitly construct the scattering solutions for a potential derived from the classical confined solutions of the massive Thirring model and find that the reflection coefficient is not zero, contrary to what happens in the mass-zero case.

In the study of the confined classical solutions of the boson form of the massive Thirring field coupled to a Schwinger field, it is observed that, regardless of their respective magnitudes and signs, the Thirring interaction is dominant over the other one, in determining whether such a solution exists. Confined solutions for the Thirring field are...

The effective potential of the bosonized Thirring model minimally coupled to a photon field is studied up to the two-loop
approximation. The electromagnetic coupling is found to be of minute significance with respect to the location and to the
value of the minimum, even when the electromagnetic coupling constant is few orders of magnitude greater t...

We construct the scattering solutions using a potential derived from the classical confined solutions of the massive Thirring
model, and find that the amplitudes in going to plus and minus infinity have the same amplitude.
Si costruiscono le soluzioni dello scattering per mezzo di un potenziale derivato dalle classiche soluzioni confinate del
model...

Summary The effective potential for the massive Thirring model with two components is obtained by means of two types of two-body interactions,
up to the two-loop diagrams. For the unusual type of interaction a «reality» symmetry is observed in the ground state.

Using the Rarita-Schwinger equation for a spin-3/2 particle in a a constant magnetic field, we explicitly calculate the propagator in 2 + 1 dimensions. From the behavior of the propagator, it is seen that the propagation is noncausal.

We show that for the derivative coupling model and for the Thirring model with anomalous spin the theory is conformally covariant
for a quantized set of coupling-constant values.
Si dimostra che per il modello di accoppiamento derivato e per il modello di Thirring con spin anomalo la teoria è conformemente
covariante per un'insieme quantizzato di v...

## Projects

Projects (2)

To find equations in quantum field theory and gravitation, where approximate solutions are given to field equations, whose actual exact solutions are of the Heun class.