**Singularities in General Relativity - Classical and Quantum**

**Özay Gürtuğ (Maltepe University)**

**Abstract**

A brief overview of space-time singularities and the quantum resolution of time-like curvature singularities will be presented. The current status of resolving singularities and future directions will also be addressed.

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**Neutron Star Structure in Scalar-Tensor Theories**

**Savaş Arapoğlu (ITU)**

**Abstract**

Neutron stars constitute an important class of extreme relativistic objects allowing one to examine the theories of gravitation in the strong field regime. Their supranuclear densities stemming from their large masses and small radii make them also interesting laboratories for matter under extreme conditions which is modelled by different equations of states (EoS). Such extreme conditions make the determination of EoS a difficult problem in nuclear physics but, on the other hand, the studies in this direction may allow, for example, to constrain even dark matter models in a way that is inaccessible to terrestrial or cosmological probes. We study the structure of neutron stars in a special class of the scalar-tensor theories for three realistic EoS and the Higgs-like potential. Using the observational bounds on the mass and the radius of the neutron stars, we put some limits on the parameters of the model.

**Reference:** arXiv: 1903.00391

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**Integrable lattice spin models from supersymmetric field theories**

**İlmar Gahramanov (MSGSU)**

**Abstract**

The theory of integrable models in statistical mechanics is a remarkably rich source of theoretical physics. The integrability of the model stems from the fact that the Boltzmann weights can be parameterized in such a way that they solve the Yang-Baxter equation. This equation implies that the transfer matrices for all values of spectral parameter commute, i.e. one can compute the partition function of a model exactly. Recently it was observed an interesting relationship between exact results in supersymmetric quantum field theories and integrable two-dimensional lattice models in statistical mechanics. Due to this relationship, the integrability in statistical models is a direct consequence of supersymmetric duality. This correspondence is a powerful tool which enables us to obtain new integrable lattice models by using supersymmetry computations. In this talk, I will review new trends in integrable models of statistical mechanics with an emphasis on the relationship to supersymmetric quantum field theory.

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**Energy observable for a quantum system with a dynamical state space and a geometric extension of quantum mechanics**

**Ali Mustafazade ****(Koç University)**

**Abstract**

We address the problem of defining the energy observable for a quantum system whose state space depends on time. The solution leads to a moderate geometric extension of QM where the role of the Hilbert space and the Hamiltonian operator is played by a complex Hermitian vector bundle E endowed with a metric-compatible connection and a global section of a real vector bundle determined by E. The axioms of QM are not replaced by others but elevated to the level of the relevant bundles. The standard description of quantum systems in terms of a Hilbert space and a Hamiltonian operator, which respectively determine the kinematical and dynamical properties of the system, is recovered locally, i.e., in local patches of E.

**Reference:** Phys. Rev. D **98**, 046022 (2018), arXiv: 1803.04175

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**Spectral Singularities in Mathematical Optics**

**Keremcan Doğan (Koç University)**

**Abstract**

Spectral singularities are certain points of the continuous spectrum of a complex scattering potential. They bring obstructions for a non-Hermitian operator to be Hermitizable. For certain complex potentials, these spectral singularities describe some key optical properties. Together with non-linear generalizations, their existence yields simple mathematical derivations of some basic results of laser physics. By using two basic postulates in the examination of spectral singularities for TE modes of a slab Fabry-Perot resonator, one can reveal the details of the threshold gain and the output intensity.

**Reference***:* K. Doğan, A. Mostafazadeh, and M. Sarisaman, “Spectral Singularities, Threshold Gain, and Output Intensity for a Slab Laser with Mirrors,” Ann. Phys. (Amsterdam) 392, 165-178 (2018); arXiv: 1710.02825.

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**BTZ Waves**

**Tahsin Çağrı Şişman (University of Turkish Aeronautical Association)**

**Abstract**

Kerr-Schild-Kundt (KSK) metrics are universal: the KSK metrics solving Einstein's gravity and quadratic curvature gravity also solve any metric based higher derivative gravity theory. The well-known members of the KSK class are the AdS-wave metrics. KSK metrics are represented in the Kerr-Schild form where the seed metric is the the anti-de Sitter (AdS) spacetime. Then, in three dimensions, a natural prospect of having BTZ metric as the seed metric arouses because it represents a rotating black hole. In this talk, I will discuss the construction of the KSK metrics with the BTZ seed which we call as BTZ-waves. The main point about the BTZ-wave deformation of the BTZ black hole is whether the black hole nature is kept intact. I will discuss the BTZ-wave(s) satisfying this property.

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**Friendly Instabilities in Gravity Theories**

**Fethi M Ramazanoğlu (Koç University)**

**Abstract**

Instabilities are often a nuisance since they spoil many ideas by introducing ever-growing degrees of freedom, rendering theories unphysical. However, if an initial exponential growth of a field can be stopped at large values, one can obtain novel nontrivial stable configurations as in phase transitions. This idea is at the core of a recently popular modification of general relativity: spontaneous scalarization. Spontaneous scalarization is a scenario in scalar-tensor theories where the zero scalar field solution that corresponds to general relativity is unstable in the presence of neutron stars. Arbitrarily small perturbations grow near the star due to a tachyonic instability, and form stable large-amplitude scalar clouds thanks to nonlinear interactions. These clouds provide order-of-unity deviations from general relativity, which are potentially easy targets for gravitational wave observations. At the same time, the scalar field decays with distance from the star, hence weak field tests are also satisfied. I will explain the basics of spontaneous scalarization, and give an overview of how it generalizes to other fields (such as vectors), other instabilities (such as ghosts), and to more general theories such as black hole scalarization due to extended Gauss-Bonnet terms. These more general phenomena, dubbed spontaneous tensorization, seem to be ubiquitous in alternative theories of gravity, and provide exciting opportunities at the age of gravitational wave astronomy.

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**New Classes of Spherically Symmetric, Inhomogeneous**

**Cosmological Models**

**Metin Gürses and Yaghoub Heydarzade (Bilkent University)**

**Abstract**

We present two classes of singular, inhomogeneous, spherically symmetric solution of the Einstein-Maxwell-Perfect ﬂuid feld equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect ﬂuid solutions of the Einstein field equation and under some other limits we obtain new charged and uncharged solutions with cosmological constant. We show that there exist some spacelike and timelike surfaces where the pressure and mass density of the ﬂuid distribution diverge. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infnity, and also in the neighborhood of the big-bang singularity as well as for the late times.

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**Geometric Potential as Perturbation**

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**Hai Viet Bui (Koç University)**

**Abstract**

The scattering of non-relativistic spinless particles moving on a cylindrically symmetric curved surface and interacting with finite multi delta potential is studied. The effect of moving on the curved surface is described by an effective geometric potential using the thin layer quantization. The effective geometric potential is approximated by using asymptotically flat approach and treated as perturbation of the finite multi delta function. The presence of the delta-function defects enhances the differential cross-section, and hence, geometric scattering effects compared to a case without defects.

Joint work with A. Mostafazadeh. Paper is submitted.

**Reference:** N. Oflaz , A. Mostafazadeh, and M. Ahmady, Phys. Rev. A 98, 022126 (2018); arXiv: 1807.10099

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**A new formulation of conserved charges in gravity**

**Bayram Tekin (METU)**

**Abstract**

I shall talk about our recent attempt of giving an explicitly gauge-invariant formulation of conserved Killing charges in cosmological Einstein's theory. The resulting expression involves only the linearized Riemann tensor and the the potential of the background Killing vector.

The work appeared as: E. Altas, B. Tekin,"Conserved charges in AdS: A new formula",Phys. Rev. D 99, 044026 (2019).

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**New approach to conserved charges of generic gravity in AdS spacetimes**

**Emel Altaş (METU)**

**Abstract**

Starting from a divergence-free rank-4 tensor of which the trace is the cosmological Einstein tensor, we give a construction of conserved charges in Einstein's gravity and its higher derivative extensions for asymptotically anti-de Sitter spacetimes. The current yielding the charge is explicitly gauge invariant, and the charge expression involves the linearized Riemann tensor at the boundary. Hence, to compute the mass and angular momenta in these spacetimes, one just needs to compute the linearized Riemann tensor. We give two examples.

**Note:** This work is published in Physical Review D as Emel Altas and Bayram Tekin Phys. Rev. D 99, 044016 – Published 12 February 2019

DOI:https://doi.org/10.1103/PhysRevD.99.044016

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**Weak Field Limit of Infinite Derivative Gravity**

**Ercan Kılıçarslan (Uşak University)**

**Abstract**

A form of infinite derivative gravity is free from ghost-like instabilities with improved small scale behavior. In this theory, we calculate the tree-level scattering amplitude and the corresponding weak field potential energy between two localized covariantly conserved spinning point-like sources that also have velocities and orbital motion. We show that the spin-spin and spin-orbit interactions take the same form as in Einstein’s gravity at large separations, whereas at small separations, the results are different. We find that not only the usual Newtonian potential energy but also the spin-spin and spin-orbit interaction terms in the potential energy are non-singular as one approaches r → 0. ”This work was published as E. Kilicarslan, ”Weak Field Limit of Infinite Derivative Gravity,” Phys.Rev. D 98, no. 6, 064048 (2018).

**References:**

[1] E. Kilicarslan, “Weak Field Limit of Infinite Derivative Gravity,” Phys. Rev. D 98, no. 6, 064048 (2018).

[2] E. Kilicarslan, “PP-waves as Exact Solutions to Ghost-free Infinite Derivative Gravity,” arXiv:1903.04283 [gr-qc].

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**Entropy in Born-Infeld Gravity**

**Gökçen Deniz Özen (METU)**

**Abstract**

There is a class of higher derivative gravity theories that are in some sense natural extensions of cosmological Einstein’s gravity with a unique maximally symmetric classical vacuum and only a massless spin-2 excitation about the vacuum and no other perturbative modes.These theories are of the Born-Infeld determinantal form. We show that the macroscopic dynamical entropy as defined by Wald for bifurcate Killing horizons in these theories are equivalent to the geometric Bekenstein-Hawking entropy (or more properly Gibbons-Hawking entropy for the case of de Sitter spacetime) but given with an effective gravitational constant which encodes all the information about the background spacetime and the underlying theory. We also show that the higher curvature terms increase the entropy. We carry out the computations in generic n-dimensions including the particularly interesting limits of three, four and infinite number of dimensions. We also give a preliminary discussion about the black hole entropy in generic dimensions for the BI theories.

This is published as Gokcen Deniz Ozen, Sahin Kurekci, Bayram Tekin Oct, 2017. 9 pp. Published in Phys.Rev. D96 (2017) no.12, 124038 DOI: 10.1103/PhysRevD.96.124038

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**Non-Abelian T-Duality and Yang-Baxter Deformations of String Sigma Models as O(d,d) Transformations**

**Aybike Özer (ITU)**

**Abstract**

Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. Yang-Baxter (YB) deformations of string sigma models is based on an R-matrix that solves Classical Yang-Baxter Equations (CYBE) and provides integrable deformations of supergravity backgrounds relevant for AdS/CFT correspondence. The aim of this talk is to show that NATD transformations and YB deformations can both be described as coordinate dependent O(d,d) transformations, where the dependence of the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group and the R-matrix, respectively. In the Yang-Baxter case, the O(d,d) transformation can be viewed as a generalization of the O(d,d) transformation that produces Lunin-Maldacena deformations (TsT deformations). Besides making the calculations significantly easier, this approach gives a natural embedding of NATD and YB deformations in Double Field Theory (DFT), which is an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it is easily proved that the transformed/deformed backgrounds indeed solve supergravity equations, when the symmetry algebra is unimodular. On the other hand, if the symmetry algebra is non-unimodular, the resulting backgrounds solve generalised supergravity equations, which have recently been introduced by Tseytlin et al as a generalisation of standard supergavity equations.

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**Gravitational Plane Waves in Brans-Dicke gravity and the equation of motion of scalar test masses**

**Yorgo Şenikoğlu (****Koç University****)**

**Abstract**

The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetimes. A gravitational plane wave metric in Rosen and Brinkman coordinates together with the Brans-Dicke scalar field are used to characterise the equations fo motion of scalar test masses. All the relevant geodesics and autoparallels are worked out. Specially, the geodesic deviation equation is also given and discussed.

Joint work with T. Dereli, Paper in progress.

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**Wave Solutions of Null Aether Theory**

**Çetin Şentürk (University of Turkish Aeronautical Association)**

**Abstract**

In this work we study wave solutions of Null Aether Theory--a modified gravity theory with a preferred direction established at every point of spacetime by a null vector field. We derive the linearized equations of motion around the flat background solution and extract all the wave modes. We also determine the propagation speeds of these modes which are in general dependent on the constant parameters of the theory.

(This is an ongoing work with Prof. Metin Gürses.)

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**Local Scale Covariant Extension of Massive Gravity Theories in Riemann-Weyl Spacetimes**

**Tekin Dereli ****(Koç University)**

**Abstract**

Local scaling laws of classical fields in Riemann-Cartan-Weyl spacetimes will be discussed in general first.Then a constrained first order variational derivation of massive gravity field equations in three dimensions will be presented. In particular we will comment on the scale covariant extensions of the topologically and minimal massive gravity theories.

(This is part of an ongoing joint work with Cem Yetişmişoğlu.)

**References:**

[1] T. Dereli, C. Yetişmişoğlu, New improved massive gravity*,* EPL**114**(2016)60004

[2] T. Dereli, C. Yetişmişoğlu, New improved massive gravity and three dimensional* spacetimes of constant curvature and constant torsion*, Phys.Rev.D94(2016)064067

[3] T. Dereli, C. Yetişmişoğlu, Weyl invariant generalisations of topologically and minimal massive gravity theories*, *(Paper in progress).

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**Kaluza-Klein Reduction of the 6 Dimensional Dirac Equation on ****𝕊**^{3}

**Cem Yetişmişoğlu**** ****(Koç University)**

**Abstract**

I will present the Kaluza-Klein reduction of Dirac Equation on a 6 dimensional Lorentzian space-time 𝕄^{1+5}:=𝕄^{1+2}×𝕊^{3}. I will discuss in detail the mathematical structures for the construction of Dirac equation and Kaluza-Klein reduction. I will also emphasize the differences between the interaction terms of the reduced Dirac equation and the usual minimally *SU*(2) coupled Dirac equation on 𝕄^{1+2} .

**Reference: **Kaluza-Klein Reduction of the 6 Dimensional Dirac Equation on 𝕊^{3}≅*SU*(2) and Non-abelian Topological Insulators, T. Dereli, K. Doğan, C.Y. [In progress].

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**Thermodynamics of Einstein-Born-Infeld-AdS Black Holes**

**Kıvanç İbrahim Ünlütürk ****(Koç University)**

**Abstract**

Born-Infeld electrodynamics is a modification of Maxwell electrodynamics which was originally introduced to remove the divergence of the electron's self energy. Recently, the interest in Born-Infeld theory was revived in a variety of fields ranging from non-linear electrodynamics to string models. In this talk, I will discuss the static black hole solution of Einstein's field equations coupled to Born-Infeld electrodynamics with a negative cosmological constant. I shall present the basic thermodynamic quantities and the equations of state of these black holes.

**Reference: **T. Dereli and K. İ. Ünlütürk 2019 EPL 125 10005

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**Initial wave-function of the universe is arbitrary**

**Ali Kaya (Boğaziçi University)**

**Abstract**

We consider quantization of the gravity-scalar field system in the minisuperspace approximation. It turns out that in the gauge fixed deparametrized theory where the scale factor plays the role of time, the Hamiltonian can be uniquely defined without any ordering ambiguity as the square root of a self-adjoint operator. Moreover, the Hamiltonian degenerates to zero and the Schrödinger equation becomes well behaved as the scale factor vanishes. Therefore, there is no technical or physical obstruction for the initial wave-function of the universe to be an arbitrary vector in the Hilbert space, which demonstrates the severeness of the initial condition problem in quantum cosmology.

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**Covariant Expressions of Dirac Bilinears**

**Mehmet Ali Olpak ****(University of Turkish Aeronautical Association)**

**Abstract**

Dirac bilinears are among the most common objects that appear in quantum field theory problems. The mostly used approach to calculate them is to choose suitable reference frames and representations. However, covariant expressions of these objects may also be needed in practice. Hadronic physics presents an example, where the calculation of covariant wavefunctions for the Fock states contributing to a hadron state can be of interest. Our work states the relevant problem and presents a recipe using which one can arrive at covariant expressions for the bilinears involving different momentum arguments.

The talk is based on the studies with Prof. Dr. Altuğ Özpineci (Middle East Technical University, Dept. of Physics, Ankara, Turkey). .

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**YARK Theory of Gravitation, **

**is it crazy enough to have a chance of being correct?**

**Metin Arık (Boğaziçi University)**

**Abstract**

The Einstein Theory of gravitation uses a riemannian spacetime which is a curved spacetime, defined ab initio in terms of coordinates of an event point. Thus an observation is a point described by spacetime coordinates in riemannian spacetime. In YARK, however, there are no ab initio coordinates. An observer sets up coordinates by placing his observation event at the origin of his coordinates and assumes spacetime is Minkowskian up to a scale factor which depends on the observer. Thus there is no spacetime if there is no observer. This statement is fully compatible with quantum physics and quantum field theory of the Standard Model which covers all interactions except gravity. The fundamental concept of YARK spacetime is that one can assume an observer at a spacetime point A but that one cannot assign coordinates to A ab initio. To assign coordinates to A one has to introduce another observer at spacetime point B. For two observers A and B one can talk of coordinates A with respect to B denoted by X_{A}(B) and coordinates of B with respect to A denoted by X_{B}(A) which are different if A and B are subject to different gravitational energies per unit mass energy. Here mass is used as in present day terminology and is an intrinsic property of a particle so it is the energy when the particle is at rest and free of any gravitational effects.

YARK’s postdictions of the precession of Mercury, the bending of light by the Sun, its consistency with the LIGO observation of gravity waves, the FLRW metric of cosmology, the Jordan-Thirry-Brans-Dicke theory of gravity and the Kant doctrine of Trancendental Idealism will be discussed.

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