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Item Open Access (2 + 1)-dimensional AKNS(−N) systems II(Elsevier BV, 2021-06) Gürses, Metin; Pekcan, AslıShow more In our previous work (Gürses and Pekcan, 2019, [40]) we started to investigate negative AKNS(−N) hierarchy in (2 + 1)-dimensions. We were able to obtain only the first three, N = 0, 1, 2, members of this hierarchy. The main difficulty was the nonexistence of the Hirota formulation of the AKNS(N) hierarchy for N ≥ 3. Here in this work we overcome this difficulty for N = 3, 4 and obtain Hirota bilinear forms of (2 + 1)-dimensional AKNS(−N) equations for these members. We study the local and nonlocal reductions of these systems of equations and obtain several new integrable local and nonlocal equations in (2 + 1)- dimensions. We also give one-, two-, and three-soliton solutions of the reduced equationsShow more Item Open Access (2+1)-dimensional local and nonlocal reductions of the negative AKNS system: soliton solutions(Elsevier, 2018) Gürses, Metin; Pekcan, A.Show more Wefirstconstructa(2+1)dimensionalnegativeAKNShierarchyandthenwegiveallpossiblelocaland(discrete)nonlocalreductionsoftheseequations.WefindHirotabilinearformsofthenegativeAKNShierarchyandgiveone-andtwo-solitonsolutions.ByusingthesolitonsolutionsofthenegativeAKNShierarchywefindone-solitonsolutionsofthelocalandnonlocalreducedequations.Show more Item Open Access Classical double copy: Kerr-Schild-Kundt metrics from Yang-Mills theory(American Physical Society, 2018) Gürses, Metin; Tekin, B.Show more The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in d dimensions in the context of possible new examples of this idea. We first show that it is possible to solve the Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon-type scalar equation when the metric is the pp-wave metric, which is the simplest member of the KSK class. In the more general KSK class, the solutions of a scalar equation also solve the Yang-Mills, Maxwell, and Einstein-Yang-Mills-Maxwell equations exactly, albeit with a null fluid source. Hence, in the general KSK class, the double copy correspondence is not as clear-cut as in the case of the pp wave. In our treatment, all the gauge fields couple to dynamical gravity and are not treated as test fields. We also briefly study Gödel-type metrics along the same lines.Show more Item Open Access Comment on “Einstein-Gauss-Bonnet Gravity in four-dimensional spacetime”(American Physical Society, 2020) Gürses, Metin; Şişman, T. Ç.; Tekin, B.Show more We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given in both the metric and the first order formalisms.Show more Item Open Access Discrete symmetries and nonlocal reductions(Elsevier, 2020) Gürses, Metin; Pekcan, A.; Zheltukhin, K.Show more We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.Show more Item Open Access Extremely charged static dust distributions in general relativity(World Scientific, 1998) Gürses, Metin; Rainer, M.Show more Conformo static charged dust distributions are investigated in the framework of general relativity. Einstein’s equations reduce to a non-linear version of Poisson’s equation and Maxwell’s equations imply the equality of the charge and mass densities. An interior solution to the extreme Reissner-Nordström metric is given. Dust distributions con-centrated on regular surfaces are discussed and a complete solution is given for a spherical thin shell.Show more Item Open Access FLRW-cosmology in generic gravity theories(Springer Science and Business Media Deutschland GmbH, 2020-11) Gürses, Metin; Heydarzade, YaghoubShow more We prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and F(R,G)F(R,G) theories are given as examples.Show more Item Open Access Integrable nonlocal reductions(Springer New York LLC, 2018) Gürses, Metin; Pekcan, A.Show more We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) and modified Korteweg-de Vries (mKdV) systems. We give soliton solutions of these nonlocal equations by using the Hirota method. We extend the nonlocal NLS equation to nonlocal Fordy-Kulish equations by utilizing the nonlocal reduction to the Fordy-Kulish system on symmetric spaces. We also consider the super AKNS system and then show that Ablowitz-Musslimani nonlocal reduction can be extended to super integrable equations. We obtain new nonlocal equations namely nonlocal super NLS and nonlocal super mKdV equations.Show more Item Open Access Is there a novel Einstein–Gauss–Bonnet theory in four dimensions?(Springer, 2020-07) Gürses, Metin; Şişman, T. Ç.; Tekin, B.Show more No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic D>4D>4 dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to D=4D=4. Therefore, the recently introduced four-dimensional, novel, Einstein–Gauss–Bonnet theory does not admit an intrinsically four-dimensional definition, in terms of metric only, as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain D>4D>4 dimensional. As there is no canonical choice of 4 spacetime dimensions out of D dimensions for generic metrics, the theory is not well defined in four dimensions.Show more Item Open Access Israel-Wilson-Perjes metrics in a theory with a dilaton field(American Physical Society, 2023-07-25) Gürses, Metin; Şişman, T. Ç.; Tekin, B.Show more We are interested in the charged dust solutions of the Einstein field equations in stationary and axially symmetric spacetimes and inquire if the naked singularities of the Israel-Wilson-Perjes (IWP) metrics can be removed. The answer is negative in four dimensions. We examine whether this negative result can be avoided by adding scalar or dilaton fields. We show that IWP metrics also arise as solutions of the Einstein-Maxwell system with a stealth dilaton field. We determine the IWP metrics completely in terms of one complex function satisfying the Laplace equation. With the inclusion of the stealth dilaton field, it is now possible to add a perfect fluid source. In this case, the field equations reduce to a complex cubic equation. Hence, this procedure provides interior solutions to each IWP metric, and it is possible to cover all naked singularities inside a compact surface where there is matter distribution.Show more Item Open Access Kerr-Schild-Kundt metrics in generic Einstein-Maxwell theories(American Physical Society, 2022-02-03) Gürses, Metin; Heydarzade, Yaghoub; Şentürk, Ç.Show more We study the Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell’s field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell’s field.Show more Item Open Access Kerr–Schild–Kundt metrics in generic gravity theories with modified Horndeski couplings(Springer, 2021-12-31) Gürses, Metin; Heydarzade, Yaghoub; Şentürk, ÇetinShow more The Kerr–Schild–Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the “universality theorem” to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of modified Horndeski theories with Maxwell’s field. We obtain exact solutions of these theories representing the pp-waves and AdS-plane waves in arbitrary D dimensions.Show more Item Open Access A Modified Gravity Theory: Null Aether*(Chinese Physical Society and IOP Publishing, 2019-03) Gürses, Metin; Şentürk, ÇetinShow more General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the “aether”. In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory (NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr¨om-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT: We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a “mass” determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.Show more Item Open Access Motion of curves on two-dimensional surfaces and soliton equations(Elsevier BV * North - Holland, 1998) Gürses, MetinShow more A connection is established between the soliton equations and curves moving in a three-dimensional space V3. The signs of the self-interacting terms of the soliton equations are related to the signature of V3. It is shown that there corresponds a moving curve to each soliton equation.Show more Item Open Access Multi-component AKNS systems(Elsevier, 2022-12-31) Gürses, Metin; Pekcan, A.Show more We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton solutions. We find all possible local and nonlocal reductions of these systems of equations and give a prescription to obtain their soliton solutions. We derive also -dimensional extensions of the multi-component AKNS systems.Show more Item Open Access NAT black holes(Springer, 2019) Gürses, Metin; Heydarzade, Yaghoub; Şentürk, Ç.Show more We study some physical properties of black holes in Null Aether Theory (NAT) – a vector-tensor theory of gravity. We first review the black hole solutions in NAT and then derive the first law of black hole thermodynamics. The temperature of the black holes depends on both the mass and the NAT “charge” of the black holes. The extreme cases where the temperature vanishes resemble the extreme Reissner–Nordström black holes. We also discuss the contribution of the NAT charge to the geodesics of massive and massless particles around the NAT black holes.Show more Item Open Access New classes of spherically symmetric, inhomogeneous cosmological models(American Physical Society, 2019) Gürses, Metin; Heydarzade, YaghoubShow more We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-perfect fluid field 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 equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the Universe may undergo a topology change and in between is a mixture of two different Friedmann-Robertson-Walker universes with different spatial curvatures. We show that there exist some spacelike surfaces where the Ricci scalar and pressure of the fluid diverge but the mass density of the fluid distribution remains finite. Such spacelike surfaces are known as (sudden) cosmological singularities. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infinity. Finally, we briefly address the null geodesics and apparent horizons associated with the obtained solutions.Show more Item Open Access New symmetries of the vacuum Einstein equations(American Physical Society, 1993) Gürses, MetinShow more Some new symmetry algebras are found for the vacuum Einstein equations. Among them there exists an infinite-dimensional algebra representing the symmetries analogous to the generalized symmetries of the integrable nonlinear partial differential equations.Show more Item Open Access Non-Einsteinian black holes in generic 3D gravity theories(American Physical Society, 2019) Gürses, Metin; Şişman, T. Ç.; Tekin, B.Show more The Bañados-Teitelboim-Zanelli (BTZ) black hole metric solves the three-dimensional Einstein’s theory with a negative cosmological constant as well as all the generic higher derivative gravity theories based on the metric; as such it is a universal solution. Here, we find, in all generic higher derivative gravity theories, new universal non-Einsteinian solutions obtained as Kerr-Schild type deformations of the BTZ black hole. Among these, the deformed nonextremal BTZ black hole loses its event horizon while the deformed extremal one remains intact as a black hole in any generic gravity theory.Show more Item Open Access Nonlocal Fordy-Kulish equations on symmetric spaces(Elsevier, 2017) Gürses, MetinShow more We present nonlocal integrable reductions of the Fordy–Kulish system of nonlinear Schrodinger equations and the Fordy system of derivative nonlinear Schrodinger equations on Hermitian symmetric spaces. Examples are given on the symmetric space SU(4)SU(2)×SU(2).Show more