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Bayram Tekin

Publications and source records attributed to Bayram Tekin.

At least 37 records · Page 2Linked to original sources
arXiv2024

Anomaly Induced Inflation in the Minimal Quartic Extension of Einstein's Gravity

A particular extension of Einstein's General Relativity up to and including quartic terms in the curvature tensor is minimal in the sense that it has a unique maximally symmetric vacuum and only a massless spin-2 excitation in its spectrum around the vacuum. We study the inflation phase of the universe in this minimal quartic extension of Einstein's gravity in the presence of trace anomaly terms coming from the Standard Model fields and the fields of the Minimal Supersymmetric Standard Model. We show that the theory allows a quasi-de Sitter phase with sufficient $e$-foldings.

gr-qc↗
arXiv2024

Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories

We study symmetry reductions in the context of Euclidean Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in certain gauge theories is a common tool for obtaining explicit soliton solutions. Although pure Chern-Simons theories do not admit solitonic solutions, symmetry reduction still leads to interesting results. We establish relations at the semiclassical regime between pure Chern-Simons theories on $S^3$ and the reduced Quantum Field Theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding $BF$-theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instantons and show that under certain circumstances, the reduced action can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions have a fermionic nature at the level of the partition function.

hep-th↗
arXiv2024

Refined Thermodynamics of Black Holes with Proper Conserved Charges

Field equations of a classical, geometric, theory of gravity, augmented with some semiclassical considerations strongly suggest that the gravitational field representing a stationary black hole can be simply described with a few thermodynamical coordinates and their conjugates that obey the four laws of thermodynamics plus the Smarr formula and the reverse isoperimetric inequality that bounds the maximum entropy for a given effective volume of space. The thermodynamics of black holes is a promising window to the quantum nature of black holes; hence, it is important to understand all the details of these laws. The identification and the meaning of these thermodynamic coordinates depend on the gravity theory under consideration. For example, the existence of dimensionful coupling constants, such as the cosmological constant, changes the scaling properties of the theory, its solutions, and the laws of thermodynamics. Here we show, using the background Killing charge method, which applies to the black hole solutions of any gravity theory that has a maximally symmetric vacuum, to define the mass and angular momentum, instead of using the Komar mass and the angular momentum, how the thermodynamics of black holes such as the $D$ dimensional Kerr-AdS black holes in cosmological Einstein's theory and the spherically symmetric black holes in the Einstein-Gauss-Bonnet theory changes. We give the effective volume of black holes even without a cosmological constant.

gr-qc↗
arXiv2024

A search for Planet Nine with small spacecraft:Three-body, post-Newtonian, non-gravitational, planetary and Kuiper Belt effects

A hypothetical gravitating body in the outer Solar System, the so-called Planet Nine, was proposed to explain the unexpected clustering of the Kuiper Belt Objects. As it has not been observed via telescopes, it was conjectured to be a primordial black hole (of the size of a quince) that could be gravitationally detected by laser-launching or solar sailing many small spacecraft. Here, we study various aspects affecting such a search for Planet Nine. Our basic observable is the angular displacement in the trajectory of a small spacecraft which will be mainly affected by the gravity of Planet Nine, augmented with several other 3-body, non-gravitational, post-Newtonian, planetary, and Kuiper Belt effects. First, we calculate the effect of the Sun in the framework of the circular restricted three-body problem of the Sun--Planet Nine-spacecraft for the two particular initial conditions. Then, we study the effects of Kuiper Belt and outer planets, namely Jupiter, Saturn, Uranus, Neptune, as well as non-gravitational perturbations such as magnetic and drag forces exerted by the interstellar medium; and the solar radiation pressure. In addition, we investigate the post-Newtonian general relativistic effects such as the frame-dragging, Schwarzschild effect, and geodetic precession on the spacecraft trajectory. We show that the leading order angular displacement is due to the solar radiation pressure for the lower spacecraft velocities, and the drag force for the higher spacecraft velocities. Among the general relativistic effects, the frame-dragging has the smallest effect; and the Schwarzschild effect due to Sun has the largest effect. However, none of the general relativistic effects produces a meaningful contribution to the detection.

astro-ph.EP↗
arXiv2024

Minimal Einstein-Aether Theory

We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by the aether field. This limit is obtained by taking three of the coupling constants of the theory to be zero but keeping the expansion coupling constant to be nonzero. We then consider the further reduction of this limited version of Einstein-Aether theory by taking the expansion of the aether field to be constant (possibly zero), and thereby we introduce the Minimal Einstein-Aether theory that supports the Einstein metrics as solutions with a reduced cosmological constant. The square of the expansion of the unit-timelike aether field shifts the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar system tests and black hole physics including gravitational waves.

gr-qc↗
arXiv2024

Constraints and Time Evolution in Generic $f$(Riemann) Gravity

We give a detailed canonical analysis of the $n$-dimensional $f$(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer-Marsden form which is amenable to identifying the non-stationary energy on a spacelike hypersurface. We give pure $R^{2}$ and $R_{μν}R^{μν}$ theories as examples.

gr-qc↗
arXiv2024

Spin-spin Interactions in General Relativity versus Linearized Massive Gravity: $N$-body Simulations

We simulated spin-spin interactions of $N$-bodies in linearized General Relativity (GR) and linearized Massive Gravity of the Fierz-Pauli type (mGR). It was noted earlier that there is a discrete difference between the spin-spin interaction potential in GR and mGR for a $2$-body system, akin to the van Dam-Veltman-Zakharov discontinuity in the static Newton's potential. Specifically, at large distances, GR favors anti-parallel spin orientation with total spin pointing along the interaction axis, while mGR favors parallel spin orientation with total spin perpendicular to the axis between the sources. For an $N$-body system, a simulation in mGR hitherto has not been done and one would like to know the total spin of the system in both theories. Here we remedy this. In the simulations of GR, we observed that the total spin tends to decrease from a random initial configuration, while for mGR with a large distance, the total spin increases.

gr-qc↗
arXiv2024

Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories

We study symmetry reductions in the context of Euclidean Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in certain gauge theories is a common tool for obtaining explicit soliton solutions. Although pure Chern-Simons theories do not admit solitonic solutions, symmetry reduction still leads to interesting results. We establish relations at the semiclassical regime between pure Chern-Simons theories on $S^3$ and the reduced Quantum Field Theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding $BF$-theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instantons and show that under certain circumstances, the reduced action can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions have a fermionic nature at the level of the partition function.

hep-th↗
arXiv2024

Membrane Paradigm Approach to the Johannsen-Psaltis Black Hole

The Johannsen-Psaltis (JP) black hole is a phenomenologically viable metric obtained by judiciously deforming the Kerr black hole such that the metric is asymptotically flat and causal and is consistent with the weak field, post-Newtonian tests of gravity; however, it has additional hairs besides its mass and angular momentum. As it deviates from the Kerr black hole in the strong coupling regime, it is a useful metric to test the Kerr hypothesis that states that all astrophysical black holes are of the Kerr type. Here we give a membrane description of this black hole that effectively amounts to replacing the observable part of the black hole with a fluid with thermal properties. A timelike membrane, a stretched horizon local in time is assumed to exist. This membrane is expected to approximate the null event horizon that is highly non-local in time. We derive the energy-momentum tensor of the fluid and all the transport coefficients using the action formulation to the membrane as advocated by Parikh and Wilczek. In the fluid description, one observes that the finiteness of the transport coefficients constrains the additional hairs of the Johannsen-Psaltis black hole. Analytically continuing the pressure of the fluid to all values of the radial coordinate $r$, one obtains interesting Van der Waals-type behavior of the pressure of the fluid which diverges at the radius of the outer ergosphere, lending support, from the membrane paradigm's perspective to the claim that relativistic astrophysical jets are produced by the ergoregion of the black hole.

gr-qc↗
arXiv2024

Coupling Constants as Conserved Charges in Black Hole Thermodynamics

In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

gr-qc↗
arXiv2024

Instability of a Kerr-type naked singularity due to light and matter accretion and its shadow

We study null and timelike constant radii geodesics in the environment of an over-spinning putative Kerr-type naked singularity. We are particularly interested in two topics: first, the differences of the shadows of the naked rotating singularity and the Kerr black hole; and second, the spinning down effect of the particles falling from the accretion disk. Around the naked singularity, the non-equatorial prograde orbits in the Kerr black hole remain intact up to a critical rotation parameter ($α=\sqrt{6 \sqrt{3}-9}$) and cease to exist above this value [Eur. Phys. J. C 78, 879 (2018)]. This has an important consequence in the shadow of the naked singularity if the shadow is registered by an observer on the polar plane or close to it as the shadow cannot be distinguished from that of a Kerr black hole viewed from the same angle considering only the light emanating from the unstable photon orbits. We show that the timelike retrograde orbits in the equatorial plane immediately (after about an 8% increase in mass for the case of initial $α=1.5$) reduce the spin parameter of the naked singularity from larger values to $α=1$ at which an event horizon appears. This happens because the retrograde orbits have a larger capture cross-section than the prograde ones. So if a naked singularity happens to have an accretion disk, it will not remain naked for long, an event horizon forms.

gr-qc↗
arXiv2024

Non-stationary Energy of Perfect Fluid Sources in General Relativity

The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a geometric invariant of the spatial hypersurface of the spacetime and is expressed as an integral on the boundary of the hypersurface. For non-stationary spacetimes, there is a refinement of the ADM energy, the so-called Dain's invariant that measures the non-stationary part, the gravitational radiation component, of the total energy. Dain's invariant uses the metric and the extrinsic curvature of the spatial hypersurface together with the so-called approximate Killing initial data and vanishes for stationary spacetimes. In our earlier work [Phys.Rev.D 101 (2020)2, 024035], we gave a reformulation of the non-stationary energy for vacuum spacetimes in the Hamiltonian form of General Relativity written succinctly in the Fischer-Marsden form. That formulation is relevant for merging black holes or other compact sources. Here we extend this formulation to non-vacuum spacetimes with a perfect fluid source. This is expected to be relevant for spacetimes that have a compact star, say a neutron star colliding with a black hole or another non-vacuum object.

gr-qc↗
arXiv2024

Mass formulas for individual black holes in merging binaries

We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency $f_1$, the maximum detected frequency (chirp frequency) $f_2$, and the time elapse $τ$ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave in Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and {suggest} a way to write down an average power formula coming from perturbative General Relativity.

gr-qc↗
arXiv2024

Kerr-Vaidya type radiating black holes in semi-classical gravity with conformal anomaly

Static black holes in the conformal anomaly-sourced semi-classical General Relativity in four dimensions were extended to rotating, stationary solutions, recently. These quantum-corrected black holes show different features compared to the Kerr black hole and need for further extensions. Here we remove the condition of stationarity and find radiating (Kerr-Vaidya-type) solutions in the same theory augmented with a cosmological constant. As long as the coupling constant $α$ of the $A$-type trace anomaly is non-zero, we show that $i)$ the cosmological constant is bounded from above, i.e $Λ\le \frac{3}{4 α}$; $ii)$ static black holes exist but they may not be unique; $iii)$ static black holes do not satisfy the second law of black hole thermodynamics; $iv)$ static black holes may have unstable inner horizons; $v)$ In the nonstationary and axially symmetric case, stability of the event horizon and the second law of thermodynamics black holes are problematic.

gr-qc↗
arXiv2023

A New Geometric Flow on 3-Manifolds: the $K$-Flow

We define a new geometric flow, which we shall call the $K$-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston's model geometries under this flow both analytically and numerically. As an example, we show that an initially arbitrarily deformed homogeneous 3-sphere flows into a round 3-sphere and shrinks to a point in the unnormalized flow; or stays as a round 3-sphere in the volume normalized flow. The $K$-flow equation arises as the gradient flow of a specific purely quadratic action functional that has appeared as the quadratic part of New Massive Gravity in physics; and a decade earlier in the mathematics literature, as a new variational characterization of three-dimensional space forms. We show the short-time existence of the $K$-flow using a DeTurck-type argument.

math.DG↗
arXiv2023

A Systematic Construction of Kastor-Traschen Currents and their Extensions to Generic Powers of Curvature

Kastor and Traschen constructed totally anti-symmetric conserved currents that are linear in the Riemann curvature in spacetimes admitting Killing-Yano tensors. The construction does not refer to any field equations and is built on the algebraic and differential symmetries of the Riemann tensor as well as on the Killing-Yano equation. Here we give a systematic generalization of their work and find divergence-free currents that are built from the powers of the curvature tensor. A rank-4 divergence-free tensor that is constructed from the powers of the curvature tensor plays a major role here and it comes from the Lanczos-Lovelock theory.

gr-qc↗
arXiv2023

Partition Function of a Volume of Space in a Higher Curvature Theory

Recently, [Phys. Rev. Lett. 130, 221501 (2023)] Jacobson and Visser calculated the quantum partition function of a fixed, finite volume of a region with the topology of a ball in the saddle point approximation within the context of Einstein's gravity with or without a cosmological constant. The result can be interpreted as the dimension of Hilbert space of the theory. Here we extend their computation to a theory defined in principle with infinitely many powers of curvature in three dimensions. We confirm their result: The partition function of a spatial region in the leading saddle point approximation is given as the exponential of the Bekenstein-Hawking or the Wald entropy of the boundary of the finite spatial region both in the case of zero and finite cosmological constant. In the latter case, the effective Newton's constant appears in the entropy formula. The calculations lend support to the holographic nature of gravity for finite regions of space with a boundary.

hep-th↗
arXiv2023

A Tribute to S. Deser: Conserved Quantities in Generic Gravity Theories

I describe parts of my joint work with S. Deser [March 19, 1931 - April 21, 2023] which started when I was working as a post-doc at Brandeis University in 2001. Our work was mostly, but not exclusively, on conserved charges of higher curvature theories of gravity. I also describe some recent developments, such as expressing the conserved charges in terms of the linearized Riemann tensor; I expound upon the computations. I also reminisce about our interaction for over two decades that went beyond our scientific collaboration. The physics part of this review is intended for graduate students and researchers interested in extended theories of gravity, especially about the conserved quantities and perturbative techniques in these theories.

gr-qc↗