arXiv subjects

Bayram Tekin

Publications and source records attributed to Bayram Tekin.

At least 55 records · Page 3Linked to original sources

arXiv2023

Israel-Wilson-Perjes Metrics in a Theory with a Dilaton Field

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.

gr-qc↗

arXiv2023

Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism

We study the momentum and Hamiltonian constraints of vacuum Einstein equations, within the Bowen-York formalism, for two interacting black holes in close separation, with anti-parallel spins and anti-parallel linear momenta. We give an analytical solution using perturbation theory. We also compute the location and the shape of the apparent horizon which generically depend on all the parameters, angles and the separation between the black holes. Our solution only works for distances far away from the black holes. To gain more insight close to the black holes, one has to go to the higher orders in perturbation theory, which is a rather cumbersome process. But the solution presented here can be of some use for numerical computations as the latter should match our result for the described problem.

gr-qc↗

arXiv2023

Hawking Temperature as the Total Gauss-Bonnet Invariant of the Region Outside a Black Hole

We provide two novel ways to compute the surface gravity ($κ$) and the Hawking temperature $(T_{H})$ of a stationary black hole: in the first method $T_{H}$ is given as the three-volume integral of the Gauss-Bonnet invariant (or the Kretschmann scalar for Ricci-flat metrics) in the total region outside the event horizon; in the second method it is given as the surface integral of the Riemann tensor contracted with the covariant derivative of a Killing vector on the event horizon. To arrive at these new formulas for the black hole temperature (and the related surface gravity), we first construct a new differential geometric identity using the Bianchi identity and an antisymmetric rank-$2$ tensor, valid for spacetimes with at least one Killing vector field. The Gauss-Bonnet tensor and the Gauss-Bonnet scalar play a particular role in this geometric identity. We calculate the surface gravity and the Hawking temperature of the Kerr and the extremal Reissner-Nordström holes as examples.

gr-qc↗

arXiv2023

Light Rings around Five Dimensional Stationary Black Holes and Naked Singularities

The existence of light rings in a spacetime is closely related to the existence of black hole horizons and observables such as the ringdown and the shadow. Black holes, compared to nonvacuum ultracompact objects, have rather unique environments. To this aim, recently [P.V.P. Cunha and C.A.R. Herdeiro, Phys. Rev. Lett. \textbf{124}, 181101 (2020)] topological arguments, independent of the underlying gravity theory, were developed to prove the existence of unstable light rings outside the Killing horizon of {\it four} dimensional asymptotically flat, stationary, axisymmetric, nonextremal black holes. Here we extend these arguments to five-dimensional stationary black holes. Generically in five dimensions, there are two possible conserved angular momenta, hence the four-dimensional discussion does not extend verbatim to five dimensions; nevertheless, we prove that there is a light ring for each rotation sense for a stationary black hole. We give the static and the Myers-Perry rotating black holes as examples. We also show that when the horizon of the black hole disappears and the singularity becomes naked, only one of the light rings survives; a similar phenomenon also occurs in four dimensions which might allow testing the cosmic censorship hypothesis.

gr-qc↗

arXiv2022

Anomalous Dispersion in Gravity Theories

A wave pulse (be it a gravitational wave or a light wave) undergoes anomalous dispersion in a vacuum in flat spacetimes with an even number of spatial dimensions even if all the frequencies move at the same speed. Such an anomalous dispersion does not occur in spacetimes with an odd number of spatial dimensions. We study various gravity theories and show that dispersion-free propagation is possible in even number of spatial dimensions if the background is not the Minkowski but the de Sitter spacetime and the gravity theory is massive gravity with a tuned mass in terms of the cosmological constant. Mass and the cosmological constant conspire to get rid of the anomalous dispersion and restore Huygens' principle.

gr-qc↗

arXiv2021

Spherical timelike orbits around Kerr black holes

We study the order ten polynomial equation satisfied by the radius of the spherical timelike orbits for a massive particle with a generic energy around a Kerr black hole. Even though the radii of the prograde and retrograde orbits at the equatorial or polar plane for particles with zero or unit energy have a monotonic dependence on the rotation parameter of the black hole, we show that there is a critical inclination angle above which the retrograde orbits have a nonmonotonic dependency on the rotation of the black hole. Thus the capture cross-section of these retrograde orbits decrease with increasing black hole spin. Hence their efficiency to reduce the black hole's spin is decreased. We also provide an equation for the critical inclination angle that shows exactly at which point the nonmonotonicity starts. In addition, we employ the Lagrange-Bürmann method to find approximate analytic solutions from the known exact solutions.

gr-qc↗

arXiv2021

Hyperbolic Metamaterials and Massive Klein-Gordon Equation in 2+1 Dimensional de Sitter Spacetime

The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave equation, unexpectedly, allows dispersionless propagation albeit having two spatial dimensions. Here we show that the same equation can be naturally interpreted as a particular massive Klein-Gordon equation with the usual one timelike and two spacelike dimensions in a de Sitter (dS) background spacetime. The mass parameter of the scalar field is given in terms of the cosmological constant, Planck constant and the speed of light as $m =\sqrtΛ\frac{\hbar}{c}$ which corresponds to the point for which the left and right conformal weights of the boundary conformal field theory (CFT) (via the de Sitter/CFT correspondence) are equal. This particular mass corresponds to the gapless mode in the dS spacetime for which the dispersion relation is linear in the wave number.

hep-th↗

arXiv2021

Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory

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 clean-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.

gr-qc↗

arXiv2021

First law of black hole thermodynamics and Smarr formula with a cosmological constant

The first law of black hole thermodynamics in the presence of a cosmological constant $Λ$ can be generalized by introducing a term containing the variation $δΛ$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc., it has been shown [Classical Quantum Gravity 35, 125012 (2018)] that the new term has the same structure: $Λ$ is a conserved charge associated with a gauge symmetry; and its role in the first law is quite similar to an ``electric charge" rather than to the pressure. Besides, its conjugate chemical potential resembles an ``electric potential" on the horizon, in contrast with the volume enclosed by horizon. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the ``effective volume" of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of ``$Λ$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Especially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well defined in principle.

gr-qc↗

arXiv2021

Basics of Apparent Horizons in Black Hole Physics

Event Horizon, a null hypersurface defining the boundary of the black hole region of a spacetime, is not particularly useful for evolving black holes since it is non-local in time. Instead, one uses the more tangible concept of Apparent Horizon for dynamical black holes out there in the sky that do all sorts of things: evolve, merge and feed on the environment. Event Horizon, being a gauge-independent, global property of the total spacetime is easy to define and locate in the stationary case; on the other hand, Apparent Horizon depends on the embedding of the surface in spacetime and hence it is somewhat tricky to define. But for numerical simulations in General Relativity, locating the Apparent Horizon helps one to excise the black hole region and the singularity to have a stable computation. Moreover, for stationary solutions the two horizons match. Here we give a detailed pedagogical exposition of the subject and work out the non-trivial case of a slowly moving and spinning black hole.

gr-qc↗

arXiv2021

Einstein-Yang-Mills Theory: Gauge Invariant Charges and Linearization Instability

We construct the gauge-invariant electric and magnetic charges in Yang-Mills theory coupled to cosmological General Relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser. For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

hep-th↗

arXiv2021

Approximate analytical description of apparent horizons for initial data with momentum and spin

We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent horizon and show the dependence of its shape on the angle between the spin and the linear momentum. In particular a dimple, whose location depends on the mentioned angle, arises on the 2-sphere geometry of the apparent horizon. We exclusively work in the case of conformally flat initial metrics.

gr-qc↗

arXiv2021

Bowen-York Model Solution Redux

Initial value problem in General Relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between $[0, 0.592)$. This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is $59.2 \%$ of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

gr-qc↗

arXiv2020

Exact Formulas for Spherical Photon Orbits Around Kerr Black Holes

Exact formulas relating the radii of the spherical photon orbits to the black hole's rotation parameter and the effective inclination angle of the orbit have been known only for equatorial and polar orbits up to now. Here we provide exact formulas for nonequatorial orbits that lie between these extreme limits. For a given rotation parameter of the black hole, there is a critical inclination angle below which there are four null photon orbits two of which are in the exterior region. At the critical angle, the radii of these orbits are explicitly found. We also provide approximate but very accurate formulas for any orbit. To arrive at these analytical solutions, we carefully study the sextic polynomial in the radius that arises for null spherical geodesics.

gr-qc↗

arXiv2020

Comment on "Einstein-Gauss-Bonnet Gravity in 4-Dimensional Space-Time''

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.

gr-qc↗

arXiv2020

Superposition of FLRW Universes

We show that (1) the Einstein field equations with a perfect fluid source admit a nonlinear superposition of two distinct homogenous Friedman-Lemaitre-Robertson-Walker (FLRW) metrics as a solution, (2) the superposed solution is an inhomogeneous geometry in general, (3) it reduces to a homogeneous one in the two asymptotes which are the early and the late stages of the universe as described by two different FLRW metrics, (4) the solution possesses a scale factor inversion symmetry and (5) the solution implies two kinds of topology changes: one during the time evolution of the superposed universe and the other occurring in the asymptotic region of space.

gr-qc↗

arXiv2020

Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?

No! We show that the field equations of Einstein-Gauss-Bonnet theory defined in generic $D>4$ dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to $D=4$. Therefore, the recently introduced four-dimensional, novel, Einstein-Gauss-Bonnet theory does not admit an intrinsically four-dimensional definition as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain $D>4$ 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.

gr-qc↗

arXiv2020

Event Horizon Detecting Invariants

Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in $D > 3$ dimensions, but they fail for the three dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here we provide an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces instead of the full spacetime. Our method is also applicable to black holes in generic dimensions but is most efficient in three, four, and five dimensions. We give four dimensional Kerr, five dimensional Myers-Perry and three dimensional warped-anti-de Sitter, and the three dimensional asymptotically flat black holes as examples.

hep-th↗