arXiv subjects

Koray Düztaş

Publications and source records attributed to Koray Düztaş.

29 records · Page 2Linked to original sources

arXiv2018

Group theoretical formulation of free fall and projectile motion

In this work we formulate the group theoretical description of free fall and projectile motion. We show that the kinematic equations for constant acceleration form a one parameter group acting on a phase space. We define the group elements $ϕ_t$ by their action on the points in the phase space. We also generalize this approach to projectile motion. We evaluate the group orbits regarding their relations to the physical orbits of particles and unphysical solutions. We note that the group theoretical formulation does not apply to more general cases involving a time dependent acceleration. This method improves our understanding of the constant acceleration problem with its global approach. It is especially beneficial for students who want to pursue a career in theoretical physics.

physics.gen-ph↗

arXiv2018

Cosmic censorship and the third law of black hole dynamics

Israel's proof of the third law of black hole dynamics is based on the semi-rigidity assumption which requires that the areas of the outermost trapped surfaces are preserved. We argue that the condition that the area of the event horizon should not decrease is necessary -but not sufficient- for the semi-rigidity assumption to hold. It is known that the presence of a naked singularity in the exterior region invalidates Hawking's proof of the area theorem. In this sense, the third law assumes the validity of the strong form of the cosmic censorship conjecture, contrary to general acceptance. Still, one cannot guarantee that the semi-rigidity assumption holds. Therefore the current proof is incomplete. Recent studies on the interactions of black holes with fermionic fields imply a generic formation of naked singularities. The presence of these singularities invalidates the laws of black hole dynamics and cosmic censorship conjecture for the processes that satisfy the weak energy condition.

gr-qc↗

arXiv2018

Can test fields destroy the event horizon in the Kerr-Taub-NUT spacetime?

In this work we investigate if the interaction of the Kerr-Taub-NUT spacetime with test scalar and neutrino fields can lead to the destruction of the event horizon. It turns out that both extremal and nearly extremal black holes can be destroyed by scalar and neutrino fields if the initial angular momentum of the spacetime is sufficiently large relative to its mass and NUT charge. This is the first example in which a classical field satisfying the null energy condition can actually destroy an extremal black hole. For scalar fields, the modes that can lead to the destruction of the horizon are restricted to a narrow range due to superradiance. Since superradiance does not occur for neutrino fields, the destruction of the horizon by neutrino fields is generic, and it cannot be fixed by backreaction effects. We also show that the extremal black holes that can be destroyed by scalar fields correspond to naked singularities in the Kerr limit, in accord with the previous results which imply that extremal Kerr black holes cannot be destroyed by scalar test fields.

gr-qc↗

arXiv2017

Coulomb fields as perturbations of type D vacuum space-times

We consider a test, non-null electromagnetic field special in the sense that the principal null directions of the field lie along the two repeated principal null directions of the type D vacuum background. We prove that the special non-null field is a valid solution of the Maxwell equations on a type D background. This field behaves as $1/r^2$ and the only non-vanishing Maxwell scalar is $ϕ_1$ so it can be called the Coulomb field. We show that the contribution to the energy and angular momentum fluxes of the Coulomb field vanishes at any surface of integration, on the type D vacuum backgrounds Kerr, Kerr-Taub-NUT, Taub-NUT, and Schwarzschild. Therefore this field does not lead to any perturbations of the mass and angular momentum parameters of these space-times.

gr-qc↗

arXiv2017

Overspinning BTZ black holes with test particles and fields

It has been claimed that in a test of an asymptotically AdS version of weak cosmic censorship conjecture by attempting to overspin a BTZ black hole with test particles, one finds that it is not possible to spin-up the black hole past its extremal limit. The result of this analysis is restricted to the case where the initial black hole is extremal. We extend this analysis to find that massive test particles can overspin the black hole, if we start with a nearly extremal black hole, instead. We also consider the interaction of the BTZ black hole with test fields. We show that overspinning of nearly extremal black holes is possible whether or not there is superradiance for the field. If there is superradiance, overspinning occurs in a narrow range of frequencies bounded below by the super-radiant limit. However, if there is no superradiance for the field, overspinning becomes generic and also applies to extremal black holes. This is in analogy with the Kerr case.

gr-qc↗

arXiv2016

Is there a mode stability paradox for neutrino perturbations of Kerr black holes?

Adopting the notation of Teukolsky and Press, we derive the connection relation for asymptotic solutions of the massless Dirac equation on a Kerr background. We show that, unlike bosonic fields, the connection relation for massless Dirac fields (neutrino) provides a rigorous proof of mode stability. The same relation also implies that every incoming mode can be absorbed by the black hole or there is no superradiance. Recent works on overspinning black holes have shown that this can lead to the formation of naked singularities. We argue that the fact that both the mode stability of the black hole under neutrino perturbations and the instability of the event horizon (therefore the instability of the black hole) can be derived from the same connection relation leads to a paradox. In other words mode, stability implies event horizon instability as far as neutrino perturbations are concerned.

gr-qc↗

arXiv2016

Hawking radiation as the cosmic censor

Hawking radiation acts as a cosmic censor since it carries away the angular momentum of the black hole, proportionally more than its mass. In this work we first show that an extremal black hole cannot exist since it will be pushed away from extremality by its own Hawking radiation, without being perturbed by any external effect. We evaluate the efficiency of Hawking radiation to prevent overspinning of black holes. We make an order of magnitude estimate to show that evaporation can prevent overspinning of black holes with an upper limit of mass $M\lesssim 10^{17}-10^{18}\rm{g}$, when we take the interaction period to be the age of the universe. Overspinning of black holes of higher masses by test fields remains possible, even if evaporation is taken into account. We also discuss the possibility to attribute a shorter interaction period for the problem which would reduce the effect of evaporation.

gr-qc↗

arXiv2016

The decoupling problem of the Proca equation; and treatment of Dirac, Maxwell and Proca fields on the resulting pp-wave spacetimes

In this work we take a formal approach to the problem of decoupling Proca equations in curved space-times. We use Newman-Penrose (NP) two-spinor formalism to represent the Proca vector by one complex and two real scalars. We show that a decoupled second order differential equation for one of the real scalars can be derived if and only if the background space-time admits a covariantly constant null vector. Thus, the background space-time must be a pp-wave vacuum. We evaluate the separability of Proca, Maxwell and Dirac equations on the resulting pp-wave background.

gr-qc↗

arXiv2015

Weak Cosmic Censorship, Superradiance and Quantum Particle Creation

Since 1970's, gedanken experiments have been devised to challenge the weak cosmic censorship conjecture (WCCC), which is the expectation that spacetime singularities will be hidden from faraway observers by event horizons so that classical predictability in a spacetime is preserved. These experiments involve the interaction of an extremal or a slightly sub-extremal black hole with a test particle or field, attempting to destroy the horizon, i.e. to create a so-called naked singularity. They usually conclude that WCCC cannot be violated starting from an extremal black hole, but may be violated starting from a slightly sub-extremal one, if backreaction and self-force effects are neglected. Some other works also analyze these effects. Starting 2007, a string of papers argue if WCCC can be violated by classically forbidden interactions occuring via the quantum nature of the particles associated with the fields; and where backrection and/or superradiance are pointed out as effects working in the direction of preserving the WCCC. We correct/modify a backrection argument, and furthermore point out that superradiance does not prevent {\em single particles} from being captured by the black hole; even if this capture would lead to WCCC violation. Then we consider the spontaneous emission (which we call the Zel'dovich-Unruh effect) of particles by the black hole, and find that at least for scalars, it can be understood without second quantization. It also completely invalidates the mentioned single- or few-particle thought experiments. However, the conclusions of our previous work on (at least) scalar fields interacting with black holes, i.e. that WCCC may be violated starting from slightly subextremal black holes, remains valid in this (semi)classical framework.

gr-qc↗

arXiv2014

Electromagnetic field and cosmic censorship

We construct a gedanken experiment in which an extremal Kerr black hole interacts with a test electromagnetic field. Using Teukolsky's solutions for electromagnetic perturbations in Kerr spacetime, and the conservation laws imposed by the energy momentum tensor of the electromagnetic field and the Killing vectors of the spacetime, we prove that this interaction cannot convert the black hole into a naked singularity, thus cosmic censorship conjecture is not violated in this case.

gr-qc↗

arXiv2013

Cosmic Censorship, Black Holes and Integer-spin Test Fields

It has been argued that, starting with a slightly sub-extremal Kerr black hole instead of an extremal one, it is possible to overspin a black hole past the extremal limit and turn it into a naked singularity by sending test bodies, if one neglects radiative and self-force effects. In this work we show that (i) an extremal Kerr black hole can not be overspun as a result of the interaction with massless integer spin test fields (scalar, electromagnetic, or gravitational), (ii) overspinning can be achieved if we start with a nearly extremal black hole instead, and (iii) for the scalar field, the argument applies to more general black holes, and also allows use of a more general field configuration. Our analysis also neglects radiative and self-force effects.

gr-qc↗