arXiv subjects

G. V. Kraniotis

Publications and source records attributed to G. V. Kraniotis.

At least 19 recordsLinked to original sources

arXiv2023

Differential curvature invariants and event horizon detection for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime

We compute analytically differential invariants for accelerating, rotating and charged black holes with a cosmological constant $Λ$. In particular, we compute in closed form novel explicit algebraic expressions for curvature invariants constructed from covariant derivatives of the Riemann and Weyl tensors, such as the Karlhede and the Abdelqader-Lake invariants, for the Kerr-Newman-(anti-)de Sitter and accelerating Kerr-Newman-(anti-)de Sitter black hole spacetimes. We explicitly show that some of the computed curvature invariants are vanishing at the event and Cauchy horizons or the ergosurface of the accelerating, charged and rotating black holes with a non-zero cosmological constant. Using a particular generalised null-tetrad and the Bianchi identities we compute in the Newman-Penrose formalism in closed-analytic form the Page-Shoom curvature invariant for the accelerating Kerr-Newman black hole in (anti-)de Sitter spacetime and prove that is vanishing at the black hole event and Cauchy horizon radii. Therefore such invariants can serve as possible detectors of the event horizon and ergosurface for such black hole metrics which belong to the most general type D solution of the Einstein-Maxwell equations with a cosmological constant. Also the norms associated with the gradients of the first two Weyl invariants in the Zakhary-McIntosh classification, were studied in detail. Although both locally single out the horizons, their global behaviour is also intriguing. Both reflect the background angular momentum and electric charge as the volume of space allowing a timelike gradient decreases with increasing angular momentum and charge.

gr-qc↗

arXiv2022

Curvature Invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime

The curvature scalar invariants of the Riemann tensor are important in General Relativity because they allow a manifestly coordinate invariant characterisation of certain geometrical properties of spacetimes such as, among others, curvature singularities, gravitomagnetism. We calculate explicit analytic expressions for the set of Zakhary-McIntosh curvature invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime as well as for the Kerr-Newman-(anti-)de Sitter black hole. These black hole metrics belong to the most general type D solution of the Einstein-Maxwell equations with a cosmological constant. Explicit analytic expressions for the Euler-Poincare density invariant, which is relevant for the computation of the Euler-Poincare characteristic $χ(M)$, and the Kretschmann scalar are also provided for both cases. We perform a detailed plotting of the curvature invariants that reveal a rich structure of the spacetime geometry surrounding the singularity of a rotating, electrically charged and accelerating black hole . These graphs also help us in an exact mathematical way to explore the interior of these black holes. Our explicit closed form expressions show that the above gravitational backgrounds possess a non-trivial Hirzebruch signature density. Possible physical applications of this property for the electromagnetic duality anomaly in curved spacetimes that can spoil helicity conservation are briefly discussed.

gr-qc↗

arXiv2021

Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr-Newman-de Sitter and Kerr-Newman black hole geometries

We investigate the redshift and blueshift of light emitted by timelike geodesic particles in orbits around a Kerr-Newman-(anti) de Sitter (KN(a)dS) black hole. Specifically we compute the redshift and blueshift of photons that are emitted by geodesic massive particles and travel along null geodesics towards a distant observer-located at a finite distance from the KN(a)dS black hole. For this purpose we use the Killing-vector formalism and the associated first integrals-constants of motion. We consider in detail stable timelike equatorial circular orbits of stars and express their corresponding redshift/blueshift in terms of the metric physical black hole parameters (angular momentum per unit mass, mass, electric charge and the cosmological constant) and the orbital radii of both the emitter star and the distant observer. These radii are linked through the constants of motion along the null geodesics followed by the photons since their emission until their detection and as a result we get closed form analytic expressions for the orbital radius of the observer in terms of the emitter radius, and the black hole parameters. In addition, we compute exact analytic expressions for the frame dragging of timelike spherical orbits in the KN(a)dS spacetime in terms of multivariable generalised hypergeometric functions of Lauricella and Appell. We solve the conditions for timelike spherical orbits in KN(a)dS and KN spacetimes. We present new, elegant compact forms for the parameters of these orbits. Last but not least we derive a very elegant and novel exact formula for the periapsis advance for a test particle in a non-spherical polar orbit in KNdS black hole spacetime in terms of Jacobi's elliptic function sn and Lauricella's hypergeometric function $F_D$.

gr-qc↗

arXiv2020

Existence and Stability of Static Spherical Fluid Shells in a Schwarzschild-Rindler-anti-de Sitter Metric

We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(dθ^2 +\sin ^2 θdϕ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\fracΛ{3}r^2$. This is an alternative to the well known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In the SRAdS spacetime the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three shell fluid equations of state: vacuum shell ($p=-σ$), stiff matter shell ($p=σ$) and dust shell ($p=0$) where $p$ is the shell pressure and $σ$ is the shell surface density. We also identify the metric parameter conditions that need to be satisfied for shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence sf stable spherical scalar field domain walls in the SRAdS spacetime.

gr-qc↗

arXiv2019

The massive Dirac equation in the Kerr-Newman-de Sitter and Kerr-Newman black hole spacetimes

Exact solutions of the Dirac general relativistic equation (DE) that describe the dynamics of a massive, electrically charged particle with half-integer spin in the curved spacetime geometry of an electrically charged, rotating Kerr-Newman-(anti) de Sitter black hole (BH) are investigated. We first, derive the DE in the Kerr-Newman-de Sitter (KNdS) BH background using a generalised Kinnersley null tetrad in the Newman-Penrose formalism. In this frame, we prove the separation of the DE into ordinary differential equations for the radial and angular parts. Under specific transformations of the independent and dependent variables we prove that the transformed radial equation for a massive charged spin $\frac{1}{2}$ fermion in the background KNdS BH constitutes a highly non-trivial generalisation of Heun's equation. Using a Regge-Wheeler-like independent variable we transform the radial equation in the KNdS background into a Schrödinger-like differential equation and investigate its asymptotic behaviour near the event and cosmological horizons. For a massive fermion (MF) in the background of a Kerr-Newman (KN) BH we first prove that the radial and angular equations that result from the separation of DE reduce to the generalised Heun differential equation (GHE). The local solutions of such GHE are derived and can be described by holomorphic functions whose power series coefficients are determined by a four-term recurrence relation. Using asymptotic analysis we derive the solutions for the MF far away from the KN BH and the solutions near the event horizon . The determination of the separation constant as an eigenvalue problem in the KN background is investigated. Using the aforementioned four-term recursion formula we prove that in the non-extreme KN geometry there are no bound states with $ω^2<μ^2$, where $ω$ and $μ$ are the energy and mass of the fermion respectively.

gr-qc↗

arXiv2016

The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole

Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of a charged, rotating Kerr-Newman-(anti) de Sitter black hole are investigated. In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation with the method of separation of variables results in Fuchsian differential equations for the radial and angular parts which contain more than three finite singularities and thereby generalise the Heun differential equations (HE). For particular values of the physical parameters (i.e mass of the scalar particle) these Fuchsian equations reduce to Heun equations and the solutions are expressed in terms of Heun functions. For other values of the parameters some of the extra singular points are false singular points. We derive the conditions on the coefficients of the generalised Fuchsian equation such that a singular point is a false point. In such a case the exact solution of the Fuchsian equation can in principle be simplified and expressed in terms of Heun functions. We also derive the exact solutions of the radial and angular equations for a massive scalar (charged) particle in the Kerr-Newman spacetime. The analytic solutions are expressed in terms of confluent Heun functions. Moreover, we derived the constraints on the parameters of the theory such that the solution simplifies and expressed in terms of confluent Kummer hypergeometric functions. We also investigate the radial solutions in the KN case in the regions near the event horizon and far from the black hole. Finally, we construct several expansions of the solutions of the HE in terms of generalised hypergeometric functions of Lauricella-Appell.

gr-qc↗

arXiv2015

Gravitational lensing and frame dragging of light in the Kerr-Newman and the Kerr-Newman-(anti) de Sitter black hole spacetimes

The null geodesics that describe photon orbits in the spacetime of a rotating electrically charged black hole (Kerr-Newman) are solved exactly including the contribution from the cosmological constant. We derive elegant closed form solutions for relativistic observables such as the deflection angle and frame dragging effect that a light ray experiences in the gravitational fields (i) of a Kerr-Newman black hole and (ii) of a Kerr-Newman-de Sitter black hole. We then solve the more involved problem of treating a Kerr-Newman black hole as a gravitational lens, i.e. a KN black hole along with a static source of light and a static observer both located far away but otherwise at arbitrary positions in space. For this model, we derive the analytic solutions of the lens equations in terms of Appell and Lauricella hypergeometric functions and the Weierstraßmodular form. The exact solutions derived for null, spherical polar and non-polar orbits, are applied for the calculation of frame dragging for the orbit of a photon around the galactic centre, assuming that the latter is a Kerr-Newman black hole. We also apply the exact solution for the deflection angle of an equatorial light ray in the gravitational field of a Kerr-Newman black hole for the calculation of bending of light from the gravitational field of the galactic centre for various values of the Kerr parameter, electric charge and impact factor. In addition, we derive analytic expressions for the Maxwell tensor components for a Zero-Angular-Momentum-Observer (ZAMO) in the Kerr-Newman-de Sitter spacetime.

gr-qc↗

arXiv2013

Closed form solution for the surface area, the capacitance and the demagnetizing factors of the ellipsoid

We derive the closed form solutions for the surface area, the capacitance and the demagnetizing factors of the ellipsoid immersed in the Euclidean space R^3. The exact solutions for the above geometrical and physical properties of the ellipsoid are expressed elegantly in terms of the generalized hypergeometric functions of Appell of two variables. Various limiting cases of the theorems of the exact solution for the surface area, the demagnetizing factors and the capacitance of the ellipsoid are derived, which agree with known solutions for the prolate and oblate spheroids and the sphere. Possible applications of the results achieved, in various fields of science, such as in physics, biology and space science are briefly discussed.

math-ph↗

arXiv2011

Exact deflection of a Neutral-Tachyon in the Kerr's Gravitational field

We solve in closed analytic form space-like geodesic equations in the Kerr gravitational field. Such geodesic equations describe the motion of neutral tachyons (faster than light particles) in the Kerr spacetime. More specifically we derive the closed form solution for the deflection angle of a neutral tachyon on an equatorial orbit in Kerr spacetime. The solution is expressed elegantly in terms of Lauricella's hypergeometric function F_{D}.We applied our results to three cases: first, for the calculation of the deflection angle of a neutral tachyon on an equatorial trajectory in the gravitational field of a Kerr black hole. Subsequently, we applied our exact solutions to compute the deflection angle of equatorial spacelike geodesics in the gravitational fields of Sun and Earth assuming the Kerr spacetime geometry.

gr-qc↗

arXiv2010

Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses

The null geodesic equations that describe motion of photons in Kerr spacetime are solved exactly in the presence of the cosmological constant $Λ$. The exact solution for the deflection angle for generic light orbits (i.e. non-polar, non-equatorial) is calculated in terms of the generalized hypergeometric functions of Appell and Lauricella. We then consider the more involved issue in which the black hole acts as a `gravitational lens'. The constructed Kerr black hole gravitational lens geometry consists of an observer and a source located far away and placed at arbitrary inclination with respect to the black hole's equatorial plane. The resulting lens equations are solved elegantly in terms of Appell-Lauricella hypergeometric functions and the Weierstrass elliptic function. We then, systematically, apply our closed form solutions for calculating the image and source positions of generic photon orbits that solve the lens equations and reach an observer located at various values of the polar angle for various values of the Kerr parameter and the first integrals of motion. In this framework, the magnification factors for generic orbits are calculated in closed analytic form for the first time. The exercise is repeated with the appropriate modifications for the case of a non-zero cosmological constant.

gr-qc↗

arXiv2007

General relativity, Lauricella's hypergeometric function $F_D$ and the theory of braids

The exact (closed form) solutions of the equations of motion in the theory of general relativity that describe motion of test particle and photon in Kerr and Kerr-(anti) de Sitter spacetimes all involve the multivariable hypergeometric function of Lauricella $F_D$: Kraniotis [Class. Quantum Grav. {\bf 21} 2004, 4743; Class. Quantum Grav. {\bf 22} 2005, 4391; Class. Quantum Grav. {\bf 24} 2007, 1775]. The domain of variables ${\cal D}_n$ of the corresponding function depends on the first integrals of motion associated with the isometries of the Kerr-(anti) de Sitter metric and Carter's constant $Q$ as well as on the cosmological constant $Λ$ and the Kerr (rotation) parameter. In this work we discuss the topological properties of the domain ${\cal D}_n$ and in particular its fundamental connection with the theory of braids. An intrinsic relationship of general relativity with the pure braids is established.

gr-qc↗

arXiv2007

Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes

The exact solution for the motion of a test particle in a non-spherical polar orbit around a Kerr black hole is derived. Exact novel expressions for frame dragging (Lense-Thirring effect), periapsis advance and the orbital period are produced. The resulting formulae, are expressed in terms of Appell's first hypergeometric function $F_1$, Jacobi's amplitude function, and Appell's $F_1$ and Gau$ß$ hypergeometric function respectively. The exact expression for frame dragging is applied for the calculation of the Lense-Thirring effect for the orbits of S-stars in the central arcsecond of our Galaxy assuming that the galactic centre is a Kerr black hole, for various values of the Kerr parameter including those supported by recent observations. In addition, we apply our solutions for the calculation of frame dragging and periapsis advance for stellar non-spherical polar orbits in regions of strong gravitational field close to the event horizon of the galactic black hole, e.g. for orbits in the central milliarcsecond of our galaxy. Such orbits are the target of the GRAVITY experiment. We provide examples with orbital periods in the range of 100min - 54 days. Detection of such stellar orbits will allow the possibility of measuring the relativistic effect of periapsis advance with high precision at the strong field realm of general relativity. Further, an exact expression for the orbital period of a test particle in a non-circular equatorial motion around a Kerr black hole is produced. We also derive exact expressions for the periapsis advance and the orbital period for a test particle in a non-circular equatorial motion in the Kerr field in the presence of the cosmological constant in terms of Lauricella's fourth hypergeometric function $F_D$.

gr-qc↗

arXiv2005

Frame dragging and bending of Light in Kerr and Kerr-(anti) de Sitter spacetimes

The equations of general relativity in the form of timelike and null geodesics that describe motion of test particles and photons in Kerr spacetime are solved exactly including the contribution from the cosmological constant. We then perform a systematic application of the exact solutions obtained to the following cases. The exact solutions derived for null, spherical, polar and non-polar orbits are applied for the calculation of frame dragging (Lense-Thirring effect) for the orbit of a photon around the galactic centre, assuming that the latter is a Kerr black hole for various values of the Kerr parameter including those supported by recent observations. Unbound null polar orbits are investigated, and an analytical expression for the deviation angle of a polar photon orbit from the gravitational Kerr field is derived. In addition, we present the exact solution for timelike and null equatorial orbits. In the former case, we derive an analytical expression for the precession of the point of closest approach (perihelion, periastron) for the orbit of a test particle around a rotating mass whose surrounding curved spacetime geometry is described by the Kerr field. In the latter case, we calculate an exact expression for the deflection angle for a light ray in the gravitational field of a rotating mass (the Kerr field). We apply this calculation for the bending of light from the gravitational field of the galactic centre for various values of the Kerr parameter and the impact factor.

gr-qc↗

arXiv2005

A K-theory Anomaly Free Supersymmetric Flipped SU(5) Model from Intersecting Branes

We construct an N=1 supersymmetric three-family flipped SU(5) model from type IIA orientifolds on $T^6/(\Z_2\times \Z_2)$ with D6-branes intersecting at general angles. The model is constrained by the requirement that Ramond-Ramond tadpoles cancel, the supersymmetry conditions, and that the gauge boson coupled to the $U(1)_X$ factor does not get a string-scale mass via a generalised Green-Schwarz mechanism. The model is further constrained by requiring cancellation of K-theory charges. The spectrum contains a complete grand unified and electroweak Higgs sector, however the latter in a non-minimal number of copies. In addition, it contains extra matter both in bi-fundamental and vector-like representations as well as two copies of matter in the symmetric representation of SU(5).

hep-th↗

arXiv2005

A Supersymmetric Flipped SU(5) Intersecting Brane World

We construct an N=1 supersymmetric three-family flipped SU(5) model from type IIA orientifolds on $T^6/(\Z_2\times \Z_2)$ with D6-branes intersecting at general angles. The spectrum contains a complete grand unified and electroweak Higgs sector. In addition, it contains extra exotic matter both in bi-fundamental and vector-like representations as well as two copies of matter in the symmetric representation of SU(5).

hep-th↗

arXiv2004

Precise relativistic orbits in Kerr and Kerr-(anti) de Sitter spacetimes

The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the Hamilton-Jacobi partial differential equation by separation of variables. The solutions can be applied in the investigation of the motion of a test particle in the Kerr and Kerr-(anti) de Sitter gravitational fields. In particular, we apply the exact solutions of the timelike geodesics i) to the precise calculation of dragging (Lense-Thirring effect) of a satellite's spherical polar orbit in the gravitational field of Earth assuming Kerr geometry, ii) assuming the galactic centre is a rotating black hole we calculate the precise dragging of a stellar polar orbit aroung the galactic centre for various values of the Kerr parameter including those supported by recent observations. The exact solution of non-spherical geodesics in Kerr geometry is obtained by using the transformation theory of elliptic functions. The exact solution of spherical polar geodesics with a nonzero cosmological constant can be expressed in terms of Abelian modular theta functions that solve the corresponding Jacobi's inversion problem.

gr-qc↗

arXiv2003

Compact calculation of the Perihelion Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion problem

The geodesic equations resulting from the Schwarzschild gravitational metric element are solved exactly including the contribution from the Cosmological constant. The exact solution is given by genus 2 Siegelsche modular forms. For zero cosmological constant the hyperelliptic curve degenerates into an elliptic curve and the resulting geodesic is solved by the Weierstra$ß$ Jacobi modular form. The solution is applied to the precise calculation of the perihelion precession of the orbit of planet Mercury around the Sun.

astro-ph↗

arXiv2002

Intersecting D5-brane models with massive vector-like leptons

We construct eight-stack intersecting D5-brane models, with an orbifold transverse space, that yield the (non-supersymmetric) standard model up to vector-like leptons. The matter includes right-chiral neutrinos and the models have the renormalisable Yukawa couplings to tachyonic Higgs doublets needed to generate mass terms for {\it all} matter, including the vector-like leptons. The models are constrained by the requirement that twisted tadpoles cancel, that the gauge boson coupled to the weak hypercharge $U(1)_Y$ does not get a string-scale mass via a generalised Green-Schwarz mechanism, and that there are no surviving, unwanted gauged U(1) symmetries coupled to matter. Gauge coupling constant ratios close to those measured are easily obtained for reasonable values of the parameters, consistently with having the string scale close to the electroweak scale, as required to avoid the hierarchy problem. Unwanted (colour-triplet, charged-singlet, and neutral-singlet) scalar tachyons can be removed by a suitable choice of the parameters.

hep-th↗