Plamen Fiziev

Sofia University "St. Kliment Ohridski"

In this paper, we discuss in brief some basic issues of quantum space gravimetry, related to standard approach of geodesy which is based on the Newton model of gravity and Euclidean geometry. We emphasize the need to apply relativistic gravity in practical high-precision geodesy. Here we do not intend to solve the existing hard experimental and the...

In this short paper we consider in brief some basic problems of quantum space gravimetry.

This is an extended version of my paper arXiv: 1912.13432. Much more pictures, figures, results and comments are added.

We briefly consider the data of collaboration LIGO/VIRGO for gravitational waves (GW) and the recent observations of Event Horizon Telescope (EHT), and we discuss difficulties for finding the right theory of gravity and the nature of the observed Extremely Compact Objects (ECOs). The only undisputable way to establish existence of event horizon of...

We present, for the first time, a correct solution of the Schwarzschild Massive Point (SMP) problem in {\em arbitrary} radial gauge and formulate the strict mathematical assumptions, which are necessary and sufficient for this. In GR, there exists a two-parameter family of such exact SMP solutions to the Einstein equations, which are physically dis...

We give short overview of: 1. The LIGO/VIRGO data, included in the First catalog of gravitational wave (GW) events. New 35 such event candidates. 2. EHT observations of the shadow of the central object in elliptic galaxy M87. 3. Right theory of the observed GW and their sources. 4. Quasi-normal modes (QNM) of black holes (BH) and other extremely...

Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a two-parameter family of such solutions to the Einstein equations which are physically distinguishable and des...

Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a two-parameter family of such solutions to the Einstein equations which are physically distinguishable and des...

In the used for analysis of LIGO GW data templates from NR calculations the presence of matter around the BH is not taken into account. Up to now NR solves only idealized two-body relativistic problems, despite the fact that: 1. In the Nature we obviously have more then two bodies and two body problem is only a not very good first approximation eve...

The used methods for processing the LIGO data where good enough to discover gravitational waves, but fail to recover the most important details needed to confirm without any doubts the right theory of these waves and the physical nature of the sources. These methods were too crude to recover QNM as a fingerprints of BH. These methods were too cru...

We present a review of the recent results of the author for realistic models of static spherically symmetric�NS with AMP1, Sly, BSk19, BSk20, BSk21 and LOCV EOS using the correct boundary conditions at the center, at the edge and at the cosmological horizon of the de Sitter like Universe. We present this dependence, as well as the influence of the...

The MDG model of extended gravity is allive after the GR170817/GRB170817a strong tests which kill a large amount of modified gravity models. We discuss the influence of the new important data from GR170817/GRB170817a on the MDG models of neutron stars with realistic EOS and further possib le developments.

This presentation is about history an last developments in observations of gravitational waves (GW) before GW170817 and comments the precise formulation of the Nobel-Price in physics for 2017 given for the grate discovery of gravitational waves as a freely spreading in space-time gravitational field detached from its sources. I comment a lot of dou...

In this talk we present a review of the recent results for models of static spherically symmetric NS with realistic EOS AMP1, Sly, BSk19, BSk20 and BSk21 EOS using correct boundary conditions at the center, at the edge and at the cosmological horizon of the de Sitter like Universe. An important step is the introduction of new field variable for the...

The model of minimal dilatonic gravity (MDG), called also the massive Branse-Dicke model with \(\omega =0\), is an alternative model of gravitation, which uses one Branse-Dicke gravitation-dilaton field \(\varPhi \) and offers a simultaneous explanation of the effects of dark energy (DE) and dark matter (DM). Here we present an extensive research o...

The Heun functions are often called the hypergemeotry successors of the 21st century, because of the wide number of their applications. In this proceeding we discuss their application to the problem of perturbations of rotating and non-rotating black holes and highlight some recent results on their late-time ring-down obtained using those functions...

The most important experimental discovery in gravity after sir Isaak Newton is the free spreading in space gravitational field detached from the bodies = GW. Without any doubts (more than 5 σ) with the LIGO observation of gravitational waves burst (GWB GW150914 and GW151222 starts a new era in fundamental physics. An example for a firm consequenc...

Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular motions of such systems and to the significance of double and triple collisions. The conclusive role of the colli...

The model of minimal dilatonic gravity (MDG), called also the massive Branse-Dicke model with $\omega =0$, is an alternative model of gravitation, which uses one Branse-Dicke gravitation-dilaton field $\Phi$ and offers a simultaneous explanation of the effects of dark energy (DE) and dark matter (DM). Here we present an extensive research of non-ro...

Talk at International Workshop Siberian Cosmology Days 2016, TUSUR, Tomsk, 9th of August 2016

Presentation at Conference QUANTUM FIELD THEORY AND GRAVITY . Tomsk, 5th of August 2016

DD 2016 Mini-symposium Heun’s equations and their applications Saint Petersburg, 27 of June 2016

We present new solution of the the connection problem for local solutions to the general Heun equation. Our approach is based on the symmetric form of the Heun's differential equation \cite{Fiziev14,Fiziev16} with four different regular singular points $z_{1,2,3,4}$. The four special regular points in the complex plane: $Z_{123},Z_{234},Z_{341},Z_{...

Talk at BAN and SU seminars on 11 of April 2016

In the present article we introduce and study a novel type of solutions to the general Heun’s equation. Our approach is based on the symmetric form of the Heun’s differential equation yielded by development of the Papperitz-Klein symmetric form of the Fuchsian equations with an arbitrary number N � 4 of regular singular points. We derive the symmet...

The Heun functions are often called the hypergemeotry successors of the 21st century, because of the wide number of their applications. In this proceeding we discuss their application to the problem of perturbations of rotating and non-rotating black holes and highlight some recent results on their late-time ring-down obtained using those functions...

In this rather popular paper we stress some basics of the theory and the huge amount of applications of the Heun functions, as well as the still existing basic unsolved problems. The point is to attract more attention to this modern powerful tool for research in different scientific domains.

We consider singularities of static spherically symmetric objects in minimal dilatonic gravity. They are only partially studied and purely understood even in the simplest models of extended gravity. We introduce the proper form of the structure equations and derive a set of all singularities, which turn to form several types of sub-manifolds of the...

The proper understanding of the electromagnetic counterpart of gravity-waves emitters is of serious interest to the multimessenger astronomy. In this article, we study the numerical stability of the quasinormal modes (QNM) and quasibound modes (QBM) obtained as solutions of the Teukolsky Angular Equation and the Teukolsky Radial Equation with appro...

We present derivation of the basic equations and boundary conditions for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) which offers an alternative and simultaneous description of the effects of dark matter (DM) and dark energy (DE) using one dilaton field Φ. The numerical results for a realis...

The difficulties in numerical investigation of realistic models of NSin the modified theories of gravity are surmounted on a general basis. We present a realistic model of static spherically symmetric NS with MPA1 EOS using correct boundary conditions. The critical step is the introduction of а new field variable for the scalar degree of freedom wh...

The perturbations of Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of GR with astrophysics of compact objects, see the recent review article by Teukolsky [1]. The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equati...

We present the basic equations and relations for the relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) which is {\em locally} equivalent to the f(R) theories of gravity and gives an alternative description of the effects of dark matter and dark energy. The results for the simplest form of the rel...

We study a novel type of solutions of the general Heun's equation, based on its symmetric form. We derive the symmetry group of this equation which is a proper extension of the Mobius group. The new series solution treat simultaneously and on an equal footing all singular points.

This talk is based on papers: P. Fiziev and D. Georgieva, Inflation and oscillations of the Universe in 4D dilatonic gravity, PHYSICAL REVIEW D 67, 064016 (2003). P. P. Fiziev , Withholding potentials, absence of ghosts, and relationship between minimal dilatonic gravity and f(R) theories, PHYSICAL REVIEW D 87, 044053 (2013). P. P. Fiziev, Compact...

In the present article we introduce and study a novel type of solutions of the general Heun’s equation. Our approach is based on the symmetric form of the Heun’s differential equation yielded by development of the Felix Klein symmetric form of the Fuchsian equations with an arbitrary number N >3 of regular singular points. We derive the symmetry gr...

We give a brief survey of the development of theory and experimental search for gravitational waves (GW) starting with A. Einstein pioneer 1916 papers, the first attempt for quantization of gravity by M. Bronstein, the first unsuccessful search of GW by J. Weber, first indirect detection of GW by R. Hulst and J. Taylor, present days unsuccessful se...

In this talk we outline novel ideas to reveal some general mysteries of the Universe: alternatives to/for the Higgs mechanism, quantum gravity, what was before the Big Bang, CPT properties of elementary particles, baryon { antibaryon asymmetry, etc., by applying new Physics on manifolds with variable topological dimension and reduction of space dim...

New Chapter in the hundred-year Saga of Gravitational Waves

Conference talk presentation

In the version \cite{Fiziev14} of this paper we presented for the first time the basic equations and relations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG). This model is {\em locally} equivalent to the f(R) theory of gravity and gives an alternative description of the effects of dark ma...

We present solution of the equations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) using the polytropic equation of state. A polytropic equation of state that has a good fitting with the realistic one is used. Results are obtained for all variables of a single neutron star in the model of...

In this talk we outline novel ideas to reveal some general mysteries of the Universe: alternatives to/for the Higgs mechanism, quantum gravity, what was before the Big Bang, CPT properties of elementary particles, baryon - antibaryon asymmetry, etc. by applying new Physics on manifolds with variable topological dimension and reduction of space dime...

We present different type of parallel computations using Maple 17 on 16 processor super computer. Specific results obtained for some physical models are also presented.

We study the relation between Minimal Dilatonic Gravity (MDG) and f(R) theories of gravity and establish strict conditions for their {\em global} equivalence. Such equivalence takes place only for a certain class of cosmological potentials, dubbed here {\em withholding potentials}, since they prevent change of the sign of dilaton $\Phi$. The withho...

Because of their wide applications in physics, the Heun functions are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is complicated and requires new algorithms able to work with them efficiently. We propose a new algorithm for solving a system of two...

The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this article, for the first time, we use those exact solutions to obtain the electromagnetic (EM) quasinormal spec...

We study a new minimal scalar–tensor model of gravity with Brans–Dicke factor ω(Φ)≡0 and cosmological factor Π(Φ). The constraints on Π(Φ) from known gravitational experiments are derived. We show that almost any time evolution of the scale factor in a homogeneous isotropic Universe can be obtained via a properly chosen Π(Φ) and discuss the general...

Although finding numerically the quasinormal modes of a nonrotating black hole is a well-studied question, the physics of the problem is often hidden behind complicated numerical procedures aimed at avoiding the direct solution of the spectral system in this case. In this article, we use the exact analytical solutions of the Regge-Wheeler equation...

The paper presents a generalization and further development of our recent publications where solutions of the Klein-Fock-Gordon equation defined on a few particular $D=(2+1)$-dim static space-time manifolds were considered. The latter involve toy models of 2-dim spaces with axial symmetry, including dimension reduction to the 1-dim space as a singu...

This rather technical paper presents some generalization of the results of recent publications \cite{Shirkov2010, DVPF2010, PFDV2010} where toy models of dimensional reduction of space-time were considered. Here we introduce and consider a specific type of multidimensional space-times with nontrivial topology and nontrivial Riemannian metric, which...

We develop the recent proposal to use dimensional reduction from the four-dimensional space-time D=(1+3) to the variant with a smaller number of space dimensions D=(1+d), d < 3, at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation on a few toy examples ("educational toys") of a space...

We propose a new algorithm for solving a system of two nonlinear transcendental equations with two complex variables based on the Muller algorithm. The two-dimensional Muller algorithm is tested on systems of different type and is found to work comparably to Newton's method and Broyden's method in many cases. The new algorithm is particularly usefu...

The Teukolsky master equation is the basic tool for the study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky radial equation and the Teukolsky angular equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confl...

We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc. Our method is based on the s...

This work develops the recent proposition to use dimensional reduction from the four-dimensional space-time to the one with a smaller number of dimensions (1+d); d < 3 at high enough energy. To this goal, we study the Klein-Gordon equation on a few toy examples of space-time with variable dimension. Here, the new trick of transforming the Klein-Gor...

The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's functions are introduced and studied. A new alternative derivation of confluent Heun's polynomials is presented.

We present a novel derivation of the Teukolsky-Starobinsky identities, based on properties of the confluent Heun functions. These functions define analytically all exact solutions to the Teukolsky master equation, as well as to the Regge-Wheeler and Zerilli ones. The class of solutions, subject to Teukolsky-Starobinsky type of identities is studied...

Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations obtained after separating the variables are the polar angle equation and the radial equation. We solve them by transforming each one into the form of a confluent Heun equati...

The Regge-Wheeler equation describes axial perturbations of Schwarzschild metric in linear approximation. Teukolsky Master Equation describes perturbations of Kerr metric in the same approximation. We present here unified description of all classes of exact solutions to these equations in terms of the confluent Heun's functions. Special attention i...

Despite all the already existing observational data, current models still cannot explain completely the excessive energy output and the time variability of GRB. One of the reasons for this is the lack of a good model of the central engine of GRB. A major problem in the proposed models with a black hole (BH) in the center is that they don't explain...

We present new developments of the simple model of the central engine of GRB, proposed recently. The model is based on minimal assumptions: some rotating compact relativistic object at the center and stable perturbations of its rotating gravitational field, described by Teukolsky Master Equation. We show that using nonstandard polynomial solutions...

The Teukolsky master equation is the basic tool for the study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky radial equation and the Teukolsky angular equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confl...

The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic properties of the general solution, novel analytical approach and numerical techniques for study of different boundary problems which correspond to quasi-n...

We show that Einstein equations are compatible with the presence of massive point particle idealization and find the corresponding two parameter family of solutions. They are complete defined by the bare mechanical mass $M>0$ and the Keplerian mass $m>0$ ($m < M$) of the point source of gravity. The global analytical properties of these solutions i...

We solve exactly the Regge-Wheeler equation for axial perturbations of the Schwarzschild metric in the black hole interior in terms of Heun functions and give a description of the spectrum and the eigenfunctions of the interior problem. The phenomenon of attraction and repulsion of the discrete eigenvalues of gravitational waves is discovered.

The well-known Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A nov...

A pioneering numerical analysis of some solutions to the relativistic equation for scalar particles in the gravitational field of a massive point source is given. The ground and other states and the corresponding eigenvalues of the discrete spectrum for various values of the momentum of scalar particles arc examined. A new feature of the solutions...

Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist a two-parameters family of such solutions to the Einstein equations which are physically distinguishable but...

We describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a two parameter family of relativistic stars without stiff functional dependence between the stelar radius and ste...

In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It turns out that there exist heavy black dwarfs: relativistic stars with arbitrary large mass, which are...

In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a two parameter family of relativistic stars without stiff functional dependence between t...

We show that Einstein equations are compatible with the presence of massive point particles and find corresponding two parameter family of their solutions which depends on the bare mechanical mass $M_0>0$ and the Keplerian mass $M<M_0$ of the point source of gravity. The global analytical properties of these solutions in the complex plane define a...

We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for different values of the orbital momentum. A novel feature of the solutions under consideration is the essentia...

Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family depending on the Keplerian mass $M$, the charge $Q$ and the bare mass $M_0$. The result can be interpreted as...

In this talk we consider the geometrical basis for the reduction of the relativistic 2-body problem, much like the non-relativistic one, to describing the motion of an effective particle in an external field. It is shown that this possibility is deeply related with the Lobachevsky geometry. The concept of relativistic reduced mass and effective rel...